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book College Physics 10th Edition by Raymond Serway,Chris Vuille cover

College Physics 10th Edition by Raymond Serway,Chris Vuille

Edition 10ISBN: 978-1285737041
book College Physics 10th Edition by Raymond Serway,Chris Vuille cover

College Physics 10th Edition by Raymond Serway,Chris Vuille

Edition 10ISBN: 978-1285737041
Exercise 1
A small sphere of mass m = 7.50 g and charge q 1 = 32.0 nC is attached to the end of a string and hangs vertically as in Figure P15.4. A second charge of equal mass and charge q 2 = 258.0 nC is located below the first charge a distance d = 2.00 cm below the first charge as in Figure P15.4. (a) Find the tension in the string. (b) If the string can withstand a maximum tension of 0.180 N, what is the smallest value d can have before the string breaks
Explanation
Verified
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(a)
Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges. (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . Here, (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . is the Coulomb's constant, (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . is the charge of the particle 1, (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . is the charge of the particle 2, and (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . is the distance between the two particles.
Substitute (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . for (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . , (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . for (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . , (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . for (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . , and (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . for (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . . (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . The tension T in the string is pointed in an upward direction and the gravitational force (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . is pointed in a downward direction. The electrical Coulomb force (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium. (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . Here, (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . is the mass of each particle and (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . is the acceleration due to gravity.
Rewrite the equation for (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . . (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . Substitute (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . for (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . , (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . for (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . , and (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . for (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . . (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . Therefore, the tension in the string is (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . .
(b)
Let (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . be the new distance between the two charges and (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . be the maximum tension in the string. Thus, the net force exerted on the system is, (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . Rewrite the equation for (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . . (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . Substitute (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . for (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . , (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . for (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . , (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . for (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . , (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . for (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . , (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . for (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . , and (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . for (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . . (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . Therefore, the smallest value of distance d possible before the string breaks is (a) Coulomb's law states that the electro static force between the two charges is directly proportional to the charge of each particle and inversely proportional to the square of the distance between the two charges.   Here,   is the Coulomb's constant,   is the charge of the particle 1,   is the charge of the particle 2, and   is the distance between the two particles. Substitute   for   ,   for   ,   for   , and   for   .   The tension T in the string is pointed in an upward direction and the gravitational force   is pointed in a downward direction. The electrical Coulomb force   exerted by the lower charge is in downward direction. Thus, the net force exerted on the system when it is in equilibrium.   Here,   is the mass of each particle and   is the acceleration due to gravity. Rewrite the equation for   .   Substitute   for   ,   for   , and   for   .   Therefore, the tension in the string is   .  (b) Let   be the new distance between the two charges and   be the maximum tension in the string. Thus, the net force exerted on the system is,   Rewrite the equation for   .   Substitute   for   ,   for   ,   for   ,   for   ,   for   , and   for   .   Therefore, the smallest value of distance d possible before the string breaks is   . .
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College Physics 10th Edition by Raymond Serway,Chris Vuille
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