Question 1

For an object in equilibrium the sum of the torques acting on it vanishes only if each torque is calculated about:

Accepted Answer

A) the center of mass 
B) the center of gravity 
C) the geometrical center 
D) the point of application of the force 
E) the same point 
A) the center of mass 
B) the center of gravity 
C) the geometrical center 
D) the point of application of the force 
E) the same point

Question 2

Young's modulus can be correctly given in:

Accepted Answer

A) N.m 
B) N/m2 
C) N.m/s 
D) N/m 
E) joules 
A) N.m 
B) N/m2 
C) N.m/s 
D) N/m 
E) joules

Question 3

The center of gravity coincides with the center of mass:

Accepted Answer

A) always 
B) never 
C) if the center of mass is at the geometrical center of the body 
D) if the acceleration due to gravity is uniform over the body 
E) if the body has a uniform distribution of mass 
A) always 
B) never 
C) if the center of mass is at the geometrical center of the body 
D) if the acceleration due to gravity is uniform over the body 
E) if the body has a uniform distribution of mass

Question 4

A cylinder placed so it can roll on a horizontal table top, with its center of gravity below its geometrical center, is:

Accepted Answer

A) in stable equilibrium 
B) in unstable equilibrium 
C) in neutral equilibrium 
D) not in equilibrium 
E) none of the above 
A) in stable equilibrium 
B) in unstable equilibrium 
C) in neutral equilibrium 
D) not in equilibrium 
E) none of the above

Question 5

The 600-N ball shown is suspended on a string AB and rests against the frictionless vertical wall.The string makes an angle of 30 $\degree$ with the wall.The line AB goes through the center of the ball, and the contact point with the wall is at the same vertical height as the center of the ball.The ball presses against the wall with a force of magnitude:

Accepted Answer

A) 300 N 
B) 350 N 
C) 520 N 
D) 600 N 
E) 690 N 
A) 300 N 
B) 350 N 
C) 520 N 
D) 600 N 
E) 690 N

Question 6

Stress can be measured in:

Accepted Answer

A) N/m2 
B) N.m2 
C) N/m 
D) N.m 
E) none of these (it is dimensionless) 
A) N/m2 
B) N.m2 
C) N/m 
D) N.m 
E) none of these (it is dimensionless)

Question 7

A horizontal beam of weight W is supported by a hinge and cable as shown.The force exerted on the beam by the hinge has a vertical component that must be:

Accepted Answer

A) nonzero and up 
B) nonzero and down 
C) nonzero but not enough information given to know whether up or down 
D) zero 
E) equal to W 
A) nonzero and up 
B) nonzero and down 
C) nonzero but not enough information given to know whether up or down 
D) zero 
E) equal to W

Question 8

The ultimate strength of a sample is the stress at which the sample:

Accepted Answer

A) returns to its original shape when the stress is removed 
B) remains underwater 
C) breaks 
D) bends 180 $\degree$ 
E) does none of these 
A) returns to its original shape when the stress is removed 
B) remains underwater 
C) breaks 
D) bends 180 $\degree$ 
E) does none of these

Question 9

Three identical uniform rods are each acted on by two or more forces, all perpendicular to the rods.Which of the rods could be in static equilibrium if an additional force is applied at the center of mass of the rod?

Accepted Answer

A) Only 1 
B) Only 2 
C) Only 3 
D) Only 1 and 2 
E) All three 
A) Only 1 
B) Only 2 
C) Only 3 
D) Only 1 and 2 
E) All three

Question 10

Two supports, made of the same material and initially of equal length, are 2.0 m apart.A stiff board with a length of 4.0 m and a mass of 10 kg is placed on the supports, with one support at the left end and the other at the midpoint.A block is placed on the board a distance of 0.50 m from left end.As a result the board is horizontal (that is, the downward force on each support is the same).The mass of the block is:

Accepted Answer

A) 0 kg 
B) 2.3 kg 
C) 6.6 kg 
D) 10 kg 
E) 20 kg 
A) 0 kg 
B) 2.3 kg 
C) 6.6 kg 
D) 10 kg 
E) 20 kg

Question 11

A uniform ladder is 10 m long and weighs 400 N.It rests with its upper end against a frictionless vertical wall.Its lower end rests on the ground and is prevented from slipping by a peg driven into the ground.The ladder makes a 30 $\degree$angle with the horizontal.The force exerted on the wall by the ladder is:

Accepted Answer

A) 47 N 
B) 74 N 
C) 120 N 
D) 350 N 
E) 460 N 
A) 47 N 
B) 74 N 
C) 120 N 
D) 350 N 
E) 460 N

Question 12

A 240-N weight is hung from two ropes as shown.The tension in the horizontal rope has magnitude:

Accepted Answer

A) 0 N 
B) 660 N 
C) 480 N 
D) 420 N 
E) 140 N 
A) 0 N 
B) 660 N 
C) 480 N 
D) 420 N 
E) 140 N

Question 13

Young's modulus is a proportionality constant that relates the force per unit area applied perpendicularly at the surface of an object to:

Accepted Answer

A) the shear 
B) the fractional change in volume 
C) the fractional change in length 
D) the pressure 
E) the spring constant 
A) the shear 
B) the fractional change in volume 
C) the fractional change in length 
D) the pressure 
E) the spring constant

Question 14

A massless meter stick on a horizontal frictionless table top is pivoted at the 80-cm mark.A force is applied perpendicularly to the end of the stick at 0 cm, as shown.A second force (not shown)is applied perpendicularly at the 60-cm mark.The forces are in the plane of the table top.If the stick does not move, the force exerted by the pivot on the stick:

Accepted Answer

A) must be zero 
B) must be in the same direction as  and have magnitude   
C) must be directed opposite to   and have magnitude   
D) must be in the same direction as   and have magnitude   
E) must be directed opposite to   and have magnitude   
A) must be zero 
B) must be in the same direction as  and have magnitude   
C) must be directed opposite to   and have magnitude   
D) must be in the same direction as   and have magnitude   
E) must be directed opposite to   and have magnitude

Question 15

For a body to be equilibrium under the combined action of several forces:

Accepted Answer

A) all the forces must be applied at the same point 
B) all of the forces are composed of pairs of equal and opposite forces 
C) any two of these forces must be balanced by a third force 
D) the sum of the torques about any point must equal zero 
E) the lines of action of all the forces must pass through the center of gravity of the body 
A) all the forces must be applied at the same point 
B) all of the forces are composed of pairs of equal and opposite forces 
C) any two of these forces must be balanced by a third force 
D) the sum of the torques about any point must equal zero 
E) the lines of action of all the forces must pass through the center of gravity of the body

Question 16

The 600-N ball shown is suspended on a string AB and rests against the frictionless vertical wall.The string makes an angle of 30 $\degree$ with the wall.The line AB goes through the center of the ball, and the contact point with the wall is at the same vertical height as the center of the ball.The magnitude of the tension in the string is:

Accepted Answer

A) 300 N 
B) 520 N 
C) 690 N 
D) 1200 N 
E) none of these 
A) 300 N 
B) 520 N 
C) 690 N 
D) 1200 N 
E) none of these

Question 17

A uniform 240-g meter stick can be balanced by a 240-g weight placed at the 100-cm mark if the fulcrum is placed at the point marked:

Accepted Answer

A) 75 cm 
B) 60 cm 
C) 50 cm 
D) 40 cm 
E) 80 cm 
A) 75 cm 
B) 60 cm 
C) 50 cm 
D) 40 cm 
E) 80 cm

Question 18

The diagram shows a stationary 5-kg uniform rod (AC), 1 m long, held against a wall by a rope (AE)and friction between the rod and the wall.To use a single equation to find the force exerted on the rod by the rope at which point should you place the reference point for computing torque?

Accepted Answer

A) A 
B) B 
C) C 
D) D 
E) E 
A) A 
B) B 
C) C 
D) D 
E) E

Question 19

A cube balanced with one edge in contact with a table top and with its center of gravity directly above the edge is in ________ equilibrium with respect to rotation about the edge and in ________ equilibrium with respect to rotation about a horizontal axis that is perpendicular to the edge.

Accepted Answer

A) stable, stable 
B) stable, unstable 
C) unstable, stable 
D) unstable, unstable 
E) unstable, neutral 
A) stable, stable 
B) stable, unstable 
C) unstable, stable 
D) unstable, unstable 
E) unstable, neutral

Question 20

The conditions that the sum of forces and the sum of the torques both vanish:

Accepted Answer

A) hold for every solid body in equilibrium 
B) hold only for elastic solid bodies in equilibrium 
C) hold for every solid body 
D) are always sufficient to calculate the forces on a solid object in equilibrium 
E) are sufficient to calculate the forces on a solid object in equilibrium only if the object is elastic 
A) hold for every solid body in equilibrium 
B) hold only for elastic solid bodies in equilibrium 
C) hold for every solid body 
D) are always sufficient to calculate the forces on a solid object in equilibrium 
E) are sufficient to calculate the forces on a solid object in equilibrium only if the object is elastic

Exam 12: Equilibrium and Elasticity

For an object in equilibrium the sum of the torques acting on it vanishes only if each torque is calculated about:

Young's modulus can be correctly given in:

The center of gravity coincides with the center of mass:

A cylinder placed so it can roll on a horizontal table top, with its center of gravity below its geometrical center, is:

Stress can be measured in:

A horizontal beam of weight W is supported by a hinge and cable as shown.The force exerted on the beam by the hinge has a vertical component that must be:

The ultimate strength of a sample is the stress at which the sample:

Three identical uniform rods are each acted on by two or more forces, all perpendicular to the rods.Which of the rods could be in static equilibrium if an additional force is applied at the center of mass of the rod?

A 240-N weight is hung from two ropes as shown.The tension in the horizontal rope has magnitude:

Young's modulus is a proportionality constant that relates the force per unit area applied perpendicularly at the surface of an object to:

For a body to be equilibrium under the combined action of several forces:

A uniform 240-g meter stick can be balanced by a 240-g weight placed at the 100-cm mark if the fulcrum is placed at the point marked:

The diagram shows a stationary 5-kg uniform rod (AC), 1 m long, held against a wall by a rope (AE)and friction between the rod and the wall.To use a single equation to find the force exerted on the rod by the rope at which point should you place the reference point for computing torque?

A cube balanced with one edge in contact with a table top and with its center of gravity directly above the edge is in ________ equilibrium with respect to rotation about the edge and in ________ equilibrium with respect to rotation about a horizontal axis that is perpendicular to the edge.

The conditions that the sum of forces and the sum of the torques both vanish:

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A cube balanced with one edge in contact with a table top and with its center of gravity directly above the edge is in equilibrium with respect to rotation about the edge and in equilibrium with respect to rotation about a horizontal axis that is perpendicular to the edge.