Deck 9: Energy in Nonisolated Systems

Question 1

A 2.0-kg particle has an initial velocity of m/s. Some time later, its velocity is m/s. How much work was done by the resultant force during this time interval, assuming no energy is lost in the process?

A)17 J
B)49 J
C)19 J
D)53 J
E)27 J

Answer 1

17 J

Question 2

A force acting on an object moving along the x axis is given by Fx = (14x − 3.0x2) N where x is in m. How much work is done by this force as the object moves from x = −1 m to x = +2 m?

A)+12 J
B)+28 J
C)+40 J
D)+42 J
E)−28 J

Answer 2

+12 J

Question 3

A 2.0-kg block slides down a frictionless incline from point A to point B. A force (magnitude P = 3.0 N) acts on the block between A and B, as shown. Points A and B are 2.0 m apart. If the kinetic energy of the block at A is 10 J, what is the kinetic energy of the block at B?

A)27 J
B)20 J
C)24 J
D)17 J
E)37 J

Answer 3

24 J

Question 4

A 2.0-kg body moving along the x axis has a velocity vx = 5.0 m/s at x = 0. The only force acting on the object is given by Fx = (−4.0x) N, where x is in m. For what value of x will this object first come (momentarily) to rest?

A)4.2 m
B)3.5 m
C)5.3 m
D)6.4 m
E)5.0 m

Question 5

How much work is done by a person lifting a 2.0-kg object from the bottom of a well at a constant speed of 2.0 m/s for 5.0 s?

A)0.22 kJ
B)0.20 kJ
C)0.24 kJ
D)0.27 kJ
E)0.31 kJ

Question 6

A block is pushed across a rough horizontal surface from point A to point B by a force (magnitude P = 5.4 N) as shown in the figure. The magnitude of the force of friction acting on the block between A and B is 1.2 N and points A and B are 0.5 m apart. If the kinetic energies of the block at A and B are 4.0 J and 5.6 J, respectively, how much work is done on the block by the force P between A and B?

A)2.7 J
B)1.0 J
C)2.2 J
D)1.6 J
E)3.2 J

Question 7

An object moving along the x axis is acted upon by a force Fx that varies with position as shown. How much work is done by this force as the object moves from x = 2 m to x = 8 m? ​ ​

A)−10 J
B)+10 J
C)+30 J
D)−30 J
E)+40 J

Question 8

The only force acting on a 1.6-kg body as it moves along the x axis is given in the figure. If the velocity of the body at x = 2.0 m is 5.0 m/s, what is its kinetic energy at x = 5.0 m?

A)52 J
B)44 J
C)36 J
D)60 J
E)25 J

Question 9

If the resultant force acting on a 2.0-kg object is equal to N, what is the change in kinetic energy as the object moves from m to m?

A)+36 J
B)+28 J
C)+32 J
D)+24 J
E)+60 J

Question 10

A 4.0-kg block is lowered down a 37° incline a distance of 5.0 m from point A to point B. A horizontal force (F = 10 N) is applied to the block between A and B as shown in the figure. The kinetic energy of the block at A is 10 J and at B it is 20 J. How much work is done on the block by the force of friction between A and B?

A)−58 J
B)−53 J
C)−68 J
D)−63 J
E)−47 J

Question 11

A body moving along the x axis is acted upon by a force Fx that varies with x as shown. How much work is done by this force as the object moves from x = 1 m to x = 8 m? ​ ​

A)−2 J
B)−18 J
C)−10 J
D)−26 J
E)+18 J

Question 12

A block slides on a rough horizontal surface from point A to point B. A force (magnitude P = 2.0 N) acts on the block between A and B, as shown. Points A and B are 1.5 m apart. If the kinetic energies of the block at A and B are 5.0 J and 4.0 J, respectively, how much work is done on the block by the force of friction as the block moves from A to B?

A)−3.3 J
B)+1.3 J
C)+3.3 J
D)−1.3 J
E)+4.6 J

Question 13

As a 2.0-kg object moves from m to m, the constant resultant force acting on it is equal to N. If the speed of the object at the initial position is 4.0 m/s, what is its kinetic energy at its final position?

A)62 J
B)53 J
C)73 J
D)86 J
E)24 J

Question 14

A 2.0-kg projectile moves from its initial position to a point that is displaced 20 m horizontally and 15 m above its initial position. How much work is done by the gravitational force on the projectile?

A)+0.29 kJ
B)−0.29 kJ
C)+30 J
D)−30 J
E)−50 J

Question 15

A 2.5-kg object falls vertically downward in a viscous medium at a constant speed of 2.5 m/s. How much work is done by the force the viscous medium exerts on the object as it falls 80 cm?

A)+2.0 J
B)+20 J
C)−2.0 J
D)−20 J
E)+40 J

Question 16

A constant force of 15 N in the negative y direction acts on a particle as it moves from the origin to the point m. How much work is done by the given force during this displacement?

A)+45 J
B)−45 J
C)+30 J
D)−30 J
E)+75 J

Question 17

A 1.5-kg object moving along the x axis has a velocity of +4.0 m/s at x = 0. If the only force acting on this object is shown in the figure, what is the kinetic energy of the object at x = +3.0 m?

A)18 J
B)21 J
C)23 J
D)26 J
E)8 J

Question 18

A constant force of 12 N in the positive x direction acts on a 4.0-kg object as it moves from the origin to the point m. How much work is done by the given force during this displacement?

A)+60 J
B)+84 J
C)+72 J
D)+48 J
E)+57 J

Question 19

A 5.0-kg object is pulled along a horizontal surface at a constant speed by a 15-N force acting 20° above the horizontal. How much work is done by this force as the object moves 6.0 m?

A)78 J
B)82 J
C)85 J
D)74 J
E)43 J

Question 20

A 3.0-kg block is dragged over a rough horizontal surface by a constant force of 16 N acting at an angle of 37° above the horizontal as shown. The speed of the block increases from 4.0 m/s to 6.0 m/s in a displacement of 5.0 m. What work was done by the friction force during this displacement?

A)−34 J
B)−64 J
C)−30 J
D)−94 J
E)+64 J

Question 21

The only force acting on a 2.0-kg body moving along the x axis is given by Fx = (2.0x) N, where x is in m. If the velocity of the object at x = 0 is +3.0 m/s, how fast is it moving at x = 2.0 m?

A)4.2 m/s
B)3.6 m/s
C)5.0 m/s
D)5.8 m/s
E)2.8 m/s

Question 22

At the instant a 2.0-kg particle has a velocity of 4.0 m/s in the positive x direction, a 3.0-kg particle has a velocity of 5.0 m/s in the positive y direction. What is the speed of the center of mass of the two-particle system?

A)3.8 m/s
B)3.4 m/s
C)5.0 m/s
D)4.4 m/s
E)4.6 m/s

Question 23

Three particles are placed in the xy plane. A 30-g particle is located at (3, 4) m, and a 40-g particle is located at (−2, −2) m. Where must a 20-g particle be placed so that the center of mass of the three-particle system is at the origin?

A)(−3, −1) m
B)(+1, +3) m
C)(+3, −1) m
D)(−1, −3) m
E)(−0.5, −2) m

Question 24

Each of two vectors, and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is . Which possibility is correct?

A) and both lie along the positive x axis.
B) lies along the positive x axis. lies along the negative x axis.
C) and both lie along the positive y axis.
D) lies along the negative x axis. lies along the negative y axis.
E) lies along the positive y axis. lies along the negative x axis.

Question 25

A conservative force on a particle moving along the x axis is given by . Which of the following is a potential that is associated with this force?

A)
B)
C)
D)
E)No answer given above is correct.

Question 26

The only force acting on a 2.0-kg body as it moves along the x axis is given by Fx = (12 − 2.0x) N, where x is in m. The velocity of the body at x = 2.0 m is 5.5 m/s. What is the maximum kinetic energy attained by the body while moving in the +x direction?

A)36 J
B)39 J
C)43 J
D)46 J
E)30 J

Question 27

If , , and the angle between and (when the two are drawn starting from the same point) is 60°, what is the scalar product of these two vectors?

A)−13
B)+13
C)+37
D)−37
E)73

Question 28

If = 5.0, = 8.0, and α = 30°, determine the scalar product of the two vectors shown. ​ ​

A)−35
B)+35
C)−20
D)+20
E)+40

Question 29

If = 10, = 15, and α = 130°, determine the scalar product of the two vectors shown. ​ ​

A)+96
B)−96
C)+51
D)−51
E)−35

Question 30

Two equal masses are raised at constant velocity by ropes that run over pulleys, as shown below. Mass B is raised twice as fast as mass A. The magnitudes of the forces are FA and FB, while the power supplied is respectively PA and PB. Which statement is correct? ​ ​

A)FB = FA; PB = PA.
B)FB = FA; PB = 2 PA.
C)FB = 2 FA; PB = PA.
D)FB = 2 FA; PB = 2 PA.
E)PA = FA; PB = FB.

Question 31

Each of two vectors, and , lies along a coordinate axis in the xy plane. Each vector has its tail at the origin, and the dot product of the two vectors is . Which possibility is correct?

A) and both lie along the positive x axis.
B) lies along the positive x axis. lies along the negative x axis.
C) and both lie along the positive y axis.
D) lies along the negative x axis. lies along the negative y axis.
E) lies along the positive y axis. lies along the negative y axis.

Question 32

Two vectors and are given by and . The scalar product of and a third vector is −16. The scalar product of and is +18. The z component of is 0. What is the magnitude of ?

A)7.8
B)6.4
C)3.6
D)5.0
E)4.8

Question 33

Three particles are placed in the xy plane. A 40-g particle is located at (3, 4) m, and a 50-g particle is positioned at (−2, −6) m. Where must a 20-g particle be placed so that the center of mass of this three-particle system is located at the origin?

A)(−1, −3) m
B)(−1, 2) m
C)(−1, 12) m
D)(−1, 7) m
E)(−1, 3) m

Question 34

If the scalar (dot) product of two vectors is negative, it means that

A)there was a calculator error.
B)the angle between the vectors is less than 90 degrees.
C)the angle between the vectors is 90 degrees.
D)the angle between the vectors is greater than 270 degrees.
E)the angle between the vectors is between 90 and 180 degrees.

Question 35

A champion athlete can produce one horsepower (746 W) for a short period of time. If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate, she would reach the summit in ____ seconds.

A)1
B)460
C)500
D)1000
E)35,000

Question 36

If = 6.0, = 5.0, and α = 40°, determine the scalar product of the two vectors shown. ​ ​

A)+19
B)+23
C)−19
D)−23
E)+30

Question 37

A champion athlete can produce one horsepower (746 W) for a short period of time. The number of 16-cm-high steps a 70-kg athlete could ascend in one minute while expending one horsepower is

A)4.
B)7.
C)65.
D)408.
E)4567.

Question 38

A champion athlete can produce one horsepower (746 W) for a short period of time. If a 70-kg athlete were to bicycle to the summit of a 500-m high mountain while expending power at this rate, she would have used at least ____ J of energy.

A)746
B)3.43 × 105
C)3.73 × 105
D)7.46 × 105
E)2.61 × 107

Question 39

If the scalar product of two vectors, and , is equal to −3.5, if , and the angle between the two vectors when they are drawn starting from the same point is equal to 130°, what is the magnitude of ?

A)2.1
B)2.5
C)2.3
D)2.7
E)3.1

Question 40

If the vectors and have magnitudes of 10 and 11, respectively, and the scalar product of these two vectors is −100, what is the magnitude of the sum of these two vectors?

A)6.6
B)4.6
C)8.3
D)9.8
E)7.6

Question 41

Two bodies with masses m1 and m² are both moving east with velocities of magnitudes v1 and v2, where v1 is less than v2. The magnitude of the velocity of the center of mass of this system of two bodies is

A)less than v1.
B)equal to v1.
C)equal to the average of v1 and v2.
D)greater than v1 and less than v2.
E)greater than v2.