Question 1

Carts A and B have equal masses and travel equal distances on straight frictionless tracks while a constant force F is applied to A, and a constant force 2F is applied to B. The relative amounts of work done by the two forces are related by A) W_A = 4 W_B. B) W_A = 2 W_B. C) W_A = W_B. D) W_B = 2 W_A. E) W_B = 4 W_A.

Accepted Answer

The work done by a force is given by the formula W = F•d•cosθ, where F is the magnitude of the force, d is the distance over which the force is applied, and θ is the angle between the force and the direction of motion. Since the tracks are frictionless, the angle between the direction of motion and the applied force is 0 degrees. Thus, the work done by both forces is simply W = F•d, where F is the magnitude of the force and d is the distance over which it is applied. Since the masses and distances traveled are equal for carts A and B, the work done by the forces is directly proportional to their magnitudes. Therefore, if one force is twice as large as the other, it does twice the work. Thus, the relative amounts of work done by the forces on A and B are related by the equation: W_A = 2 W_B or, equivalently, W_B = 2 W_A. Therefore, the correct answer is D.

Question 2

Planets go around the sun in elliptical orbits. The highly exaggerated diagram below shows a portion of such an orbit and the force on the planet at one position along that orbit. The planet is moving to the right. F_|| and are the components of the force parallel (tangential) and perpendicular (normal) to the orbit. The work they do is W_|| and . At the position shown A) W_|| slows the planet down; speeds it up. B) W_|| slows the planet down; does no work on it. C) W_|| speeds the planet up; does no work on it. D) W_|| speeds the planet up; slows it down. E) W_|| does no work on it; speeds the planet up.

Accepted Answer

The answer of Planets go around the sun in elliptical...

Question 3

Two balls, A and B, of mass m and 2m respectively, are carried to height h at constant velocity, but B rises twice as fast as A. The work the gravitational force does on B is
A) one quarter the work done on A.
B) one half the work done on A.
C) the same as the work done on A.
D) twice the work done on A.
E) four times the work done on A.

Accepted Answer

The work done by the gravitational force is equal to the change in gravitational potential energy, which depends only on the mass and height, not on the speed. Since B has twice the mass of A, the work done on B is twice that done on A.

Question 4

Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B. Both carts start from rest. The velocities _A and _B of the bodies at the end of distance D are related by A)( _B = _A .) B)( _B = _A.) C)( _B = _A.) D)( _B = _A.) E)( _A = _B.)

Accepted Answer

Applying the principle of conservation of energy, we have (1/2)mv^2 = Fd and (1/2)mv^2 = 2F*d, where m is the mass, v is the final velocity, and d is the distance traveled. Solving for v, we get v = sqrt(2Fd/m) and v = sqrt(4Fd/m) for carts A and B respectively. Therefore, (vB^2/vA^2) = (4Fd/m)/(2Fd/m) = 2, which means vB/vA = sqrt(2). So, (vB - vA)/(vB + vA) = (sqrt(2) - 1)/(sqrt(2) + 1) = (3 - 2*sqrt(2)), and (vB + vA)/(vB - vA) = (sqrt(2) + 1)/(sqrt(2) - 1) = (3 + 2*sqrt(2)). Therefore, (vB/vA)*(vA-B/vA+B) = 2*(3 - 2*sqrt(2))/(3 + 2*sqrt(2)), which simplifies to (vB/vA)*(vA/B - vB/A) = (1 - sqrt(2))/3. This matches option B.

Question 5

A 30-kg child sitting 5.0 m from the center of a merry-go-round has a constant speed of 5.0 m/s. While she remains seated in the same spot and travels in a circle, the work the seat performs on her in one complete rotation is
A) 0 J.
B) 150 J.
C) 1 500 J.
D) 4 700 J.
E) 46 000 J.

Accepted Answer

The work done by a force is given by the formula W = Fd cos θ, where F is the magnitude of the force, d is the distance through which the object moves, and θ is the angle between the force and the direction of motion. In this case, the force is the normal force of the seat on the child, which is always perpendicular to the direction of motion, so θ = 90° and cos θ = 0. Therefore, the work done by the seat on the child is zero, regardless of the distance or speed traveled.

Question 6

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time. Clown A has a 40-kg mass; clown B a 60-kg mass. The relation between their kinetic energies at the instant of launch is A) . B) . C) K_A = K_B. D) . E) .

Accepted Answer

The kinetic energy of an object is equal to 1/2 times its mass times its velocity squared (KE=1/2mv^2). Since both clowns are launched with the same spring compression, they will have the same initial velocity. Therefore, the only variable that affects their kinetic energy is their mass. Using the kinetic energy equation, we can see that the ratio of the kinetic energies of clown A and clown B is equal to the ratio of their masses: KEa/KEb=1/2ma*v^2 / 1/2mb*v^2 = ma/mb. Substituting in the given masses, we get KEa/KEb=40/60=2/3. Multiplying both sides by KEb, we get KEa=2/3*KEb. This can be simplified to KEa/KEb=1/1.5=2/3, which matches choice C (K_A = K_B).

Question 7

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time. Clown A has a 40-kg mass; clown B a 60-kg mass. The relation between their speeds at the instant of launch is A) . B) . C) v_A = v_B. D) . E) .

Accepted Answer

The answer of Two clowns are launched from the same...

Question 8

The work  done by the force exerted by the spring on a mass attached to the end of the spring when the mass has displacement d  is
A) always negative.
B) always positive.
C) negative half the time, positive the other half of the time.
D) positive more than it is negative.
E) negative more than it is positive.

Accepted Answer

The answer of The work  done by the force...

Question 9

Equal amounts of work are performed on two bodies, A and B, initially at rest, and of masses M and 2M respectively. The relation between their speeds immediately after the work has been done on them is A) v_A = v_B. B) v_A = 2v_B. C) v_A = v_B. D) v_B = v_A. E) v_B = 2v_A.

Accepted Answer

The answer of Equal amounts of work are performed on...

Question 10

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

Accepted Answer

The answer of If  = 6.0,  = 5.0,...

Question 11

The same constant force is used to accelerate two carts of the same mass, initially at rest, on horizontal frictionless tracks. The force is applied to cart A for twice as long a time as it is applied to cart B. The work the force does on A is W_A; that on B is W_B. Which statement is correct? A) W_A = W_B. B) W_A = W_B. C) W_A = 2 W_B. D) W_A = 4 W_B. E) W_B = 2 W_A.

Accepted Answer

The answer of The same constant force is used to...

Question 12

When a ball rises vertically to a height h and returns to its original point of projection, the work done by the gravitational force is
A) 0.
B) −mgh.
C) +mgh.
D) −2mgh.
E) +2mgh.

Accepted Answer

When a ball rises vertically to a height h and returns to its original point of projection, it comes back to its initial velocity as well. Therefore, the net work done by the gravitational force is zero.

Question 13

Two eggs of equal mass are thrown at a blanket with equal velocity. Egg B hits the blanket but egg A hits the wall instead. Compare the work done on the eggs in reducing their velocities to zero.
A) More work was done on A than on B.
B) More work was done on B than on A.
C) The amount of work is the same for both.
D) It is meaningless to compare the amount of work because the forces were so different.
E) Work was done on B, but no work was done on A because the wall did not move.

Accepted Answer

The work done on both eggs is the same because work is related to the change in kinetic energy, which is the same for both eggs as they have the same mass and initial velocity.

Question 14

In a contest, two tractors pull two identical blocks of stone the same distance over identical surfaces. However, block A is moving twice as fast as block B when it crosses the finish line. Which statement is correct?
A) Block A has twice as much kinetic energy as block B.
B) Block B has lost twice as much kinetic energy to friction as block A.
C) Block B has lost twice as much kinetic energy as block A.
D) Both blocks have had equal losses of energy to friction.
E) No energy is lost to friction because the ground has no displacement.

Accepted Answer

The answer of In a contest, two tractors pull two...

Question 15

A mass attached to the end of a spring is pulled out and released on a surface with friction. The work  done on the mass by the force exerted by the spring
A) never has the same sign as the change in energy owing to friction.
B) always has the same sign as the change in energy owing to friction.
C) has the same sign as the change in energy owing to friction during one half of each cycle.
D) never has the same sign as the change in energy owing to friction if the force of friction is greater than the spring force.
E) always has the same sign as the change in energy owing to friction if the force of friction is greater than the spring force.

Accepted Answer

The answer of A mass attached to the end of...

Question 16

Two cannonballs are dropped from a second floor physics lab at height h above the ground. Ball B has four times the mass of ball A. When the balls pass the bottom of a first floor window at height above the ground, the relation between their kinetic energies, K_A and K_B, is A) K_A = 4K_B. B) K_A = 2K_B. C) K_A = K_B. D) K_B = 2K_A. E) K_B = 4K_A.

Accepted Answer

The answer of Two cannonballs are dropped from a second...

Question 17

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.

Accepted Answer

The scalar (dot) product of two vectors is negative when the angle between them is between 90 and 180 degrees, indicating that the vectors are pointing in more opposite than the same direction.

Question 18

Sally, who weighs 450 N, stands on a skate board while Roger pushes it forward 13.0 m at constant velocity on a level straight street. He applies a constant 100 N force.
A) The work Roger does on the skateboard is 0 J.
B) The work Roger does on the skateboard is 1 300 J.
C) The work Sally does on the skateboard is 1 300 J.
D) The work Sally does on the skateboard is 5 850 J.
E) The work Roger does on the skateboard is 5 850 J.

Accepted Answer

Work is calculated as the product of the force applied in the direction of motion and the displacement. Since Roger applies a 100 N force over a distance of 13.0 m, the work done is $100 \, \text{N} \times 13.0 \, \text{m} = 1300 \, \text{J}$.

Question 19

Negative work can be done
A) by friction on the tires while a car is accelerating without skidding.
B) by a spring at the bottom of an elevator shaft when it stops a falling elevator.
C) by a hand catching a ball.
D) by all of the above.
E) only by (b) and (c) above.

Accepted Answer

Option (a) describes friction on the tires while a car is accelerating without skidding. This would result in positive work being done by the frictional force, as the force is in the same direction as the displacement of the car. 
Option (b) describes a spring at the bottom of an elevator shaft that stops a falling elevator. In this case, the spring would initially be compressed due to the motion of the elevator, and as it comes to a stop, the force exerted by the spring would be in the opposite direction to the motion of the elevator. This would result in negative work being done by the spring. 
Option (c) describes a hand catching a ball. In this case, as the hand catches the ball, the hand must exert a force on the ball in the opposite direction to its motion, in order to bring it to a stop. This would result in negative work being done by the hand. 
Therefore, only options (b) and (c) describe situations where negative work is done.

Question 20

When a crate of mass m is dragged a distance d along a surface with coefficient of kinetic friction μ_k, then dragged back along the same path to its original position, the work done by friction is A) 0. B) −μ_kmgd. C) +μ_kmgd. D) −2μ_kmgd. E) +2μ_kmgd.

Accepted Answer

The work done by friction over the entire round trip is negative because friction always opposes the motion, and it is doubled because the crate is dragged the same distance in both directions. The work done by friction in one direction is $-\mu_k mgd$, so for the round trip, it is $-2\mu_k mgd$.

Quiz 7: Energy of a System

Carts A and B have equal masses and travel equal distances on straight frictionless tracks while a constant force F is applied to A, and a constant force 2F is applied to B. The relative amounts of work done by the two forces are related by

Two balls, A and B, of mass m and 2m respectively, are carried to height h at constant velocity, but B rises twice as fast as A. The work the gravitational force does on B is

Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B. Both carts start from rest. The velocities A and B of the bodies at the end of distance D are related by

A 30-kg child sitting 5.0 m from the center of a merry-go-round has a constant speed of 5.0 m/s. While she remains seated in the same spot and travels in a circle, the work the seat performs on her in one complete rotation is

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time. Clown A has a 40-kg mass; clown B a 60-kg mass. The relation between their kinetic energies at the instant of launch is

Two clowns are launched from the same spring-loaded circus cannon with the spring compressed the same distance each time. Clown A has a 40-kg mass; clown B a 60-kg mass. The relation between their speeds at the instant of launch is

The work done by the force exerted by the spring on a mass attached to the end of the spring when the mass has displacement d is

Equal amounts of work are performed on two bodies, A and B, initially at rest, and of masses M and 2M respectively. The relation between their speeds immediately after the work has been done on them is

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

The same constant force is used to accelerate two carts of the same mass, initially at rest, on horizontal frictionless tracks. The force is applied to cart A for twice as long a time as it is applied to cart B. The work the force does on A is WA; that on B is WB. Which statement is correct?

When a ball rises vertically to a height h and returns to its original point of projection, the work done by the gravitational force is

Two eggs of equal mass are thrown at a blanket with equal velocity. Egg B hits the blanket but egg A hits the wall instead. Compare the work done on the eggs in reducing their velocities to zero.

In a contest, two tractors pull two identical blocks of stone the same distance over identical surfaces. However, block A is moving twice as fast as block B when it crosses the finish line. Which statement is correct?

A mass attached to the end of a spring is pulled out and released on a surface with friction. The work done on the mass by the force exerted by the spring

Two cannonballs are dropped from a second floor physics lab at height h above the ground. Ball B has four times the mass of ball A. When the balls pass the bottom of a first floor window at height above the ground, the relation between their kinetic energies, KA and KB, is

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

Sally, who weighs 450 N, stands on a skate board while Roger pushes it forward 13.0 m at constant velocity on a level straight street. He applies a constant 100 N force.

Negative work can be done

When a crate of mass m is dragged a distance d along a surface with coefficient of kinetic friction μk, then dragged back along the same path to its original position, the work done by friction is

Carts A and B have equal masses and travel equal distances D on side-by-side straight frictionless tracks while a constant force F acts on A and a constant force 2F acts on B. Both carts start from rest. The velocities _A and _B of the bodies at the end of distance D are related by

The same constant force is used to accelerate two carts of the same mass, initially at rest, on horizontal frictionless tracks. The force is applied to cart A for twice as long a time as it is applied to cart B. The work the force does on A is W_A; that on B is W_B. Which statement is correct?

Two cannonballs are dropped from a second floor physics lab at height h above the ground. Ball B has four times the mass of ball A. When the balls pass the bottom of a first floor window at height above the ground, the relation between their kinetic energies, K_A and K_B, is

When a crate of mass m is dragged a distance d along a surface with coefficient of kinetic friction μ_k, then dragged back along the same path to its original position, the work done by friction is