Question 1

A space vehicle of mass m has a speed v. At some instant, it separates into two pieces, each of mass 0.5m. One of the pieces is at rest just after the separation. -How much work was done by the internal forces that caused the separation? A)zero joules B) C) D)mv² E)2mv²

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Question 2

A comet fragment of mass 1.96 × 10S1U1P113S1S1P0 kg is moving at 6.50 × 10S1U1P14S1S1P0 m/s when it crashes into Callisto, a moon of Jupiter. The mass of Callisto is 1.08 × 10S1U1P123S1S1P0 kg. The collision is completely inelastic. -How much kinetic energy was released in the collision? A)8.28 × 10²² J B)3.51 × 10²⁷ J C)7.02 × 10²⁷ J D)4.14 × 10²² J E)1.50 × 10¹³ J

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Question 3

A rocket is launched vertically from rest; and it burns fuel at a constant rate of 136 kg/s. Exhaust gases are expelled with a speed of 5.25 × 10³m/s relative to the rocket. What is the magnitude of the thrust? A)7.14 × 10⁵ N B)3.64 × 10⁶ N C)2.59 × 10^-² N D)808 N E)38.6 N

Accepted Answer

The thrust is calculated using the formula: Thrust = rate of fuel consumption × exhaust velocity = 136 kg/s × 5.25 × 10^3 m/s = 7.14 × 10^5 N.

Question 4

In the game of billiards, all the balls have approximately the same mass, about 0.17 kg. In the figure, the cue ball strikes another ball such that it follows the path shown. The other ball has a speed of 1.5 m/s immediately after the collision. What is the speed of the cue ball after the collision? 
A)1.5 m/s
B)1.8 m/s
C)2.6 m/s
D)4.3 m/s
E)5.2 m/s

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Question 5

A 100-kg fisherman and a 500-kg supply crate are on a frozen pond that is essentially frictionless. The man and the crate are initially separated by a distance of 600 meters. The fisherman uses a very light rope to pull the crate closer to him. How far has the man moved when the crate reaches the fisherman?
A)zero meters
B)10 m
C)50 m
D)100 m
E)500 m

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Question 6

A 0.50-kg bomb is sliding along an icy pond (frictionless surface) with a velocity of 2.0 m/s to the west. The bomb explodes into two pieces. After the explosion, a 0.20-kg piece moves south at 4.0 m/s. What are the components of the velocity of the 0.30-kg piece?
A)4.0 m/s north, 0 m/s
B)2.7 m/s north, 3.3 m/s west
C)4.0 m/s north, 2.7 m/s west
D)0 m/s, 2.0 m/s east
E)4.0 m/s north, 2.0 m/s east

Accepted Answer

The initial momentum is 1.0 kg·m/s west. After the explosion, the momentum of the 0.20-kg piece is 0.8 kg·m/s south. Using conservation of momentum, the 0.30-kg piece must have a momentum of 0.9 kg·m/s west and 0.8 kg·m/s north, resulting in a velocity of 2.7 m/s north and 3.3 m/s west.

Question 7

A 35-kg girl is standing near and to the left of a 43-kg boy on the frictionless surface of a frozen pond. The boy throws a 0.75-kg ice ball to the girl with a horizontal speed of 6.2 m/s. What are the velocities of the boy and the girl immediately after the girl catches the ice ball? girl boy
A)0.81 m/s, left 0.67 m/s, right
B)0.17 m/s, left 0.14 m/s, left
C)0.18 m/s, right 0.13 m/s, left
D)0.42 m/s, left 0.49 m/s, right
E)0.13 m/s, left 0.11 m/s, right

Accepted Answer

The conservation of momentum principle applies. The initial momentum is zero, so the final momentum must also be zero. The boy's velocity is calculated using the momentum of the ice ball, and the girl's velocity is calculated using the combined mass of the girl and the ice ball.

Question 8

A 7.30-kg bowling ball strikes a 1.60-kg pin at rest head-on. Before the collision, the velocity of the ball is +6.00 m/s. After the collision, the velocity of the ball is +5.40 m/s. What is the velocity of the pin after the collision?
A)+0.6 m/s
B)+5.4 m/s
C)+1.2 m/s
D)+2.7 m/s
E)+3.2 m/s

Accepted Answer

Using the conservation of momentum: (7.30 kg * 6.00 m/s) = (7.30 kg * 5.40 m/s) + (1.60 kg * v_pin). Solving for v_pin gives v_pin = 2.7 m/s.

Question 9

Two asteroids are drifting in space with trajectories shown. Assuming the collision at point O between them is completely inelastic, at what angle from its original direction is the larger asteroid deflected? 
A)80° above the +x axis
B)69° above the +x axis
C)42° above the +x axis
D)47° above the +x axis
E)90° above the +x axis

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Question 10

During hockey practice, two pucks are sliding across the ice in the same direction. At one instant, a 0.18-kg puck is moving at 16 m/s while the other puck has a mass of 0.14 kg and a speed of 3.8 m/s. What is the velocity of the center of mass of the two pucks?
A)5.0 m/s
B)7.0 m/s
C)9.0 m/s
D)11 m/s
E)13 m/s

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Question 11

Two objects constitute an isolated system. In an elastic collision between the two objects, which one of the following statements is a false statement?
A)The total kinetic energy is conserved.
B)The kinetic energy of each object is the same before and after the collision.
C)The total momentum is conserved.
D)The magnitude of the force exerted by each object on the other object is equal.
E)The total kinetic energy before the collision is equal to the total kinetic energy after the collision.

Accepted Answer

In an elastic collision, the kinetic energy is conserved, but the kinetic energy of each object may change before and after the collision. Therefore, statement B is false.

Question 12

A 2.5-kg ball and a 5.0-kg ball have an elastic collision. Before the collision, the 2.5-kg ball was at rest and the other ball had a speed of 3.5 m/s. What is the kinetic energy of the 2.5-kg ball after the collision?
A)1.7 J
B)3.4 J
C)8.1 J
D)14 J
E)27 J

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Question 13

A space vehicle of mass m has a speed v. At some instant, it separates into two pieces, each of mass 0.5m. One of the pieces is at rest just after the separation.
-Which one of the following statements concerning this situation is true?
A)The moving piece has speed 2v.
B)This process conserves kinetic energy.
C)The piece at rest possesses kinetic energy.
D)The process does not conserve total energy.
E)This process does not conserve momentum.

Accepted Answer

The total momentum before separation is mv. After separation, the piece at rest has zero momentum, so the moving piece must have momentum mv to conserve momentum. Since its mass is 0.5m, its speed must be 2v.

Question 14

A juggler demonstrates his abilities by keeping a 2.3-kg pipe wrench, a 1.5-kg hatchet, and a 1.0-kg hammer flying through the air above his head. The white circles on the graph represent the positions of the center of mass of each of the flying objects at one instant. What are the x and y coordinates of the center of mass for the system of these three objects?  x y
A)0.46 m 0.47 m
B)0.30 m 0.54 m
C)0.42 m 0.60 m
D)0.47 m 0.26 m
E)0.60 m 0.42 m

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Question 15

Which one of the following statements concerning center of mass is true?
A)All of an object's mass is located at its center of mass.
B)The center of mass of an object must be located within the object.
C)The center of mass of a system of objects cannot change even if there are forces acting on the objects.
D)The velocity of the center of mass of a system of objects is greatly affected by a collision of objects within the system.
E)The velocity of the center of mass of a system of objects is constant when the sum of the external forces acting on the system is zero.

Accepted Answer

The statement "The velocity of the center of mass of a system of objects is constant when the sum of the external forces acting on the system is zero" is true. This is known as the law of conservation of momentum. The center of mass is the average position of all the mass in the system and its velocity depends on the net external forces acting on the system. If there are no external forces acting on the system, the total momentum of the system is conserved and the velocity of the center of mass remains constant.

Question 16

Car One is traveling due north and Car Two is traveling due east. After the collision shown, Car One rebounds in the due south direction. Which of the numbered arrows is the only one that can represent the final direction of Car Two? 
A)1
B)2
C)3
D)4
E)5

Accepted Answer

Since Car One rebounds to the south after the collision, this means that Car Two must have hit it from the east, meaning the only arrow that lines up with Car Two's direction of travel is arrow 4.

Question 17

A mother is holding her 4.5-kg baby in her arms while riding in a car moving at 22 m/s. The car is involved in a head-on collision and stops within 1.5 seconds. What is the magnitude of the force exerted by the baby on his mother's arms?
A)45 N
B)66 N
C)90 N
D)99 N
E)150 N

Accepted Answer

The force exerted by the baby can be calculated using the formula F = ma, where m is the mass and a is the acceleration. The acceleration can be found using a = Δv/Δt = (0 - 22 m/s) / 1.5 s = -14.67 m/s². Thus, F = 4.5 kg * 14.67 m/s² = 66 N.

Question 18

The drawing shows two 4.5-kg balls located on the y axis at 1.0 and 9.0 m, respectively, and a third ball with a mass 2.3 kg which is located at 6.0 m. What is the location of the center of mass of this system? 
A)4.8 m
B)5.2 m
C)5.6 m
D)6.0 m
E)6.4 m

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Question 19

A space vehicle of mass m has a speed v. At some instant, it separates into two pieces, each of mass 0.5m. One of the pieces is at rest just after the separation. -What is the kinetic energy of the moving piece just after the separation? A)zero joules B) C) D)mv² E)2mv²

Accepted Answer

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Question 20

A comet fragment of mass 1.96 × 10S1U1P113S1S1P0 kg is moving at 6.50 × 10S1U1P14S1S1P0 m/s when it crashes into Callisto, a moon of Jupiter. The mass of Callisto is 1.08 × 10S1U1P123S1S1P0 kg. The collision is completely inelastic. -Assuming for this calculation that Callisto's initial momentum is zero kg . m/s, what is the recoil speed of Callisto immediately after the collision? A)3.34 × 10^-¹⁸ m/s B)1.27 × 10^-¹⁴ m/s C)3.58 × 10^-¹² m/s D)6.13 × 10^-⁷ m/s E)1.18 × 10^-⁵ m/s

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Quiz 7: Impulse and Momentum

A space vehicle of mass m has a speed v. At some instant, it separates into two pieces, each of mass 0.5m. One of the pieces is at rest just after the separation. -How much work was done by the internal forces that caused the separation?

A comet fragment of mass 1.96 × 10¹³ kg is moving at 6.50 × 10⁴ m/s when it crashes into Callisto, a moon of Jupiter. The mass of Callisto is 1.08 × 10²³ kg. The collision is completely inelastic. -How much kinetic energy was released in the collision?

A rocket is launched vertically from rest; and it burns fuel at a constant rate of 136 kg/s. Exhaust gases are expelled with a speed of 5.25 × 10³m/s relative to the rocket. What is the magnitude of the thrust?

In the game of billiards, all the balls have approximately the same mass, about 0.17 kg. In the figure, the cue ball strikes another ball such that it follows the path shown. The other ball has a speed of 1.5 m/s immediately after the collision. What is the speed of the cue ball after the collision?

A 0.50-kg bomb is sliding along an icy pond (frictionless surface) with a velocity of 2.0 m/s to the west. The bomb explodes into two pieces. After the explosion, a 0.20-kg piece moves south at 4.0 m/s. What are the components of the velocity of the 0.30-kg piece?

A 35-kg girl is standing near and to the left of a 43-kg boy on the frictionless surface of a frozen pond. The boy throws a 0.75-kg ice ball to the girl with a horizontal speed of 6.2 m/s. What are the velocities of the boy and the girl immediately after the girl catches the ice ball? girl boy

A 7.30-kg bowling ball strikes a 1.60-kg pin at rest head-on. Before the collision, the velocity of the ball is +6.00 m/s. After the collision, the velocity of the ball is +5.40 m/s. What is the velocity of the pin after the collision?

Two asteroids are drifting in space with trajectories shown. Assuming the collision at point O between them is completely inelastic, at what angle from its original direction is the larger asteroid deflected?

During hockey practice, two pucks are sliding across the ice in the same direction. At one instant, a 0.18-kg puck is moving at 16 m/s while the other puck has a mass of 0.14 kg and a speed of 3.8 m/s. What is the velocity of the center of mass of the two pucks?

Two objects constitute an isolated system. In an elastic collision between the two objects, which one of the following statements is a false statement?

A 2.5-kg ball and a 5.0-kg ball have an elastic collision. Before the collision, the 2.5-kg ball was at rest and the other ball had a speed of 3.5 m/s. What is the kinetic energy of the 2.5-kg ball after the collision?

A space vehicle of mass m has a speed v. At some instant, it separates into two pieces, each of mass 0.5m. One of the pieces is at rest just after the separation. -Which one of the following statements concerning this situation is true?

Which one of the following statements concerning center of mass is true?

Car One is traveling due north and Car Two is traveling due east. After the collision shown, Car One rebounds in the due south direction. Which of the numbered arrows is the only one that can represent the final direction of Car Two?

A mother is holding her 4.5-kg baby in her arms while riding in a car moving at 22 m/s. The car is involved in a head-on collision and stops within 1.5 seconds. What is the magnitude of the force exerted by the baby on his mother's arms?

The drawing shows two 4.5-kg balls located on the y axis at 1.0 and 9.0 m, respectively, and a third ball with a mass 2.3 kg which is located at 6.0 m. What is the location of the center of mass of this system?

A space vehicle of mass m has a speed v. At some instant, it separates into two pieces, each of mass 0.5m. One of the pieces is at rest just after the separation. -What is the kinetic energy of the moving piece just after the separation?