Q: A 50.0 kg person pushes off a 5.0 kg skateboard and moves to the left at 0.600 m/s. What is the speed of the skateboard just after the push, assuming no external forces?

$$v_{skateboard} = \frac{50.0 \times 0.600}{5.0} = 6.00\ \mathrm{m/s}$$

Q: A 1.5 × $$10^3 kg $$car moving north at 35.0 m/s collides head-on with a 7.5 × $$10^3 kg $$truck moving south at 25.0 m/s. If they stick together after the collision, what is their velocity just after the collision?

$$v = \frac{(1.5 \times 10^3$ \times 35.0) + (7.5 \times 10^3$ \times (-25.0))}{1.5 \times 10^3$ + 7.5 \times 10^3$} = -13.75\ \mathrm{m/s} ($$south)

Q: A tennis player hits a 57 g ball with a force of 560 N for 0.0050 s. What is the speed of the ball just after the hit, assuming it started from rest?

$$v = \frac{F \Delta t}{m} = \frac{560 \times 0.0050}{0.057} = 49.1\ \mathrm{m/s}$$

Q: A 60-kg person lands straight down and comes to a halt in 0.10 s. If his velocity just before contact is 6.0 m/s, what is the average force exerted by the ground?

$$F = \frac{\Delta p}{\Delta t} = \frac{60 \times 6.0}{0.10} = 3,600\ \mathrm{N}$$

Q: A 75 kg boxer punches a heavy bag at 8 m/s and stops in 0.02 s. What is the average force exerted by the bag on the boxer’s hand?

$$F = \frac{\Delta p}{\Delta t} = \frac{75 \times 8}{0.02} = 30,000\ \mathrm{N}$$

Question 1

Which of the following best describes the law of conservation of linear momentum in a closed system?

Accepted Answer

The total linear momentum of the system remains constant if no external forces act on it.

Question 2

A 50.0 kg person pushes off a 5.0 kg skateboard and moves to the left at 0.600 m/s. What is the speed of the skateboard just after the push, assuming no external forces?

Accepted Answer

$$v_{skateboard} = \frac{50.0 	imes 0.600}{5.0} = 6.00\ \mathrm{m/s}$$

Question 3

Which equation correctly expresses the linear momentum $$\vec{p} of an $$object?

Accepted Answer

$$\vec{p} = m \vec{v}$$

Question 4

Two objects have the same magnitude of momentum but different masses. Which statement is true about their kinetic energies?

Accepted Answer

The object with the smaller mass has greater kinetic energy.

Question 5

A 1.5 × $$10^3 kg $$car moving north at 35.0 m/s collides head-on with a 7.5 × $$10^3 kg $$truck moving south at 25.0 m/s. If they stick together after the collision, what is their velocity just after the collision?

Accepted Answer

$$v = \frac{(1.5 	imes 10^3$ 	imes 35.0) + (7.5 	imes 10^3$ 	imes (-25.0))}{1.5 	imes 10^3$ + 7.5 	imes 10^3$} = -13.75\ \mathrm{m/s} ($$south)

Question 6

In a completely inelastic collision, which of the following is true?

Accepted Answer

The colliding objects stick together and move with a common velocity after the collision.

Question 7

A tennis player hits a 57 g ball with a force of 560 N for 0.0050 s. What is the speed of the ball just after the hit, assuming it started from rest?

Accepted Answer

$$v = \frac{F \Delta t}{m} = \frac{560 	imes 0.0050}{0.057} = 49.1\ \mathrm{m/s}$$

Question 8

Which of the following best describes an elastic collision?

Accepted Answer

Both total momentum and total kinetic energy are conserved.

Question 9

A 1.60 kg block moving right at 4.00 m/s collides elastically with a 2.10 kg block moving left at 2.51 m/s. What is the velocity of the 1.60 kg block after the collision?

Accepted Answer

$$v_1$$' = \frac{($$m_1$$ - $$m_2$$)$$v_1 + 2m_2$$ $$v_2$$}{$$m_1$$ + $$m_2$$} = \frac{(1.60 - 2.10)	imes 4.00 + 2	imes 2.10 	imes (-2.51)}{1.60 + 2.10} = -2.51\ \mathrm{m/s}$$

Question 10

A 60-kg person lands straight down and comes to a halt in 0.10 s. If his velocity just before contact is 6.0 m/s, what is the average force exerted by the ground?

Accepted Answer

$$F = \frac{\Delta p}{\Delta t} = \frac{60 	imes 6.0}{0.10} = 3,600\ \mathrm{N}$$

Question 11

Which of the following is a vector quantity?

Accepted Answer

Linear momentum

Question 12

During a collision, the product of the force and the duration of contact is known as:

Accepted Answer

Impulse

Question 13

A 75 kg boxer punches a heavy bag at 8 m/s and stops in 0.02 s. What is the average force exerted by the bag on the boxer’s hand?

Accepted Answer

$$F = \frac{\Delta p}{\Delta t} = \frac{75 	imes 8}{0.02} = 30,000\ \mathrm{N}$$

Question 14

A rock of mass $$m$$ falls freely under gravity for time $$t. $$What is its momentum as a function of time?

Accepted Answer

$$p = mgt$$

Question 15

In a two-dimensional collision, which principle must be applied to both the $$x$$ and $$y$$ components?

Accepted Answer

Conservation of momentum

Question 16

A hockey player of mass 80.0 kg at rest is hit by another player of mass 100 kg moving at 5.00 m/s. After the collision, both move together at 3.75 m/s. What is the change in momentum of the stationary player?

Accepted Answer

$$\Delta p = m(v_{final} - v_{initial}) = 80.0 	imes (3.75 - 0) = 300\ \mathrm{kg\cdot m/s}$$

Question 17

Which of the following actions will reduce the force of impact when landing from a jump?

Accepted Answer

Bending your knees to increase the contact time with the ground.

Question 18

In a head-on collision between two vehicles of different masses, which vehicle experiences the greater change in momentum?

Accepted Answer

Both vehicles experience the same magnitude of momentum change.

Question 19

A Cooper’s hawk (0.600 kg) dives at 12.0 m/s at 30° below the horizontal and grabs a pigeon (0.600 kg) gliding west at 8.00 m/s. What is the magnitude of their velocity just after the collision?

Accepted Answer

$$v = \sqrt{(8.00 + 12.0 \cos 30^\$$circ)^2$$ + (12.0 \sin 30^\$$circ)^2$$} / 2 = 9.2\ \mathrm{m/s}$$

Chapter 8: Linear Momentum and Collisions – Study Notes

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