Q: A 4,000 kg truck moves to the right with 10 m/s. What is its momentum?

$$p = 4,000 \times 10 = 40,000\ \mathrm{kg \cdot m/s}$$

Q: A 2-kg object moves with $$10\ \mathrm{m/s} at$$ $$37^\circ$$ above the horizontal. What is the horizontal component of its momentum?

$$p_x = 2 \times 10 \times \cos(37^\circ) \approx 16\ \mathrm{kg \cdot m/s}$$

Q: A 150-g rubber ball is moving at $$40\ \mathrm{m/s} to $$the right, hits a wall, and bounces back at $$45\ \mathrm{m/s} to $$the left. What is the impulse delivered to the ball?

$$J = m(v_f - v_0$) = 0.15 \times (-45 - 40) = -12.75\ \mathrm{kg \cdot m/s}$$

Q: Two objects, A (4 kg) moving at $$12\ \mathrm{m/s} to $$the right and B (5 kg) moving at $$9\ \mathrm{m/s} to $$the left, collide. What is the total momentum of the system?

$$p_{sys} = 4 \times 12 + 5 \times (-9) = 48 - 45 = 3\ \mathrm{kg \cdot m/s}$$

Q: A 0.250 kg puck A moves to the right and collides with a 0.38 kg puck B at rest. After the collision, puck A moves left at $$0.12\ \mathrm{m/s}$$ and puck B moves right at $$0.65\ \mathrm{m/s}. $$What was the initial velocity of puck A?

$$v_{A,i} = \frac{0.250 \times (-0.12) + 0.38 \times 0.65}{0.250} = 0.92\ \mathrm{m/s}$$

Q: A 4-kg sniper rifle shoots a 5-g bullet at $$600\ \mathrm{m/s}. $$What is the recoil speed of the rifle?

$$v_{rifle} = -\frac{0.005 \times 600}{4} = -0.75\ \mathrm{m/s}$$

Question 1

A 4,000 kg truck moves to the right with 10 m/s. What is its momentum?

Accepted Answer

$$p = 4,000 	imes 10 = 40,000\ \mathrm{kg \cdot m/s}$$

Question 2

A 2-kg object moves with $$10\ \mathrm{m/s} at$$ $$37^\circ$$ above the horizontal. What is the horizontal component of its momentum?

Accepted Answer

$$p_x = 2 	imes 10 	imes \cos(37^\circ) \approx 16\ \mathrm{kg \cdot m/s}$$

Question 3

Which of the following best describes impulse?

Accepted Answer

Impulse is the change in momentum of an object, $$J = F \Delta t = \Delta p$$

Question 4

A 100-g ball is thrown with $$30\ \mathrm{m/s}$$ and is in your hand for $$0.2\ \mathrm{s}. $$What is the average force you exert on the ball?

Accepted Answer

$$F_{avg} = \frac{3\ \mathrm{kg \cdot m/s}}{0.2\ \mathrm{s}} = 15\ \mathrm{N}$$

Question 5

A 150-g rubber ball is moving at $$40\ \mathrm{m/s} to $$the right, hits a wall, and bounces back at $$45\ \mathrm{m/s} to $$the left. What is the impulse delivered to the ball?

Accepted Answer

$$J = m(v_f - v_0$) = 0.15 	imes (-45 - 40) = -12.75\ \mathrm{kg \cdot m/s}$$

Question 6

A 1200-kg car moving at $$20\ \mathrm{m/s}$$ slams into a wall and comes to a stop after compressing $$1.0\ \mathrm{m}$$ into the wall. What is the magnitude of the average force exerted by the wall?

Accepted Answer

$$F_{avg} = \frac{m(v_f - v_0$)}{\Delta t}$$, \; \Delta t = \frac{2\Delta x}{$$v_0 + v_f$$} = \frac{2 	imes 1}{20} = 0.1\ \mathrm{s}$$, \; F_{avg} = \frac{1200 	imes (-20)}{0.1} = -240,000\ \mathrm{N}$$

Question 7

Which area under a force vs. time graph represents impulse?

Accepted Answer

The area under the $$F vs$$. $$t$$ graph

Question 8

Two objects, A (4 kg) moving at $$12\ \mathrm{m/s} to $$the right and B (5 kg) moving at $$9\ \mathrm{m/s} to $$the left, collide. What is the total momentum of the system?

Accepted Answer

$$p_{sys} = 4 	imes 12 + 5 	imes (-9) = 48 - 45 = 3\ \mathrm{kg \cdot m/s}$$

Question 9

A 0.250 kg puck A moves to the right and collides with a 0.38 kg puck B at rest. After the collision, puck A moves left at $$0.12\ \mathrm{m/s}$$ and puck B moves right at $$0.65\ \mathrm{m/s}. $$What was the initial velocity of puck A?

Accepted Answer

$$v_{A,i} = \frac{0.250 	imes (-0.12) + 0.38 	imes 0.65}{0.250} = 0.92\ \mathrm{m/s}$$

Question 10

A 4-kg sniper rifle shoots a 5-g bullet at $$600\ \mathrm{m/s}. $$What is the recoil speed of the rifle?

Accepted Answer

$$v_{rifle} = -\frac{0.005 	imes 600}{4} = -0.75\ \mathrm{m/s}$$

Question 11

Which of the following is true for a perfectly inelastic collision?

Accepted Answer

Momentum is conserved, mechanical energy is not conserved, and objects stick together.

Question 12

A 1-kg block moving at $$20\ \mathrm{m/s}$$ collides with a 9-kg block at rest. If they stick together, what is their final speed?

Accepted Answer

$$v_f = \frac{1 	imes 20 + 9 	imes 0}{1 + 9} = 2\ \mathrm{m/s}$$

Question 13

A 1000 kg car traveling east at $$20\ \mathrm{m/s}$$ collides with a 3000 kg truck heading north at $$10\ \mathrm{m/s}. If $$they stick together, what is the magnitude of their final velocity?

Accepted Answer

$$v_f = \sqrt{\left(\frac{1000 	imes 20}{4000}\$$right)^2$$ + \left(\frac{3000 	imes 10}{4000}\$$right)^2$$} = 9.35\ \mathrm{m/s}$$

Question 14

Which of the following is the correct formula for the center of mass $$X_{com} of a $$system of particles?

Accepted Answer

$$X_{com} = \frac{m_1$ x_1$ + m_2$ x_2$ + \ldots}{m_1$ + m_2$ + \ldots}$$

Question 15

Two blocks of equal mass undergo a head-on elastic collision. Object A moves right at $$5\ \mathrm{m/s}$$, Object B moves left at $$3\ \mathrm{m/s}. $$What are their final velocities?

Accepted Answer

A: $$-3\ \mathrm{m/s}$$, B: $$5\ \mathrm{m/s}$$

Question 16

A 6g bullet is fired upwards at $$800\ \mathrm{m/s}$$ into a $$1.2\ \mathrm{kg}$$ block at rest. The bullet emerges at $$150\ \mathrm{m/s}. $$What is the maximum height the block reaches? (Ignore air resistance.)

Accepted Answer

Use conservation of momentum to find block's velocity, then $$h = \frac{v^2$}{2g}$$; $$h \approx 1.5\ \mathrm{m}$$

Question 17

Which of the following is true for an elastic collision?

Accepted Answer

Momentum and mechanical energy are both conserved.

Momentum, Impulse, and Collisions – Study Notes

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