Q: A 0.100-kg ball is thrown straight up with an initial speed of 15.0 m/s. What is the momentum of the ball halfway up to its maximum height?

$$p = 0.100 \times 10.6 = 1.06\,\mathrm{kg\cdot m/s}$$

Q: A pitcher throws a 0.145-kg baseball at 40.0 m/s. What is the momentum of the baseball?

$$p = 0.145 \times 40.0 = 5.8\,\mathrm{kg\cdot m/s}$$

Q: In a slow-pitch softball game, a 0.200-kg ball is hit at 40.0 m/s and then decelerates to zero linearly in another 4.00 ms. What is the maximum force exerted on the ball?

$$F_{max} = \frac{\Delta p}{\Delta t} = \frac{0.200 \times 40.0}{0.004} = 2000\,\mathrm{N}$$

Q: A 0.100-kg ball is thrown straight up at 15.0 m/s. What is the maximum height reached by the ball?

$$h = \frac{v^2$}{2g} = \frac{(15.0)^2$}{2 \times 9.8} = 11.5\,\mathrm{m}$$

Q: A 0.030-kg bullet moving at 1,500 m/s has the same momentum as a baseball of mass 0.145 kg. What is the kinetic energy of the baseball at this speed?

$$KE = \frac{1}{2} m v^2$ = \frac{1}{2} \times 0.145 \times (310)^2$ = 6,980\,\mathrm{J}$$

Q: If you jump straight up with a speed of 3.0 m/s, what is the recoil speed of the Earth? Assume your mass is 70 kg and the Earth's mass is $$6.0 \times 10$$^{24}$$ kg.

$$v_{Earth} = -\frac{70 \times 3.0}{6.0 \times 10$$^{24}$$} = -3.5 \times 10$$^{-23}$$\,\mathrm{m/s}$$

Question 1

A 0.100-kg ball is thrown straight up with an initial speed of 15.0 m/s. What is the momentum of the ball at its maximum height?

Accepted Answer

$$p = 0$$

Question 2

A 0.500-kg stone is thrown east at 5.00 m/s by a 40.0-kg child standing on a frozen pond. Neglecting friction, what is the recoil velocity of the child?

Accepted Answer

$$v_{child} = -0.0625\,\mathrm{m/s}$$

Question 3

A pitcher claims he can throw a baseball with as much momentum as a 0.030-kg bullet moving at 1,500 m/s. What speed must the baseball (mass 0.145 kg) have to match the bullet's momentum?

Accepted Answer

$$v = 310\,\mathrm{m/s}$$

Question 4

If you jump straight up as high as you can, can you set the Earth moving? Model the Earth as a perfectly solid object. Which physical principle best explains your answer?

Accepted Answer

Conservation of momentum: your jump imparts a tiny recoil velocity to the Earth.

Question 5

Two blocks of masses $$M$$ and $$3M$$ are placed on a frictionless surface and pushed together with a spring between them. If the block of mass $$3M$$ moves to the right at $$2.00\,\mathrm{m/s}$$ after the spring is released, what is the speed of the block of mass $$M$$?

Accepted Answer

$$v_M = 6.00\,\mathrm{m/s}$$

Question 6

A 0.200-kg softball crosses the plate at 15.0 m/s at an angle of $$45^\	ext{o}$$ below the horizontal. If the ball is hit at 40.0 m/s, $$30^\	ext{o}$$ above the horizontal, what is the change in the $$y-$$component of the ball's velocity?

Accepted Answer

$$\Delta v_y = 40.0 \sin 30^\	ext{o} - 15.0 \sin 45^\	ext{o} = 20.0 - 10.6 = 9.4\,\mathrm{m/s}$$

Question 7

A 0.100-kg ball is thrown straight up with an initial speed of 15.0 m/s. What is the momentum of the ball halfway up to its maximum height?

Accepted Answer

$$p = 0.100 	imes 10.6 = 1.06\,\mathrm{kg\cdot m/s}$$

Question 8

A 40.0-kg child throws a 0.500-kg stone east at 5.00 m/s on a frictionless frozen pond. What is the total momentum of the system after the throw?

Accepted Answer

$$p_{total} = 0$$

Question 9

A pitcher throws a 0.145-kg baseball at 40.0 m/s. What is the momentum of the baseball?

Accepted Answer

$$p = 0.145 	imes 40.0 = 5.8\,\mathrm{kg\cdot m/s}$$

Question 10

In a slow-pitch softball game, a 0.200-kg ball is hit at 40.0 m/s and then decelerates to zero linearly in another 4.00 ms. What is the maximum force exerted on the ball?

Accepted Answer

$$F_{max} = \frac{\Delta p}{\Delta t} = \frac{0.200 	imes 40.0}{0.004} = 2000\,\mathrm{N}$$

Question 11

Two blocks, $$M$$ and $$3M$$, are pushed together with a spring between them. If the spring is compressed and then released, and the block of mass $$M$$ moves left at $$v_M$$, what is the ratio of the kinetic energies of the two blocks after release?

Accepted Answer

$$KE_M / KE_{3M} = 3$$

Question 12

A 0.100-kg ball is thrown straight up at 15.0 m/s. What is the maximum height reached by the ball?

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{(15.0)^2$}{2 	imes 9.8} = 11.5\,\mathrm{m}$$

Question 13

A 0.500-kg stone is thrown east at 5.00 m/s by a child on a frictionless pond. If the child recoils west at 0.0625 m/s, what is the total kinetic energy of the system after the throw?

Accepted Answer

$$KE_{total} = \frac{1}{2} m_{stone} v_{stone}^2 + \frac{1}{2} m_{child} v_{child}^2 = 6.25 + 0.078 = 6.33\,\mathrm{J}$$

Question 14

A 0.030-kg bullet moving at 1,500 m/s has the same momentum as a baseball of mass 0.145 kg. What is the kinetic energy of the baseball at this speed?

Accepted Answer

$$KE = \frac{1}{2} m v^2$ = \frac{1}{2} 	imes 0.145 	imes (310)^2$ = 6,980\,\mathrm{J}$$

Question 15

If you jump straight up with a speed of 3.0 m/s, what is the recoil speed of the Earth? Assume your mass is 70 kg and the Earth's mass is $$6.0 	imes 10$$^{24}$$ kg.

Accepted Answer

$$v_{Earth} = -\frac{70 	imes 3.0}{6.0 	imes 10$$^{24}$$} = -3.5 	imes 10$$^{-23}$$\,\mathrm{m/s}$$

Question 16

Two blocks, $$M$$ and $$3M$$, are pushed together with a spring between them. If the block of mass $$3M$$ moves at $$2.00\,\mathrm{m/s}$$, what is the original elastic energy stored in the spring if $$M = 0.500\,\mathrm{kg}$$?

Accepted Answer

$$E = \frac{1}{2} M v_M^2$ + \frac{1}{2} 3M v_{3M}^2 = \frac{1}{2} 	imes 0.500 	imes (6.00)^2$ + \frac{1}{2} 	imes 1.50 	imes (2.00)^2$ = 9.0 + 3.0 = 12.0\,\mathrm{J}$$

Question 17

A 0.200-kg softball is hit at 40.0 m/s and then decelerates to zero in 4.00 ms. What is the impulse delivered to the ball?

Accepted Answer

$$J = \Delta p = m \Delta v = 0.200 	imes 40.0 = 8.0\,\mathrm{kg\cdot m/s}$$

Linear Momentum, Collisions, and Impulse: Homework Study Notes

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