Q: A woman of mass $$120\ \mathrm{kg}$$ and a man of mass $$180\ \mathrm{kg}$$ stand side by side on a stationary boat of mass $$320\ \mathrm{kg}. If $$the woman dives first with a velocity of $$9.2\ \mathrm{ft/s}$$, what is the velocity of the boat immediately after she dives?

$$V_{\text{boat}} = -\dfrac{120 \times 9.2}{320} = -3.45\ \mathrm{ft/s}$$

Q: Which of the following is true about the mechanical efficiency $$E of a $$machine?

$$E = \dfrac{\text{Power output}}{\text{Power input}}$$

Q: A 50 kg block is attached to a spring and slides on a frictionless surface. If the spring is compressed by $$0.1744\ \mathrm{m}$$ and the spring constant is $$k = 100\ \mathrm{N/m}$$, what is the potential energy stored in the spring?

$$U = \dfrac{1}{2} \times 100 \times (0.1744)^2$ = 1.52\ \mathrm{J}$$

Question 1

A 0.4 kg ball A moving at $$5.0\ \mathrm{m/s}$$ collides with a stationary 0.5 kg ball B. After the collision, ball A moves at $$0.5\ \mathrm{m/s}$$ and ball B moves at $$4.5\ \mathrm{m/s}. $$What is the coefficient of restitution $$e$$ for this collision?

Accepted Answer

$$e = \dfrac{4.5 - 0.5}{5.0 - 0} = 0.8$$

Question 2

Which of the following best describes the principle of conservation of linear momentum for a system of particles?

Accepted Answer

The total linear momentum of a system remains constant if the net external force acting on the system is zero.

Question 3

A woman of mass $$120\ \mathrm{kg}$$ and a man of mass $$180\ \mathrm{kg}$$ stand side by side on a stationary boat of mass $$320\ \mathrm{kg}. If $$the woman dives first with a velocity of $$9.2\ \mathrm{ft/s}$$, what is the velocity of the boat immediately after she dives?

Accepted Answer

$$V_{	ext{boat}} = -\dfrac{120 	imes 9.2}{320} = -3.45\ \mathrm{ft/s}$$

Question 4

Which equation correctly expresses the principle of linear impulse and momentum for a single particle?

Accepted Answer

$$m v_1$ + \sum F \Delta t = m v_2$

Question 5

A spring with stiffness $$k is $$compressed by a distance $$x. $$What is the elastic potential energy stored in the spring?

Accepted Answer

$$U = \dfrac{1}{2} k x^2$

Question 6

A block of mass $$m$$ slides down a frictionless incline of height $$h. $$What is its velocity at the bottom?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 7

Which of the following is true about the mechanical efficiency $$E of a $$machine?

Accepted Answer

$$E = \dfrac{	ext{Power output}}{	ext{Power input}}$$

Question 8

During a central impact between two spheres, which quantity is conserved?

Accepted Answer

Linear momentum along the line of impact

Question 9

A 50 kg block is attached to a spring and slides on a frictionless surface. If the spring is compressed by $$0.1744\ \mathrm{m}$$ and the spring constant is $$k = 100\ \mathrm{N/m}$$, what is the potential energy stored in the spring?

Accepted Answer

$$U = \dfrac{1}{2} 	imes 100 	imes (0.1744)^2$ = 1.52\ \mathrm{J}$$

Question 10

Which formula correctly relates the force exerted by a spring to its displacement $$x$$?

Accepted Answer

$$F = -k x$$

Question 11

A ball is dropped from a height $$h$$ and rebounds to a height $$h'. $$What is the coefficient of restitution $$e$$ for the collision with the ground?

Accepted Answer

$$e = \sqrt{\dfrac{h'}{h}}$$

Question 12

Which of the following best describes the work-energy principle for a particle?

Accepted Answer

$$T_1$$ + \sum U_{1,2} = $$T_2$$

Question 13

A projectile is fired with velocity $$v_0 at an $$angle $$	heta$$ above the horizontal. What is the horizontal component of its initial velocity?

Accepted Answer

$$v_{0x} = v_0$ \cos 	heta$$

Question 14

Which equation represents the relationship between conservative force and potential energy?

Accepted Answer

$$\vec{F} = -
abla V$$

Question 15

A machine does $$550\ \mathrm{ft} \cdot \mathrm{lb}/\mathrm{s} of $$work. How much power is this in watts?

Accepted Answer

$$1\ \mathrm{hp} = 550\ \mathrm{ft} \cdot \mathrm{lb}/\mathrm{s} = 745.7\ \mathrm{W}$$

Question 16

In an oblique impact, which component of velocity is affected by the coefficient of restitution?

Accepted Answer

The component along the line of impact

Question 17

A block slides down a ramp and compresses a spring at the bottom. If the block has mass $$m$$, the ramp height is $$h$$, and the spring constant is $$k$$, what is the maximum compression $$x of $$the spring?

Accepted Answer

$$x = \sqrt{\dfrac{2 m g h}{k}}$$

Question 18

Which of the following is true for the conservation of energy in a system with only conservative forces?

Accepted Answer

$$T_1$$ + $$V_1$$ = $$T_2$$ + $$V_2$$

Question 19

A $$2\ \mathrm{kg}$$ ball moving at $$3\ \mathrm{m/s}$$ collides elastically with a $$1\ \mathrm{kg}$$ ball at rest. What is the velocity of the $$1\ \mathrm{kg}$$ ball after the collision?

Accepted Answer

$$v = \dfrac{2 	imes 3}{2 + 1} = 2\ \mathrm{m/s}$$

Momentum, Impulse, Work, Energy, and Collisions: Study Notes

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