Q: A 1000-kg roller-coaster car starts from rest at a height of 40 m. Ignoring friction, what is its speed at the bottom of the hill? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 40} \approx 28\ \mathrm{m/s}$$

Q: A 0.145-kg baseball is thrown at 25 m/s. What is its kinetic energy?

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} \times 0.145 \times 25^2$ = 45.3\ \mathrm{J}$$

Question 1

Which of the following best describes Newton’s Law of Universal Gravitation as shown in the equation $$F = G \frac{m_1$ m_2$}{r^2$}$$?

Accepted Answer

The gravitational force between two objects is proportional to the product of their masses and inversely proportional to the square of the distance between them.

Question 2

A satellite is in a circular orbit at a distance $$2r_E$$ from the center of the Earth. If the mass of the satellite is $$m$$ and the mass of the Earth is $$m_E$$, what is the gravitational force acting on the satellite?

Accepted Answer

$$F = G \frac{m m_E}{(2r_E)^2$}$$

Question 3

The acceleration due to gravity at the surface of the Earth is given by $$g = G \frac{m_E}{r_E^2$}. If $$the radius of the Earth were doubled but its mass remained the same, what would be the new value of $$g at $$the surface?

Accepted Answer

$$g_{new} = \frac{1}{4}g$$

Question 4

Which of the following is a correct statement about the gravitational force inside a thin spherical shell of mass?

Accepted Answer

The gravitational force is zero everywhere inside the shell.

Question 5

A 1000-kg roller-coaster car starts from rest at a height of 40 m. Ignoring friction, what is its speed at the bottom of the hill? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 40} \approx 28\ \mathrm{m/s}$$

Question 6

Which of the following forces is NOT a conservative force?

Accepted Answer

Friction

Question 7

A block of mass $$m$$ slides on a rough horizontal surface with initial speed $$v_0$$ and compresses a spring (spring constant $$k) by a $$maximum distance $$X. If $$the coefficient of kinetic friction is $$\mu_k$$, which equation correctly relates these quantities?

Accepted Answer

$$\frac{1}{2}mv_0$^2 = \frac{1}{2}kX^2$ + \mu_k mg X$$

Question 8

A 0.145-kg baseball is thrown at 25 m/s. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 0.145 	imes 25^2$ = 45.3\ \mathrm{J}$$

Question 9

Which of the following best describes the work-energy principle?

Accepted Answer

The net work done on an object equals the change in its kinetic energy.

Question 10

A 10,000-kg railroad car moving at 24 m/s collides and couples with an identical car at rest. What is their common speed after the collision?

Accepted Answer

$$v = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{10,000 	imes 24 + 10,000 	imes 0}{20,000} = 12\ \mathrm{m/s}$$

Question 11

Which of the following is true about elastic collisions?

Accepted Answer

Both kinetic energy and momentum are conserved.

Question 12

A force $$F(x) = F_0$ \left(1 + \frac{1}{6} \frac{x^2$}{x_0$^2}\right)$$ acts on a robot arm as it moves from $$x_1 = 0.010$$\ \mathrm{m}$$ to x_2$ = 0.050\ \mathrm{m}. $$Which integral gives the work done by this force?

Accepted Answer

$$W = \int_{x_1$}^{x_2$} F(x) dx$$

Question 13

A jogger of mass 60 kg runs up a flight of stairs of vertical height 4.5 m in 4.0 s. What is the average power output in watts?

Accepted Answer

$$P = \frac{mgh}{t} = \frac{60 	imes 9.8 	imes 4.5}{4.0} = 661.5\ \mathrm{W}$$

Question 14

Which of the following is the correct expression for the gravitational potential energy of an object of mass $$m at $$height $$y$$ above a reference point?

Accepted Answer

$$U = mgy$$

Question 15

A block of mass $$m is $$attached to a spring with spring constant $$k$$ and compressed a distance $$x. $$What is the elastic potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2}kx^2$

Question 16

A 5.0-kg rifle fires a 0.020-kg bullet at 620 m/s. What is the recoil velocity of the rifle?

Accepted Answer

$$v_{rifle} = -\frac{m_{bullet} v_{bullet}}{m_{rifle}} = -\frac{0.020 	imes 620}{5.0} = -2.48\ \mathrm{m/s}$$

Question 17

Which of the following best describes the center of mass (CM) of a system?

Accepted Answer

It is the point that moves as if all the mass of the system were concentrated there and all external forces were applied there.

Unit 2 Study Guide: Gravitation, Work & Energy, Conservation of Energy, and Linear Momentum

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