Q: A person stands on a scale in an elevator that is accelerating upward at $$a. If $$the person’s mass is $$m$$, what is the apparent weight shown on the scale?

$$W_{\text{apparent}} = m(g + a)$$

Q: A uniform beam of length $$L$$ and mass $$M is $$supported horizontally at its ends. A mass $$m is $$placed at a distance $$d$$ from one end. What is the condition for static equilibrium?

The sum of all torques about any point is zero: $$\sum \tau = 0$$

Question 1

A 0.5 kg mass is attached to a spring with a spring constant $$k = 200 \ \mathrm{N/m}$$ and oscillates on a frictionless surface. What is the period of oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\frac{0.5}{200}}$$

Question 2

A simple pendulum of length $$L is $$released from rest at an angle $$\$$theta_0$$ from the vertical. Which of the following best describes the restoring force acting on the pendulum bob?

Accepted Answer

$$F = -mg \sin 	heta$$

Question 3

A satellite orbits Earth in a circular orbit of radius $$r. $$According to Newton's law of universal gravitation, what is the magnitude of the gravitational force acting on the satellite?

Accepted Answer

$$F = \frac{GMm}{r^2$}$$

Question 4

Which of the following correctly expresses Kepler’s Third Law for a planet orbiting the Sun?

Accepted Answer

$$T^2$$ \propto $$r^3$$

Question 5

A person stands on a scale in an elevator that is accelerating upward at $$a. If $$the person’s mass is $$m$$, what is the apparent weight shown on the scale?

Accepted Answer

$$W_{	ext{apparent}} = m(g + a)$$

Question 6

A uniform beam of length $$L$$ and mass $$M is $$supported horizontally at its ends. A mass $$m is $$placed at a distance $$d$$ from one end. What is the condition for static equilibrium?

Accepted Answer

The sum of all torques about any point is zero: $$\sum 	au = 0$$

Question 7

A disk of mass $$M$$ and radius $$R$$ rotates about its center. If a force $$F is $$applied tangentially at the rim, what is the resulting angular acceleration $$\alpha$$?

Accepted Answer

$$\alpha = \frac{F}{\frac{1}{2}MR^2$}$$

Question 8

A figure skater pulls in her arms while spinning, reducing her moment of inertia from $$I_1 to$$ $$I_2. If $$her initial angular velocity is $$\$$omega_1$$, what is her final angular velocity $$\$$omega_2$$?

Accepted Answer

$$\$$omega_2$$ = \frac{I_1$}{I_2$} \$$omega_1$$

Question 9

A solid sphere of mass $$M$$ and radius $$R$$ rolls without slipping down an incline of height $$h. $$What is its speed at the bottom, assuming it started from rest?

Accepted Answer

$$v = \sqrt{\frac{10gh}{7}}$$

Question 10

Which of the following is the correct expression for the moment of inertia of a thin rod of mass $$M$$ and length $$L$$ about an axis through its center perpendicular to its length?

Accepted Answer

$$I = \frac{1}{12}ML^2$

Question 11

A uniform solid cylinder of mass $$M$$ and radius $$R$$ rotates about an axis parallel to its center and a distance $$d$$ away. What is its moment of inertia using the parallel axis theorem?

Accepted Answer

$$I = \frac{1}{2}MR^2$ + Md^2$

Question 12

Two carts of masses $$m_1$$ and $$m_2$$ collide elastically in one dimension. If $$m_1 is $$initially moving with velocity $$v_1$$ and $$m_2 is at $$rest, what is the final velocity of $$m_1$$ after the collision?

Accepted Answer

$$v_1$$' = \frac{$$m_1$$ - $$m_2$$}{$$m_1$$ + $$m_2$$} $$v_1$$

Question 13

A ball of mass $$m is $$dropped from height $$h$$ and bounces back to height $$h'. $$Which law explains the loss of height after the bounce?

Accepted Answer

Law of mechanical energy conservation, with energy lost to non-conservative forces

Question 14

A car of mass $$m$$ accelerates from rest to velocity $$v$$ over a distance $$d. $$What is the work done by the net force on the car?

Accepted Answer

$$W = \frac{1}{2}mv^2$

Question 15

A block slides down a frictionless incline of height $$h. $$Which principle allows you to equate its potential energy at the top to its kinetic energy at the bottom?

Accepted Answer

Law of mechanical energy conservation: $$mgh = \frac{1}{2}mv^2$

Question 16

A force $$F is $$applied to a mass $$m$$ for a time $$t$$, causing a change in velocity $$\Delta v. $$Which law relates the force to the change in momentum?

Accepted Answer

Newton's Second Law: $$F = \frac{dp}{dt}$$

Question 17

A child on a swing (length $$L) $$reaches a maximum speed $$v_{max} at $$the lowest point. Which formula relates $$v_{max} to $$the initial height $$h$$ above the lowest point?

Accepted Answer

$$v_{max} = \sqrt{2gh}$$

Question 18

A wheel of radius $$R$$ rolls without slipping with angular velocity $$\omega. $$What is the speed of the center of mass?

Accepted Answer

$$v_{cm} = \omega R$$

Question 19

A gymnast performs a flip and tucks her body, decreasing her moment of inertia. Which physical law explains why her rotation rate increases?

Accepted Answer

Conservation of angular momentum: $$L = I\omega$$

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