Q: A box of mass $$M is at $$the bottom of a ramp of angle $$\theta$$ and is at rest. A rope is attached to the box and passes over a massless pulley, with a brick of mass $$m$$ hanging from the other end of the rope vertically. For the extreme case, what must be the minimum mass $$m of $$the brick to just start moving the box up the ramp? The coefficient of static friction between the ramp and box is $$\mu_s.$$

$$M(\sin\theta + \mu_s \cos\theta)$$

Q: A uniform rod of length $$l$$ and mass $$m is $$attached from a ceiling from one end with a hinge so that it can swing freely. The rod is pulled up to one side by angle $$\theta$$ and released. Which of the following expresses the Newton's 2nd law for rotation about the hinge?

$$mg \cdot \frac{l}{2} \sin\theta = \frac{1}{3}ml^2$ \alpha$$

Question 1

A block of mass $$m$$ sits on a ramp of angle $$	heta$$ without sliding due to friction. The coefficients of static and kinetic friction are $$\mu_s$$ and $$\mu_k$$ respectively. What is the magnitude of the friction force acting on the block?

Accepted Answer

$$mg\sin	heta$$

Question 2

A box of mass $$M is at $$the bottom of a ramp of angle $$	heta$$ and is at rest. A rope is attached to the box and passes over a massless pulley, with a brick of mass $$m$$ hanging from the other end of the rope vertically. For the extreme case, what must be the minimum mass $$m of $$the brick to just start moving the box up the ramp? The coefficient of static friction between the ramp and box is $$\mu_s.$$

Accepted Answer

$$M(\sin	heta + \mu_s \cos	heta)$$

Question 3

A ball of mass $$m is $$thrown vertically upwards and reaches the maximum height $$h$$, then falls back to the original position. What is the work done by the gravitational force on the ball in the whole process?

Accepted Answer

$$0$$

Question 4

Two bodies of masses $$m_1$$ and $$m_2$$ are connected by a massless string and released from rest in a system where $$m_1 is on $$the ground and $$m_2 is $$kept at height $$h$$ above the ground. Find the total kinetic energy of the system right before body 2 just hits the ground.

Accepted Answer

$$\frac{m_1$ m_2$}{m_1$ + m_2$}gh$$

Question 5

Alice and Bob play 'tug-of-war' pulling each other on two ends of a rope on a frictionless horizontal surface. If they both start from rest and Alice has mass $$m_A$$ and Bob has mass $$m_B$$, where do they meet if they stop only after colliding?

Accepted Answer

They meet at the center of mass, $$x = \frac{m_B}{m_A + m_B}L$$

Question 6

A particle is moving in a circle of radius $$r$$ with constant speed $$v. $$What is the magnitude of its acceleration?

Accepted Answer

$$\frac{v^2$}{r}$$

Question 7

Two identical blocks hang from the ceiling by strings side by side. One of the blocks (A) is raised by height $$h$$ and released. The two blocks collide and stick together. What is the maximum height to which the combined block rises after the collision?

Accepted Answer

$$\frac{h}{2}$$

Question 8

A uniform rod of length $$l$$ and mass $$m is $$attached from a ceiling from one end with a hinge so that it can swing freely. The rod is pulled up to one side by angle $$	heta$$ and released. Which of the following expresses the Newton's 2nd law for rotation about the hinge?

Accepted Answer

$$mg \cdot \frac{l}{2} \sin	heta = \frac{1}{3}ml^2$ \alpha$$

Question 9

Two point masses of mass $$m$$ and $$2m$$ are connected by a massless rod of length $$l. $$Find the rotational inertia of the system around an axis perpendicular to the rod and passing through the center of mass of the rod.

Accepted Answer

$$\frac{2}{3}ml^2$

Question 10

A disk rotates about its center. At two points A and B on the rim, which is true about the (i) radial and (ii) tangential components of acceleration?

Accepted Answer

(i) Tie; (ii) Tie

Question 11

A car of mass $$m is $$moving at speed $$v$$ around a flat circular track of radius $$r. $$What is the minimum coefficient of static friction $$\mu_s$$ required to prevent the car from sliding?

Accepted Answer

$$\frac{v^2$}{rg}$$

Question 12

A block slides down a frictionless incline of height $$h$$ and then moves onto a horizontal surface with kinetic friction coefficient $$\mu_k. $$How far does the block travel on the horizontal surface before coming to rest?

Accepted Answer

$$\frac{h}{\mu_k}$$

Physics College Exam Study Guidance: Mechanics, Energy, and Rotational Motion

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