Q: A spring of constant $k$ is attached to a block of mass $M$ on a frictionless ramp inclined at angle $\theta$. The spring stretches parallel to the ramp. What is the equilibrium stretch $x$ of the spring?

$x = \dfrac{Mg \sin \theta}{k}$

Q: A block of mass $M$ slides down a rough incline of angle $\theta$ with coefficient of kinetic friction $\mu_k$. What is the acceleration $a$ of the block?

$a = g(\sin \theta - \mu_k \cos \theta)$

Question 1

A block of mass $M$ is at rest on a frictionless ramp inclined at an angle $	heta$ to the horizontal. The block is attached to a wall by a string parallel to the ramp. What is the tension $T$ in the string?

Accepted Answer

$T = Mg \sin 	heta$

Question 2

A car with initial velocity $v_0 = 30\,\mathrm{m/s}$ skids to a stop over a distance $d = 51.0\,\mathrm{m}$ on a flat road. What is the coefficient of kinetic friction $\mu_k$ between the tires and the road?

Accepted Answer

$\mu_k = 0.70$

Question 3

A block of mass $M$ is released from rest at the top of a frictionless ramp inclined at $	heta = 30^\circ$. What is the acceleration $a$ of the block down the ramp?

Accepted Answer

$a = g \sin 30^\circ$

Question 4

A spring of constant $k$ is attached to a block of mass $M$ on a frictionless ramp inclined at angle $	heta$. The spring stretches parallel to the ramp. What is the equilibrium stretch $x$ of the spring?

Accepted Answer

$x = \dfrac{Mg \sin 	heta}{k}$

Question 5

A car of mass $M$ moves with constant speed $v = \sqrt{3gR}$ through a dip of radius $R$. What is the normal force $N$ on the car at the bottom of the dip?

Accepted Answer

$N = 4Mg$

Question 6

A block is pushed to the right with constant velocity on a horizontal surface. Which of the following free-body diagrams best describes the forces acting on the block?

Accepted Answer

A rightward force equal in magnitude to the leftward kinetic friction force, and upward and downward forces of equal magnitude.

Question 7

A block of mass $M$ is at rest on a horizontal table. Which of the following statements is true?

Accepted Answer

The normal force from the table equals the gravitational force on the block.

Question 8

A cart of mass $M_c$ rolls on a frictionless horizontal ground. A block of mass $M_b$ is pressed against the vertical front of the cart. An applied force $F_{app}$ causes the cart to accelerate, keeping the block from falling due to static friction. What is the minimum coefficient of static friction $\mu_s$ required between the cart and the block?

Accepted Answer

$\mu_s = \dfrac{a}{g}$

Question 9

A block of mass $M$ slides down a rough incline of angle $	heta$ with coefficient of kinetic friction $\mu_k$. What is the acceleration $a$ of the block?

Accepted Answer

$a = g(\sin 	heta - \mu_k \cos 	heta)$

Question 10

A solid sphere of mass $M$ and radius $R$ rolls without slipping down an incline of height $h$. What is its speed $v$ at the bottom?

Accepted Answer

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

Question 11

A block of mass $M$ is attached to a horizontal spring of constant $k$ and oscillates with amplitude $A$. What is the maximum speed $v_{max}$ of the block?

Accepted Answer

$v_{max} = A \sqrt{\dfrac{k}{M}}$

Question 12

A rod of length $L$ and mass $M$ rotates about its center. What is its moment of inertia $I$?

Accepted Answer

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

Question 13

A block of mass $M$ is pushed up a frictionless ramp inclined at angle $	heta$ with initial speed $v_0$. What is the maximum height $h_{max}$ reached by the block?

Accepted Answer

$h_{max} = \dfrac{v_0^2}{2g}$

Question 14

A block of mass $M$ is attached to a spring of constant $k$ and oscillates with period $T$. What is the period $T$?

Accepted Answer

$T = 2\pi \sqrt{\dfrac{M}{k}}$

Question 15

A block of mass $M$ is dropped from height $h$ onto a spring of constant $k$. What is the maximum compression $x_{max}$ of the spring?

Accepted Answer

$x_{max} = \sqrt{\dfrac{2Mh}{k}}$

Question 16

A block of mass $M$ is pulled at constant velocity $v$ across a rough horizontal surface with coefficient of kinetic friction $\mu_k$. What is the work $W$ done by the pulling force over distance $d$?

Accepted Answer

$W = \mu_k M g d$

Question 17

A block of mass $M$ is attached to a string and whirled in a horizontal circle of radius $R$ at constant speed $v$. What is the tension $T$ in the string?

Accepted Answer

$T = \dfrac{Mv^2}{R}$

Question 18

A block of mass $M$ is released from rest at the top of a frictionless ramp of height $h$. What is its speed $v$ at the bottom?

Accepted Answer

$v = \sqrt{2gh}$

Question 19

A block of mass $M$ is attached to a spring of constant $k$ and oscillates with amplitude $A$. What is the total mechanical energy $E$ of the system?

Accepted Answer

$E = \dfrac{1}{2}kA^2$

Physics I: Mechanics – Quiz Study Guide (Forces, Motion, Energy, Rotational Dynamics)

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