Q: A block of mass $M$ is at rest on a ramp inclined at angle $\theta$ with respect to the horizontal. What is the reading on the spring scale, $F_s$, and what is the normal force, $N$? Let $x$ point to the right, and $y$ point upwards.

$F_s = M g \sin\theta$ and $N = M g \cos\theta$

Q: A block of mass $m$ is sliding down a ramp inclined at angle $\theta$ with coefficient of kinetic friction $\mu_k$. What is the acceleration $a$ of the block?

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

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

$h_{max} = \frac{v_0^2}{2g \sin\theta}$

Question 1

A ball of mass $m$ hangs from the ceiling of an elevator. The elevator is accelerating upwards with acceleration $a$. What is the tension in the cord that is holding the mass?

Accepted Answer

$m(g+a)$

Question 2

Two blocks with masses $2.0\ \mathrm{kg}$ and $1.0\ \mathrm{kg}$ lie on a frictionless table. Suppose you push with force $3.0\ \mathrm{N}$, applied as shown (on the $2.0\ \mathrm{kg}$ block). What is the magnitude of the force pushing back on you?

Accepted Answer

$3.0\ \mathrm{N}$

Question 3

A block of mass $30.0\ \mathrm{kg}$ needs to be pushed along the floor a distance $1.00\ \mathrm{m}$, starting from rest. There is a constant, horizontal applied force of magnitude $12\ \mathrm{N}$ pushing the block in its direction of motion. The coefficient of kinetic friction is $0.50$. Which of the following best describes the motion of the block?

Accepted Answer

The block travels the $1.00\ \mathrm{m}$ with constant velocity of magnitude $0.17\ \mathrm{m/s}$.

Question 4

A block of mass $M$ is at rest on a ramp inclined at angle $	heta$ with respect to the horizontal. What is the reading on the spring scale, $F_s$, and what is the normal force, $N$? Let $x$ point to the right, and $y$ point upwards.

Accepted Answer

$F_s = M g \sin	heta$ and $N = M g \cos	heta$

Question 5

Shown below are two different setups involving a pulley system. In case a, block A is connected (via a massless rope) to another block of weight $10\ \mathrm{N}$. In case b, block A is connected (via a massless rope) to a person pulling with a force $10\ \mathrm{N}$. Which of the following is true about the acceleration of block A ($a_A$) in the two cases? Assume no friction.

Accepted Answer

$a_A$ is greater in case b.

Question 6

In an amusement park ride called The Roundup, passengers stand inside a rotating ring. After the ring has acquired sufficient speed, it tilts into a vertical plane, as shown in the figure. The minimum normal force that people feel has magnitude $1.0mg$. What is the maximum normal force that people feel as they undergo uniform circular motion in this vertical loop?

Accepted Answer

$4.0mg$

Question 7

In the figure below, the coefficient of static friction between mass $m_3$ and the table is $0.40$, whereas the coefficient of kinetic friction is $0.20$. Mass $m_2 = 2.0\ \mathrm{kg}$ is hanging, as shown. What minimum value of $m_4$ will keep the system from starting to move?

Accepted Answer

$5.0\ \mathrm{kg}$

Question 8

A rotating rod of length $2L$ has a mass attached at each end. The tension in the top string is twice the tension in the bottom string. What is the speed $v$ of the masses?

Accepted Answer

$v = \sqrt{3gL}$

Question 9

A block of mass $M$ is pushed rightwards on a frictionless ramp inclined at angle $	heta$ relative to the horizontal. What is the magnitude of the force $F$ required to keep the block in equilibrium?

Accepted Answer

$F = M g \sin	heta$

Question 10

A solid sphere of mass $M$ and radius $R$ rotates about an axis through its center. What is its moment of inertia?

Accepted Answer

$I = \frac{2}{5}MR^2$

Question 11

A block of mass $m$ slides down a frictionless incline of angle $	heta$. What is its acceleration?

Accepted Answer

$a = g \sin	heta$

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

$T = m v^2 / r$

Question 14

A block of mass $m$ is at rest on a horizontal surface. The coefficient of static friction is $\mu_s$. What is the maximum force $F_{max}$ that can be applied horizontally before the block starts to move?

Accepted Answer

$F_{max} = \mu_s m g$

Question 15

A pendulum of length $L$ swings with small amplitude. What is the period $T$ of its oscillation?

Accepted Answer

$T = 2\pi \sqrt{L/g}$

Question 16

A block of mass $m$ is dropped from height $h$. What is its speed $v$ just before hitting the ground?

Accepted Answer

$v = \sqrt{2gh}$

Question 17

A block of mass $m$ is sliding down a ramp inclined at 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 18

A block of mass $m$ is attached to a spring and oscillates with angular frequency $\omega$. What is the relationship between $\omega$, $k$, and $m$?

Accepted Answer

$\omega = \sqrt{k/m}$

Question 19

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

$h_{max} = \frac{v_0^2}{2g \sin	heta}$

Practice Quiz Study Guide: Newtonian Mechanics and Rotational Motion

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