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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