Question 1

Hannah is pulling her pet rabbit on a sled across level snow using a rope at an angle above the ground. The sled and rabbit have a combined mass of 50 kg and are accelerating at $$3.00\ \mathrm{m/s^2$}. $$The rope exerts forces of $$100.0\ \mathrm{N}$$ upward and $$250.0\ \mathrm{N} to $$the right. What is the magnitude of the force of friction acting on the sled?

Accepted Answer

$$400\ \mathrm{N}$$

Question 2

A standard clock is running out of batteries. As the second hand slows to a stop, what are the signs of angular velocity $$\omega$$ and angular acceleration $$\alpha$$?

Accepted Answer

$$\omega is $$positive and $$\alpha is $$negative.

Question 3

Blocks A and B, with masses $$1\ \mathrm{kg}$$ and $$2\ \mathrm{kg}$$ respectively, are connected via a massless string. If a hand exerts a $$9\ \mathrm{N}$$ force on block A, what is the net force on mass A?

Accepted Answer

$$6\ \mathrm{N}$$

Question 4

Two people are playing tug-of-war and are presently at a standstill, each pulling with $$100\ \mathrm{N} of $$force. What is the tension in the rope? Ignore the mass of the rope and assume it is equally stretched.

Accepted Answer

$$100\ \mathrm{N}$$

Question 5

A $$50\ \mathrm{g}$$ rock is attached to a $$50\ \mathrm{cm}$$ long string. If it is spun in uniform circular motion and has an acceleration of $$2.0\ \mathrm{m/s^2$}$$, what is the angular speed of the rock?

Accepted Answer

$$2.0\ \mathrm{rad/s}$$

Question 6

A spool has a thin, negligible-mass cable attached to it, which is pulled with an acceleration of $$1.5\ \mathrm{m/s^2$}. $$The diameter of the spool is $$6.0\ \mathrm{cm}$$ and it rotates on a frictionless bearing from rest. After $$1.0\ \mathrm{m} of $$the cable has been unwound, what is the angular speed of the spool? Assume the cable is pulled at an angle that allows maximum speed to be obtained.

Accepted Answer

$$57\ \mathrm{rad/s}$$

Question 7

A $$2.0\ \mathrm{m}$$ diameter merry-go-round is initially turning with a $$4.0\ \mathrm{s}$$ period counterclockwise. What is the tangential speed of a child on the rim?

Accepted Answer

$$1.57\ \mathrm{m/s}$$

Question 8

A $$2.0\ \mathrm{m}$$ diameter merry-go-round is initially turning with a $$4.0\ \mathrm{s}$$ period counterclockwise. It slows down and stops in $$20\ \mathrm{s}. $$What is the angular acceleration of the merry-go-round as it stops?

Accepted Answer

$$-0.079\ \mathrm{$$rad/s^2$$}$$

Question 9

A $$2.0\ \mathrm{m}$$ diameter merry-go-round is initially turning with a $$4.0\ \mathrm{s}$$ period counterclockwise. It slows down and stops in $$20\ \mathrm{s}. $$How many revolutions does the merry-go-round make as it stops?

Accepted Answer

$$2.5$$ revolutions

Question 10

A steel disc is launched up a dry steel ramp that is inclined at a $$40^\circ$$ angle. If the block's initial speed is $$10\ \mathrm{m/s}$$, what is the normal force acting on the disc while on the ramp? (Assume mass $$m$$ and $$g=9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$mg\cos(40^\circ)$$

Question 11

A steel disc is launched up a dry steel ramp at $$40^\circ. If $$the coefficient of kinetic friction is $$\mu_k$$, what is the friction force acting on the disc, and in which direction does it act?

Accepted Answer

$$\mu_k mg\cos(40^\circ)$$, down the ramp

Question 12

A steel disc is launched up a $$40^\circ$$ ramp with initial speed $$v_0. $$What is the net acceleration of the disc parallel to the ramp? (Assume friction coefficient $$\mu_k.)$$

Accepted Answer

$$-g\sin(40^\circ) - \mu_k g\cos(40^\circ)$$

Question 13

A $$0.50\ \mathrm{kg}$$ mass is attached to a $$0.50\ \mathrm{m}$$ string and spun in a horizontal circle. If the tension in the string is $$4.0\ \mathrm{N}$$, what is the angular speed of the mass?

Accepted Answer

$$2.83\ \mathrm{rad/s}$$

Question 14

A $$1.0\ \mathrm{kg}$$ block and a $$2.0\ \mathrm{kg}$$ block are connected by a massless string and pulled with a $$9.0\ \mathrm{N}$$ force. What is the acceleration of the system?

Accepted Answer

$$3.0\ \mathrm{m/s^2$}$$

Question 15

A $$0.06\ \mathrm{m}$$ diameter spool is pulled so that $$1.0\ \mathrm{m} of $$cable unwinds with constant acceleration. What is the relationship between the linear acceleration $$a of $$the cable and the angular acceleration $$\alpha of $$the spool?

Accepted Answer

$$a = r\alpha$$

Question 16

A merry-go-round of radius $$1.0\ \mathrm{m} is $$rotating at $$0.5\ \mathrm{rev/s}. $$What is the centripetal acceleration of a child on the rim?

Accepted Answer

$$9.87\ \mathrm{m/s^2$}$$

PHY 130 Exam #2 Practice: Dynamics, Forces, and Rotational Motion

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