Question 1

An object slides down a frictionless ramp that is 5 meters long and tilted 20 degrees from the horizontal. How fast is the object moving at the bottom, assuming it started from rest? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$3.7\ \mathrm{m/s}$$

Question 2

How long does it take for the object in the previous question to slide down the 5 meter ramp?

Accepted Answer

$$1.4\ \mathrm{seconds}$$

Question 3

The moment of inertia for a solid sphere is $$0.4MR^2. $$What is the rotational kinetic energy of a solid sphere with a radius of $$50\ \mathrm{cm}$$, a mass of $$5\ \mathrm{kg}$$, and a density of $$5\ \mathrm{g/cm^3$}$$ that is spinning at a rate of $$80\ \mathrm{revolutions/minute}$$?

Accepted Answer

$$8.57\ \mathrm{Joules}$$

Question 4

Which of the following forces exerts the most torque on a door about its hinges?

Accepted Answer

A force applied at the edge of the door, perpendicular to the direction from the hinges

Question 5

Suppose you have a solid cylinder and a hollow sphere, each with the same radius, mass, and released from rest at the top of a ramp. Which will reach the bottom first?

Accepted Answer

The solid cylinder, because it has a smaller moment of inertia

Question 6

A spring with a spring constant of $$500\ \mathrm{N/m} is $$compressed until the stored energy is $$2,250\ \mathrm{J}. By $$how many meters is the spring compressed?

Accepted Answer

$$3\ \mathrm{m}$$

Question 7

Two rocks of equal mass collide and bounce off one another. The initial velocities were $$4\ \mathrm{m/s}$$ upward and $$7\ \mathrm{m/s}$$ per second, both in the same direction. Following the collision, which of the following is a possible set of values for the two rocks? (Remember the momentum and kinetic energy must be conserved in an elastic collision.)

Accepted Answer

6 meters per second and 5 meters per second

Question 8

What is the acceleration of an object sliding down a ramp angled $$60$$ degrees with respect to horizontal if the coefficient of sliding friction between the object and the ramp is $$0.3$$?

Accepted Answer

$$6.1\ \mathrm{m/s^2$}$$

Question 9

Which of the following objects has the most angular momentum?

Accepted Answer

A hollow sphere with radius of $$0.5\ \mathrm{meters}$$, and a density of $$4\ \mathrm{g/cm^3$}$$, rotating at $$60\ \mathrm{revolutions/minute}$$

Question 10

Which of the following objects has the most kinetic energy associated with their rotation?

Accepted Answer

A solid sphere with a radius of $$0.5\ \mathrm{meters}$$, and a density of $$8\ \mathrm{g/cm^3$}$$, rotating at $$60\ \mathrm{revolutions/minute}$$

Question 11

Suppose you walk two miles north, one mile east, and then $$1.5$$ miles in a direction $$15$$ degrees south of due west. Where are you relative to your starting point?

Accepted Answer

$$0.72$$ miles north and $$1.38$$ miles east

Question 12

Suppose you drive around a flat circular track with radius $$20$$ meters. If you drive at a constant speed of $$10\ \mathrm{m/s}$$, what is the minimum value for the coefficient of static friction, $$\mu_s$$, between your tires and the road so that you do not skid?

Accepted Answer

The coefficient of static friction between my tires and the road is greater than $$0.5$$

Question 13

Suppose two weights are attached to a massless frictionless pulley as shown in the diagram. One weight is $$20\ \mathrm{kg}$$ and the other is $$10\ \mathrm{kg}. $$What is the magnitude of the acceleration of the $$20\ \mathrm{kg}$$ weight?

Accepted Answer

$$3.3\ \mathrm{m/s^2$}$$

Question 14

If the system in the previous question did include the mass of the pulley, how would this affect the acceleration of the $$20\ \mathrm{kg}$$ weight?

Accepted Answer

It would decrease

Question 15

Which of the following spheres would have the largest terminal velocity? Assume that the Reynolds number of the air flow around the balls is very high in each case, so the drag is proportional to the square of the velocity.

Accepted Answer

A ball that is $$1$$ meter in diameter, and weighs $$1000\ \mathrm{kilograms}$$

Physics 1403 Practice Final: Study Notes on Mechanics, Energy, and Rotational Motion

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