Question 1

An object slides down a frictionless ramp that is 20 degrees from the horizontal and 5 meters long. How fast is the object moving at the bottom, assuming it started from rest at the top?

Accepted Answer

$$7.1$$ meters per second

Question 2

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

Accepted Answer

$$1.8$$ 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 $$50$$ centimeters, and a density of $$5$$ grams/cm$$^3$$, that is spinning at a rate of $$80$$ revolutions per minute?

Accepted Answer

$$8.37$$ Joules

Question 4

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

Accepted Answer

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

Question 5

Two spheres of equal mass and radius roll down a solid incline, one solid and one hollow. Which will reach the bottom first?

Accepted Answer

The solid sphere, because it has a lower moment of inertia

Question 6

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

Accepted Answer

$$2.1$$ meters

Question 7

Two rocks of equal mass collide and bounce off one another. The initial velocities were $$1$$ meter per second and $$7$$ meters per second, both in the same direction. Following the collision, which of the following is a possible set of values for the two rocks?

Accepted Answer

6 meters per second and 2 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

$$6.1 m/s$^2$$

Question 9

Which of the following objects has the most angular momentum?

Accepted Answer

A hollow sphere with a radius of $$0.5$$ meters, and a density of $$4$$ grams/cm$$^3$$, rotating at $$60$$ 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 $$0.5$$ meters, and a density of $$8$$ grams/cm$$^3$$, rotating at $$60$$ 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

$$0.7$$ miles north and $$1.3$$ miles east

Question 12

Suppose I drive around a flat circular track with radius $$20$$ meters. I drive at a constant speed of $$10$$ meters/second. I notice my tires start to skid when the road is wet, provided that the coefficient of static friction between my tires and the road is less than $$1.3. $$What can you conclude?

Accepted Answer

The coefficient of static friction between my tires and the road is less than $$1.3$$

Question 13

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

Accepted Answer

$$3.3 m/s$^2$$

Question 14

If the system in the previous question did include the mass of the pulley, how would this affect the acceleration of the $$20 kg $$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 $$2$$ meters in diameter, and weighs $$1000$$ kilograms

Question 16

A $$10 kg $$mass is simultaneously acted upon by a $$3 N $$force directed eastward, and a $$4 N $$force directed northward. What is the magnitude of the resulting acceleration vector?

Accepted Answer

$$0.7 m/s$^2$$

Question 17

You are stranded in space, $$50$$ meters from your spaceship. You have an apple, weighing $$0.2 kg. To $$get back to the spaceship, you throw the apple. What is the greatest velocity you can achieve if you throw the apple at $$20 m/s$$?

Accepted Answer

$$0.04 m/s$$

Question 18

Suppose you are riding your bicycle at $$9 m/s $$and you exert a torque to stop the wheel. The wheel has a radius of $$0.5$$ meters and a mass of $$2 kg. $$What is the friction force from the ground if the torque applied by the brakes is $$9 Nm$$?

Accepted Answer

$$9 N$$

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

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