Lesson 2 has thus far focused on how to analyze motion situations
using the work and energy relationship. The relationship could be
summarized by the following statements:

There is a relationship between work and mechanical energy change.
Whenever work is done upon an object by an external or nonconservative
force, there will be a change in the total mechanical energy of the
object. If only internal forces are doing work (no work done by
external forces), there is no change in total mechanical energy; the
total mechanical energy is said to be "conserved." The quantitative
relationship between work and the two forms of mechanical energy is
expressed by the following equation:
KEi + PEi + Wext = KEf + PEf

Now an effort will be made to apply this relationship to a variety of
motion scenarios in order to test our understanding.

Check Your Understanding

Use your understanding of the work-energy theorem to answer the
following questions. Then click the button to view the answers.

1. Consider the falling and rolling motion of the ball in the
following two resistance-free situations. In one situation, the ball
falls off the top of the platform to the floor. In the other
situation, the ball rolls from the top of the platform along the
staircase-like pathway to the floor. For each situation, indicate what
types of forces are doing work upon the ball. Indicate whether the
energy of the ball is conserved and explain why. Finally, fill in the
blanks for the 2-kg ball.

2. If frictional forces and air resistance were acting upon the
falling ball in #1 would the kinetic energy of the ball just prior to
striking the ground be more, less, or equal to the value predicted in
#1?

Use the following diagram to answer questions #3 - #5. Neglect the
affect of resistance forces.

3. As the object moves from point A to point D across the surface, the
sum of its gravitational potential and kinetic energies ____.

a. decreases, only

b. decreases and then increases

c. increases and then decreases

d. remains the same

4. The object will have a minimum gravitational potential energy at point ____.

a. A

b. B

c. C

d. D

e. E

5. The object's kinetic energy at point C is less than its kinetic
energy at point ____.

a. A only

b. A, D, and E

c. B only

d. D and E

6. Many drivers' education books provide tables that relate a car's
braking distance to the speed of the car (see table below). Utilize
what you have learned about the stopping distance-velocity
relationship to complete the table.

7. Some driver's license exams have the following question.

A car moving 50 km/hr skids 15 meters with locked brakes.
How far will the car skid with locked brakes if it is moving at 150
km/hr?

8. Two baseballs are fired into a pile of hay. If one has twice the
speed of the other, how much farther does the faster baseball
penetrate? (Assume that the force of the haystack on the baseballs is
constant).

9. Use the law of conservation of energy (assume no friction) to fill
in the blanks at the various marked positions for a 1000-kg roller
coaster car.

10. If the angle of the initial drop in the roller coaster diagram
above were 60 degrees (and all other factors were kept constant),
would the speed at the bottom of the hill be any different? Explain.

11. Determine Li Ping Phar's (a mass of approximately 50 kg) speed at
locations B, C, D and E.

12. An object which weighs 10 N is dropped from rest from a height of
4 meters above the ground. When it has free-fallen 1 meter its total
mechanical energy with respect to the ground is ____.

a. 2.5 J

b. 10 J

c. 30 J

d. 40 J

13. During a certain time interval, a 20-N object free-falls 10
meters. The object gains _____ Joules of kinetic energy during this
interval.

a. 10

b. 20

c. 200

d. 2000

14. A rope is attached to a 50.0-kg crate to pull it up a frictionless
incline at constant speed to a height of 3-meters. A diagram of the
situation and a free-body diagram are shown below. Note that the force
of gravity has two components (parallel and perpendicular component);
the parallel component balances the applied force and the
perpendicular component balances the normal force.

Of the forces acting upon the crate, which one(s) do work upon it?

Based upon the types of forces acting upon the system and their
classification as internal or external forces, is energy conserved?
Explain.

Calculate the amount of work done upon the crate.