. The theorem 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 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 the theorem to a variety of motion scenarios in order to test our understanding.

Use your understanding of the work-energy theorem to answer the following questions. Then depress mouse on the "pop-up menu" to view the answers.

1. Consider the falling motion of the ball in the following two frictionless situations. For each situation, indicate what type of forces are doing work upon the ball. Indicate whether the energy of the ball is conserved and explain why. Finally, indicate the kinetic energy and the velocity of the 2-kg ball just prior to striking the ground.

Depress mouse to view answer to Diagram A.The only force doing work is gravity. Sinceit is an internal force, the total mechanicalenergy is conserved. Thus, all 100 J of PE isconverted into KE. The kinetic energy at thebottom of the hill is 100 J. Using the equationKE=0.5*m*v^2, the velocity is 10 m/s.

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?

Depress mouse to view answer.The kinetic energy would be less in a situationthat involves friction. Friction would donegative work and thus remove mechanical energyfrom the falling ball.

3. The cartoon strip below depicts a pile-driver falling from a high elevation (diagram A) to a low elevation (diagram B) before it encounters the force of a spike which ultimately brings it to rest (diagram C). Assume that there is no air resistance and that the spike moves only slightly. Fill in the blanks in the cartoon strip.

4. A worker pushes a 50.0-kg cylinder up a frictionless incline at constant speed to a height of 3-meters. A diagram of the situation and a free-body diagram is 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 cylinder, which one(s) do work upon it?

Depress mouse to view answer.Both gravity and applied forces do work.The normal force does not do work sincethe angle between Fnorm and the displacementis 90 degrees. (If necessary, review thelesson on work.)

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

Depress mouse to view answer.No! The applied force is an external force,and since it does work, the total mechanicalenergy is not conserved.

Calculate the amount of work which the man does upon the cylinder.

Depress mouse to view answer.Wext=1500 J.Start with TMEi + Wext = TMEfKEi + PEi + Wext = KEf + PEfKEi + 0 J + Wext = KEf + 50*10*3(KEi = KEf since speed is constant; thus,both KE terms can be eliminated from the eq'n)Wext = 50*10*3 = 1500 J

Use the following diagram to answer questions #5 - #7. Neglect the effect of friction and air resistance.

a. A.

b. B.

c. C.

d. D.

e. E.

Depress mouse to view answer.The answer is B. Gravitaional potential energydepends upon height (PE=m*g*h). The PE is a minimumwhen the height is a minimum. Position B is thelowest position in the diagram.

a. A only.

b. A, D, and E.

c. B only.

d. D and E.

8. Many drivers education books provide tables which 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.

9. 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?

10. Two arrows are fired into a bale of hay. If one has twice the speed of the other, how much farther does the faster arrow penetrate? (Assume that the force of the haystack on the arrows are constant).

11. 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.

 

12. 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.

13. Determine Li Ping Phar's (m=50 kg) speed at locations B, C, D and E.

 

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