WOE - Conservation of Energy

Conservation of Energy

The Law of Conservation of Energy states that energy can not be created or destroyed, it can only change forms. We are primarily concerned with the mechanical energy in a system.

Mechanical energy is the energy due to either the position of the particle, or the motion of the particle. If a system is isolated, then the mechanical energy before an event must equal the mechanical energy after an event.

If the system is not isolated, then the amount of mechanical energy will change depending on the work done to, or by the system. Conservative forces are those where the amount of work is independent of the pathway, like the change in gravitational potential energy.

Non-Conservative forces are those where the amount of work done is dependent on the pathway, like the work done by friction. Please watch the following presentation that will discuss the conservation of energy.

Conservation of Energy Practice

The Law of Conservation of Energy is used to predict the motion and position of objects as energy is changed from one form to another. Please watch the following presentation of some example problems. 

Conservation of Energy Self-Assessment

Now it is your turn. Complete the following Conservation of Energy problems to verify that you understand how to apply conservation of energy and work to a system.

  1. A little 35kg girl slides down a 10.0 m long slide. The slide makes an angle of 35.0o to the horizontal and the coefficient of friction between the girl and the slide is 0.400. The girl's father gives her an initial push by applying a force of 20.0 N parallel to the slide for 50.0 cm. What is the velocity of the girl at the bottom of the slide?

SOLUTIONS Links to an external site.

  1. Tarzan is running at 20 m/s when he grabs a vine that is 30m long and makes an angle of 15o to the vertical.  
    1. What will be his velocity at the lowest point that he reaches? 
    2. Assuming the air friction is negligible, what is the maximum height that he will reach? 

SOLUTIONS Links to an external site.

  1. A 250kg car is at the top of a roller coaster that is 100 m tall and makes an angle of 81o to the horizontal. The coefficient of friction between the car and the track is 0.14.
    1. If the car leaves the top of the track traveling at 12 m/s, how fast is it going at the bottom? 
    2. At the very bottom of the slope the roller coaster enters a loop that has a diameter of 50m.  The average force of friction between the track and the car is 125N while it is in the loop.   What will be the centripetal force on the car at the top of the loop?
    3. What must be the minimum force that the track can apply to the car?

SOLUTIONS Links to an external site.

Conservation of Energy Practice Problems

Download Conservation of Energy Practice Problems Links to an external site. for more practice. 

Download solutions Links to an external site. to the practice problems. 

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