## Conservation of Mechanical Energy

### Abstract:

How does Conservation of Mechanical Energy work? This is an experiment that shows how to demonstrate the physical phenomenon.

### Full Story:

**Purpose**

Determine how differing the angle of a cart changes the motion of the cart. Further, demonstrate the conversation of mechanical energy– height should be the same at each angle and that average velocity should stay constant with differing angles.

**Hypotheses and Background Knowledge:**

Superficially, a cart was compressed a constant distance x and then rolled up a ramp; multiple ramp angles were tested to show conservation of energy. This conservation of energy will be demonstrated by observing how angle changes average velocity and height of the cart when the KE of the cart is 0.

The hypothesis: if a spring cart transfers it’s energy from potential energy to KE to gravitational PE while it rolls up a ramp, and the angle of the ramp to the horizontal varies, mechanical energy will be conserved. As a result, as the angle increases, the average velocity and height when KE of the car is 0 should be the same; and the time and distance traveled up the ramp should decrease.

**Procedure: Part 1:**

1) Place the ramp on top of three objects such that the length of the hypotenuse of the ramp is constant

2) Find the angle that the ramp creates by measuring the height from the floor to the top of the ramp.

**Part 2:**

3) Close switch and put the cart at the bottom of the ramp

4) When on the ramp, click the switch with a ruler and then measure the exact time between the switch click and the time at which the cart stops moving. Also keep track of max distance that the cart goes up.

5) Repeat steps 3 and 4, 3-4x to decrease variance in data.

**Part 3:**

6) Increase number of objects to six; adjust the hypotenuse such that the ramp is the same length.

7) As in step 2, figure out angle for 6 objects

8) Repeat part 2 for 6 objects

**Part 4:**

9) Increase the amount of books to nine books; adjust the hypotenuse such that the ramp is the same length.

10) As in step 2, figure out the angle for 6 books.

11) Repeat part 2 for 6 books.

**4. Analysis and Conclusions:**

As the angle increased from 11 to 16 to 26 degrees, the average time decreased and the average distance the cart travelled on the cart decreased. Still, as expected, the average velocity and height of the cart when Kinetic energy=0 was fairly constant. The reason that the average velocity should be constant is that as the angle increases, both the time decreases and the distance travelled decreases.

This demonstrates that the ME is conserved. Because all the spring potential energy at the beginning (excluding non-conservative forces) was transferred into gravitational potential energy; since this GPE is not determined by the angle of the ramp, the height should stay constant. A similar argument can be made to demonstrate the constancy of average velocity.

However, in this experiment, friction was not considered; still, since friction was present and constant in each of the trials, the concept of conservation of mechanical energy still becomes clear.

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