06. Apr. 2015: Work-Kinetic Energy Theorem

 What is the Work- Kinetic Energy Theorem?

The work done by the net force on a particle equals the change in the particle's kinetic energy.

W(total) = K(2) - K(1) = change in K

Purpose: We will calculate the work done in a stretched spring through the force vs distance graph. We want to prove that the area under the force v position graph is equal to the work done in the spring graph.

Materials: ramp, cart, motion detector, force probe, spring, balance 

SET UP: 

The force sensor is attached to the spring which is attached to the cart. The calculator was there so that we can make the spring straight and unstretched. We added masses on our cart, however we ended up taking it off for our experiment. It doesn't matter whether you have masses or not. If you do, you just have to take in account that the mass of the cart is different.

On the other side of the track is a motion detector to monitor the position of the cart. 

Procedure: 

1.  set up :) of course.

2. Start recording on logger pro and give your cart a little push. This will generate a force vs distance graph. The slope of that graph will give you the spring constant. 

3. Now we will pull the cart close to the motion detector but not too close or else the motion detector won't read it. Then record and let it go. This will give you another force vs. distance graph.

3. Drink a glass of water because it gets a little confusing right here. 

4. Data should include time/position (from your graph). 

Velocity is from the derivative of "force", "time." 

Acceleration is the second derivative of the force v time. 

KE (kinetic energy) is following the formula 1/2 * m * v^2

Force should have been on there already. 

Our Fadj (Force adjusted) is because of the fact that our graph did not start at 0 so we subtracted it by the difference so that the beginning of our graph would be zero.

It would look like this: 

DATA

5.  After you have this, you should graph the position vs force graph and the position vs. Kinetic energy graph on the same screen.

6. If you take the integral of your position vs force graph the integral under the curve should equal to your KE or close to it. Ours was a little off but we took more and more area it started getting even closer and closer. 

This is the first integral

Second integral

Third Integral

Conclusion

Through this experiment we saw that the work done at any position is the same as the kinetic energy at any position. There were ways to mess up this experiment. One, there could have been friction on the track. Second was the force position graph did not start at zero (which was what we had). Make sure the position is zero and that your force sensor is reading it right. After we got rid of that data the values were a bit closer. So the work and kinetic energy theorem holds true that it is equal. 

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There is another part to this experiment where we watch a video of how they would have done the same experiment but in the olden days. 

The professor has a machine pull back on a rubber band that is attached to an unknown mass. The cart passes through two photogates a 15 cm apart. Since we know the distance and the time of the cart passing through both we can calculate the final speed and kinetic energy of the cart. 

The woman also pulls on the board when the data is printed on a piece of paper. She supposedly pulls on it with a constant rate. She repeats the experiment about 4 times.

It had a bunch of squiggles but the squiggles made shapes that we did know how to find the area of. 

So we broke it down into shapes and found areas and added it up. 

Conclusion: 

This was just an addition to the previous lab, however the thing is this one had much more uncertainty than our labs. Which I thought was the point of this lab. The woman pulled the board at what she wanted to be constant speed but it wasn't. There was also friction in the board when she was pulling the lines were always off. And she took the best shape that the squiggly lines made and took the area of that like we did. The squiggly lines were in about three different places so we assumed the middle of the three was the most accurate.