4/6 Work-Kinetic Energy Theorem Activity

Purpose: To prove the work-kinetic energy theorem.

Procedure:

PART ONE

FIGURE (1)

We started this lab by setting up a cart attached to a force sensor with a horizontal unstretched spring (FIGURE (1)). We had the cart on a track that had a motion sensor on the other end.
Once we had the cart all set up we pulled it slowly towards the motion detector  for about 1 m while LoggerPro was graphing (FIGURE(2)).

FIGURE (2)

We integrated the graph for force in order to find the work done at a certain position.

PART TWO

We used the same set up in the second part as we did in the first part. This time, we measured the mass of the cart (m= .503 kg) and we created a new calculated column in LoggerPro that allowed us to calculate the kinetic energy of the cart at any point. For this part of the experiment we puled the cart to a distance of about 1 m from its initial position and then graphed (FIGURE (3)-(5)) as we let go of the cart and the spring pulled it back to its initial position. 

FIGURE (3)

FIGURE (4)

FIGURE (5)

In FIGURES (3)-(5), we analyzed different points of the graph and we got different integration/work, kinetic energy, force, and position values. 

Conclusion:

The values of work and kinetic energy are pretty similar in values. Friction could account for the difference in the values. Other errors could be related to problems with the motion sensor (we were initially having some issues with our motion sensor.)

PART THREE

Procedure:
For the third part of the lab, we watched a movie in which a professor uses a machine to pull back on a large rubber band. The force being exerted on the rubber band is recorder by an analog force transducer onto a graph, which we recreated (FIGURE (6))

FIGURE (6)

The stretched rubber band is then attached to a cart of known mass. Once the cart is released, it passes through two photo-gates a given distance apart. This will give us the distance and time interval between the front of the cart passing through the first photo-gate and then the second. Once we obtained that data we calculated the final speed and kinetic energy:

v = 3.33 m/s

K.E = 23.9 J

Conclusion:

The kinetic energy we calculated from the area under the graph is off by about 7%. The way the professor took that data in the movie was an old way of finding kinetic energy, so we can expect it to be off a little. We also copied the graph that was shown in the video onto our own paper, which leaves room for more error.