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lab 11- Work and KE

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Purpose:
Measure the work done by a non-constant spring which stretches a cart by a measured distance with force sensor, motion detector and Lab Pro. Graph the data collected during stretching and determine the relationship between work done and the kinetic energy, which are equal to each other in theory. The proportion of the force area is exactly the point of kinetic energy at the same time point.

EXPT1: work done by a constant force

First set up the track, cart, motion detector, force probe and other equipment like the picture shown. Plug force sensor and motion detector and zero them. Adjust the force sensor with a 500-g mass hanging on the string over the pulley. Then remove the mass and add it to the cart. Enter its value as the mass in the data-user parameters menu. Level the track so that the car rolls at a constant speed after a push.


Hang 50 grams from the end of the string and then pull the cart back. Hit collect and release the cart. Then we will get the data below.




From those data we can derive that the integral is 0.07522J and the kinetic energy of cart is 0.077 J, which are quite similar. So we can derive the conclusion that work done by 50g mass is equal to the kinetic energy. The little difference may be caused by unconscious pushing when releasing the cart. Another possible reason is that the track was not leveled properly, which will also cause the cart’s kinetic bigger than the work. It is not due to the friction otherwise the actual kinetic energy would be smaller than the work.
Repeat the steps with highlighting a larger area of the graph and starting at the leftmost end. The value for the integral is 0.2203J and the kinetic energy of the cart is 0.211J. The kinetic energy is bigger than the work, too. So the reasons are the same.

EXPT2: work done by a non-constant spring force
First set the equipment as plotted.
Detect the force over distance with specific file. Stretch the force vs distance about 0.6m. Pay attention to keep hands away from the detector. The graph is attached below.



EXPT3: kinetic energy and the work-kinetic energy principle
The mass of cart is 0.550kg. Collect the force and the kinetic energy with detectors. The stretching is followed.





Position of cart (m)
Work done (J)
Change in KE (J)
Initial:0.581


0.450
-0.2345
0.247
0.343
-0.3891
0.386
0.214
-0.5271
0.500
The work done is close to the change in kinetic energy. That is because the work done by spring change to the kinetic energy.
EXPT$: Work-KE theorem


Conclusion:

In this lab we examine the relationship between work and kinetic energy and the work-KE theory, which is that the work done by the net force on a system equals to the change in kinetic energy of the system. 

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