Elise Livingston                                                                    

Potential Energy Lab

Purpose

- To analyze a body in motion in a conservative force field and develop a mathematical model describing the relationship between potential energy    
   of the body and the distance travelled.
- Apply the mathematical model to calculate the force acting on the bady throughout its journey
- Analyze the work done and power generated by the body.

Equipment

- Pasco track and cart with two 250-gram masses
- Motion detector and CBL system                                                                                                                                                                                                                                           - Triple beam balance
- Metric ruler
- Level
- Ring stand and mounting clamp for the motion detector
Picture


Data

Potential Energy vs. Distance

Picture
x (m)
0.106066
0.110508
0.108009
0.105788
0.106066
0.10551
0.105233
0.10551
0.104955
0.108009
0.121614
0.140218
0.156044
0.173814
0.191862
0.211298
0.233233
0.254057
0.273494
0.295706
0.320418
0.344574
0.372618
0.393164
0.415932
0.442865
0.470909
0.499785
0.529217
0.559759
0.59058
0.622788
0.657495
0.690814
0.724966
0.759674
0.795214
0.831587
0.870182
0.904889
0.944594
0.983189
1.02178
1.06371
1.10369
1.14423
1.18671
1.22781
1.26918
1.31027
PE (J)
0.13315231743
0.133864807107
0.133689424719
0.133864807107
0.133899883235
0.13389403721
0.133900614
0.133899883235
0.133841422986
0.13126989177
0.124067538556
0.12266452881
0.123201649995
0.121740049565
0.120582493885
0.117677011194
0.116569987044
0.118536509943
0.117458560585
0.113029538778
0.111264772484
0.108072734765
0.111521213817
0.116117013839
0.110486494656
0.105251996805
0.103190540786
0.101674321952
0.0998064539005
0.0982096256362
0.0962452898732
0.0914576386004
0.0900368348896
0.0907501606471
0.0889562732411
0.087125586508
0.0848806340575
0.0806284177845
0.0829698316292
0.0814148295113
0.0757877372865
0.077424878162
0.0724441977736
0.0703065708131
0.0724438924786
0.0685703467784
0.0676933077757
0.0694412253128
0.0694412253128
0.0698744732325

Data Analysis

- Using the relationship between potential energy, distance and force, determine the force acting on the cart during its journey down the track:
      The force is -du/dx, which is the slope of the graph: +0.05786 m/s

Extensions

- Using the basic principles of F=-dU/dx and U=mgh, prove that the force experienced by the cart moving down the track is equal to the x-component of the cart's weight vector.
Picture
Picture
- Determine the work done by gravity from x0 to xf
Picture
- Determine the power generated when work is done from x0 to xf
Picture

Conclusion

In this lab we calculated potential energy using a Pasco track and a motion detector. We obtained data and the used it to calculate work and power as well as analyzing the potential energy of the cart on the track. The mathematical model that we found to go with our data was y=-0.05786x+0.1340. In order to obtain values for power and work, we had to utilize our knowledge of physics formulas. This lab helped me better understand a practical use of power and work calculation and I now feel as though I understand the concept far better.