Masses
Cart: .2561kg
Mass 1: .2475kg
Mass 2: .2568kg
Total Mass: .7604kg
Mass 1: .2475kg
Mass 2: .2568kg
Total Mass: .7604kg
Potential Energy (Joules)
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
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
Heights
H2: .085m
H1: .066m
deltaH: .019m
H1: .066m
deltaH: .019m
Distance (Meters)
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
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
Data has 50 points collected in time increments of .1 seconds. Therefore, the total time elapsing was 5 seconds.
Potential Energy vs. Distance
#1!
Linear Regression: y = -0.05786x + 0.1340
#2!
F = -dU/dx
F = - slope (slope of a linear function is its derivative)
F = 0.05786N
F = - slope (slope of a linear function is its derivative)
F = 0.05786N
EXTENSIONS
#1!
F = -dU/dx <---- Definition!
F = -d(mgh)/dx <---- Substitution!
F = -d(mgxsin(theta))/dx
F = -mgsin(theta)
F = -d(mgh)/dx <---- Substitution!
F = -d(mgxsin(theta))/dx
F = -mgsin(theta)
#3!
P = W/t
P = .0734/5
P = .01468
P = .0734/5
P = .01468
#2!
W = INT F(x)dx
W = INT f(x)dx
W = INT-du/dx dx
W = 0.05786x(f) - 0.05786x(i)
W = 0.05786(1.27) - 0.05786(0)
W = .0734
W = INT f(x)dx
W = INT-du/dx dx
W = 0.05786x(f) - 0.05786x(i)
W = 0.05786(1.27) - 0.05786(0)
W = .0734
Conclusion
We determined the mathmatical model to be Linear Regression: y = -0.05786x + 0.1340
What was the purpose of the lab? To find work in a real-life, physical environment. It shows how, by gathering simple data points, one can calulate not only where the car will be at any given time, but the work that the car is doing, the power that it produces, and much, much more.
We learned how force, Potential energy, and power are all interconnected. (Force is the negative derivative of PE, work is the intergral of force--yes, that is one step fprward and one step back, because that itself is the work-energy theorem--and power work over time)
What was the purpose of the lab? To find work in a real-life, physical environment. It shows how, by gathering simple data points, one can calulate not only where the car will be at any given time, but the work that the car is doing, the power that it produces, and much, much more.
We learned how force, Potential energy, and power are all interconnected. (Force is the negative derivative of PE, work is the intergral of force--yes, that is one step fprward and one step back, because that itself is the work-energy theorem--and power work over time)
