Lab partners Collin and Kate are performing the same experiment that you did in
ID: 1502299 • Letter: L
Question
Lab partners Collin and Kate are performing the same experiment that you did in lab to verify the conservation of energy. To make a ramp, they use a 2.50 m long track. The lower end of the track is set on the table, while the upper end is clamped h = 1.15 m above the table. They set the motion detector even with the upper end of the track and place bean bags at the bottom as shown in the picture below. They then place small pieces of tape at the initial location and final location of the toy car.
They then take the following measurements:
The distance from the face of the motion detector to the initial location of the car along the track is 0.36 m.
The distance from the face of the motion detector to the final location of the car is 1.06 m.
They place the back of the car at the starting point and release it so that it rolls freely down the ramp, and determine the speed at the final location from the resulting graphs of the motion. Repeating this four additional times, they obtain the following speeds: 2.444 m/s, 2.311 m/s, 2.336 m/s, 2.638 m/s, 2.562 m/s. Satisfied they have all the data they need, Collin and Kate both go home.
Six days later, Collin calls Kate in a panic. "We measured the wrong thing! We were supposed to measure the height of the car above the table at the initial and final points, not the distance from the motion detector along the track. We can't write our lab report, and it's duetomorrow!"
"Relax," said Kate. "I noticed this a few days ago when I was writing my lab report. I looked up the manufacturer's website and found out that the length of the motion detector is 0.18 m. Knowing that, you can use the other stuff we know to figure out the initial and final heights. No problem."
(a) What is the initial height of the car in Kate and Collin's experiment?
(b) What is the final height of the car in Kate and Collin's experiment?
(c) Assuming that energy is conserved, what is the theoretical prediction for the speed of the car at the final point in Kate and Collin's experiment?
(d) What is the percent error between the predicted value of the final speed, and the average of the measured speeds?
Motion Detector Bean BagsExplanation / Answer
sin() = h/2.50
sin() = 1.15/2.50
(a)
length of the motion detector = 0.18 m
The distance from the face of the motion detector to the initial location of the car along the track is 0.36 m.
Let the initial height of the car be , hi.
hi/(2.50 - 0.18 - 0.36) = 1.15/2.50
hi = 0.902 m
(b)
Let the final height of the car be , hf.
The distance from the face of the motion detector to the final location of the car is 1.06 m.
hf/(2.50 - 0.18 - 1.06) = 1.15/2.50
hf = 0.58 m
(c)
Using Energy Conservation,
Initial P.E + Initial K.E = Final P.E + Final K.E
m*g*hi + 1/2*mvi^2 = m*g*hf + 1/2*m*vf^2
9.8*0.902 + 0 = 9.8*0.58 + 1/2*vf^2
vf = 2.51 m/s
(d)
Average of the measured speeds = (2.444 + 2.311 + 2.336 + 2.638 + 2.562)/ 5 = 2.458 m/s
% error = (2.51 - 2.458)/2.51 * 100%
% error = 2.07 %
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