block and pulleys systems lab
TRANSCRIPT
Purpose: The purpose of this lab is to compare the theoretical
acceleration of a PAScar on an inclined track calculated using instantaneous velocities versus the experimental acceleration induced by brass weights in a pulley system.
Background: Average velocity is a measure of displacement in a given
period of time; it is ratio of displacement per time. Instantaneous velocity is the first derivative of position.
Materials:
PASCO PAS Track (2) Duracell D
Batteries (7) Textbooks (2) PASCO Photogates PASCar Piece of tape (to
mount as a flag in the middle of the racecar)
(2) Ring stand Brass weights, 0.2kg
and 0.05kg CPO Science Timer
LLE 250g PASCOBar
Procedure:
Part 1 – Calculate angle of ramp1) Elevate ramp by stacking textbooks and propping the track on batteries.2) Set up photogates at 30 cm AND 60 cm.3) Take the difference of the height of the track at 60cm and 10cm and
take the inverse sin of the calculated height/the length of the track to calculate the angle of elevation.
Part 2 – Measure Instantaneous Velocity & Time Elapsed of PAScar UP the ramp
1) Clamp photogates on the stand mounts.2) Place 250kg PASCOBar on PASCar3) Release the 0.2kg brass weight hanging off of the ramp.4) Record the time elapsed between photogate 1 & 2 AND the time
elapsed in the passing of the flag at each photogate.5) Reset the screen and clear the time.6) Repeat Steps 2-4 for (3) trials.
Part 3 – Compare theoretical acceleration vs measured acceleration
1) Use the equation VF = V0 + at to calculate the measured acceleration of the PAScar. Use speed values at G1 and G2.
2) Use the equation a = (m2gsin(ϴ) + m1g)/(m1 + m2) to calculate the theoretical acceleration.
Part 4 – Measure Instantaneous Velocity & Time Elapsed of PAScar DOWN the ramp
1) Clamp photogates on the stand mounts.2) Release the 0.05kg brass weight hanging off of the ramp.3) Record the time elapsed between photogate 1 & 2 AND the time
elapsed in the passing of the flag at each photogate.4) Reset the screen and clear the time. 5) Repeat Steps 2-4 for (3) trials.
Data:
Mass of PAScar: 0.499kg
Uphill: Trial G1 G2 G1 – G2
1 0.0648s 0.0329s 0.7310s2 0.0627s 0.0330s 0.7336s3 0.0651s 0.0331s 0.7421sAvg. Time 0.0642s 0.0330s 0.7356sVelocity 0.3115
m/s0.6061 m/s
N/A
Downhill: Trial G1 G2 G1 – G2
1 0.0277s 0.015s 0.2830s2 0.0273s 0.015s 0.2812s
20.08°
3 0.0275s 0.015s 0.2818sAvg. Time 0.0275s 0.015s 0.2817sVelocity 0.727 m/s 1.333 m/s N/A
Analysis/Observations:The acceleration of the PASCar downhill was greater
than the acceleration uphill.
Percent ErrorUphill: [(0.4006 – 0.4005)/0.4006] X 100 = 0.02%
Percent ErrorDownhill: [(2.1700 – 2.1400)/2.1700] X 100 = 1.40%
Conclusion:The acceleration of the PASCar uphill and downhill was
calculated using Juxtaposing the average velocity with the instantaneous
velocity reveals that the instantaneous velocity is more accurate because it factors the velocity of several regions of the track.