Note: h, and theta are shown in the table below. S = 1200mm, R = 81mm, r = 20mm, w1 = w3 = 10mm, w2 = 31mm Aluminium roller with brass center used, roller weighs 1.75kg| Trial Number 1 2 3 Height, h (m) 0.007 0.02 0.16 Angle of Elevation, e () 0.033 0.95 7.66 1st Run (s) 2nd Run (s) 3rd Run (s) 14.37 10.35 9.05 15.36 10.13 8.90 15.13 10.35 8.97 Average Time (s) 14.95 10.28 8.973 6. Calculate the mass and mass moment of inertia of the roller using basic principles (theoretically). The specific gravities of brass and aluminium are 8.47 and 2.7, respectively. 7. Calculate the linear and angular velocities and accelerations of the roller using the results from the first experiment. Assume that no slip occurs. 8. By applying the conservation of energy to the results from the first experiment and the velocities calculated in Step 7, calculate the mass moment of inertia of the roller.
Note: h, and theta are shown in the table below. S = 1200mm, R = 81mm, r = 20mm, w1 = w3 = 10mm, w2 = 31mm Aluminium roller with brass center used, roller weighs 1.75kg| Trial Number 1 2 3 Height, h (m) 0.007 0.02 0.16 Angle of Elevation, e () 0.033 0.95 7.66 1st Run (s) 2nd Run (s) 3rd Run (s) 14.37 10.35 9.05 15.36 10.13 8.90 15.13 10.35 8.97 Average Time (s) 14.95 10.28 8.973 6. Calculate the mass and mass moment of inertia of the roller using basic principles (theoretically). The specific gravities of brass and aluminium are 8.47 and 2.7, respectively. 7. Calculate the linear and angular velocities and accelerations of the roller using the results from the first experiment. Assume that no slip occurs. 8. By applying the conservation of energy to the results from the first experiment and the velocities calculated in Step 7, calculate the mass moment of inertia of the roller.
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Please answer as many parts as possible, I dont mind if you cannot answer all parts.
Transcribed Image Text:Trial
Number
1
2
h
3
Height, h
(m)
Note: h, and theta are shown in the table below.
S = 1200mm, R = 81mm, r = 20mm, w1 = w3 = 10mm, w2 = 31mm
Aluminium roller with brass center used, roller weighs 1.75kg|
0.007
0.02
Rail
0.16
0
sin =
Angle of
Elevation, 8
(°)
0.033
0.95
7.66
h
S
14.37
R
1st Run (s) 2nd Run (s) 3rd Run (s)
10.35
Roller
9.05
15.36
10.13
8.90
15.13
10.35
8.97
Average
Time (s)
14.95
10.28
8.973
6. Calculate the mass and mass moment of inertia of the roller using basic principles (theoretically).
The specific gravities of brass and aluminium are 8.47 and 2.7, respectively.
7.
Calculate the linear and angular velocities and accelerations of the roller using the results from the
first experiment. Assume that no slip occurs.
8.
By applying the conservation of energy to the results from the first experiment and the velocities
calculated in Step 7, calculate the mass moment of inertia of the roller.
9. Derive the linear and angular equations of motion from the free body diagram, as shown in Figure
2.
mgcose
y
N
mg
va
mgsine
Figure 2: Free body diagram.
10. By applying the equations of motion that you have derived in Step 9 to the results from the first
experiment and the accelerations calculated in Step 7, calculate the mass moment of inertia of the
roller.
11. Compare the theoretical value obtained from Step 6 and the two experimental values obtained
from Steps 8 and 10. Tabulate these three values;
Data from
Theoretical value
Experimental value from Step 8
Experimental value from Step 10
Data from
Theoretical value
Experimental value from Step 8
Experimental value from Step 10
Predicted linear acceleration, a =
Moment of inertia, I
12. Using the three values that you have tabulated in Step 11, predict the linear acceleration of the
roller for the second rail height.
Moment of inertia, I
Acceleration, a
a₁ =
a2=
a3 =
13. Using the results from the second rail height, calculate the linear acceleration of the roller.
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