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The Relationship between Acceleration and Rolling Angle

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Introduction

The Relationship between Acceleration and Rolling Angle

Design

The purpose of this experiment was to assess whether or not there is a directly proportional relationship with respect to the acceleration (a) of a ball descending from the height of a ramp, and the ramp’s angle (θ). It can then be inferred that an increase in the angle (θ) of the ramp, would render an increase in the acceleration (a) of the ball. If the acceleration (a) is to increase, then by Newton’s Second Law of Motion (the Law of Inertia), the increase in acceleration (a) must be a direct result of an increase in force, considering the mass doesn’t change.

Newton’s Second Law of Motion states that:

Force = (image00.pngimage00.png; where force = ΣFn = net force, mass is measured in kilograms, and acceleration is measured in ms-1


acceleration=image06.pngimage06.png

...read more.

Middle

18.4

.173

10

0.67 ms-1

0.898 ms-2

26.9

.259

15

0.862 ms-1

1.49ms-2

51

.5

30

1.36ms-1

3.7ms-2

Calculations        

image09.pngimage09.png = image01.pngimage01.png = image02.pngimage02.png = 0.173              

sin-1(17.3)= 10˚

velocity (average) = image03.pngimage03.png= image04.pngimage04.pngms-1

Velocityfinal = (acceleration)(time)

a = image05.pngimage05.png = image07.pngimage07.png = image08.pngimage08.png 0.

...read more.

Conclusion

-2. Another improvement could have been to have an automatic timer to eliminate human error with respect to the time trials. The timing of the ball rolling down the ramp is subjective to some degree, though it is timed with a timer, it is subjective to some degree, as the student doing the timing decides when to stop and start. A longer ramp may have improved the time trials, as the time interval to measure steeper angles would not have been so small.  A smoother ball such as a bowling ball (on a much larger apparatus), or a billiard ball would have been more effective as some of the frictional force would have been reduced. Lastly, the inclusion of measurements of uncertainty would have helped as it would have been easier to assume whether or not the inaccurate results were acceptable.

...read more.

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