Acceleration Due to Gravity

  • #1

Homework Statement


[/B]
Lucy is measuring the acceleration due to gravity in Melbourne by dropping a ball through a vertical distance 1.00 m and timing how long it takes.
The ball starts at rest, and Lucy times its fall four times. The results are: 0.47 s, 0.42 s, 0.48 s and 0.41 s. The uncertainty in her distance measurement is 1 cm and theuncertainty in the timer is 0.01 s. What is the uncertainty in the value of g that Lucy calculates?

Select one:
a. at least 0.01 ms−2 and at most 0.03ms−2.
b. more than 0.03 ms−2but at most ms−2.
c. more than 0.1 ms−2 but at most 0.4 ms−2.
d. more than 0.4 ms−2 but at most 0.6 ms−2.
e. more than 0.6ms−2 but at most 2ms−2.http://asoeonline.edu.au/theme/image.php/essential/core/1427682940/i/grade_correct


Homework Equations


I am not sure about the equations to use, but I think that these ones might help:
GPE = mgh
F = ma

The Attempt at a Solution



Average of time values = 0.45s
Uncertainty = 0.45s +/- 0.04 s

Distance uncertainty = 1m +/- 0.01m


This is as far as I go. How do I calculate the g values from here on?

Thanks in advance :)
 

Answers and Replies

  • #2
CWatters
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The experiment involves finding an acceleration given a distance and a time. The initial velocity is zero. The final velocity is unknown.

Are you familiar with the SUVAT equations or similar? One of the standard equations is more useful than the others.
 
  • #3
s = ut + (0.5*a)*(t^2)
0.99 = 1/2 * a * (0.41)^2
a = 11.78 m/s^2,

Which is way "off" the multiple choice answers
 
  • #4
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It looks to me like they want you to calculate the propagation of error, not necessarily the acceleration itself. There are some examples http://www.rit.edu/cos/uphysics/uncertainties/Uncertaintiespart2.html [Broken].
 
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  • #5
PeroK
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Homework Statement


[/B]
Lucy is measuring the acceleration due to gravity in Melbourne by dropping a ball through a vertical distance 1.00 m and timing how long it takes.
The ball starts at rest, and Lucy times its fall four times. The results are: 0.47 s, 0.42 s, 0.48 s and 0.41 s. The uncertainty in her distance measurement is 1 cm and theuncertainty in the timer is 0.01 s. What is the uncertainty in the value of g that Lucy calculates?

Select one:
a. at least 0.01 ms−2 and at most 0.03ms−2.
b. more than 0.03 ms−2but at most ms−2.
c. more than 0.1 ms−2 but at most 0.4 ms−2.
d. more than 0.4 ms−2 but at most 0.6 ms−2.
e. more than 0.6ms−2 but at most 2ms−2.http://asoeonline.edu.au/theme/image.php/essential/core/1427682940/i/grade_correct


Homework Equations


I am not sure about the equations to use, but I think that these ones might help:
GPE = mgh
F = ma

The Attempt at a Solution



Average of time values = 0.45s
Uncertainty = 0.45s +/- 0.04 s

Distance uncertainty = 1m +/- 0.01m


This is as far as I go. How do I calculate the g values from here on?

Thanks in advance :)

I might be tempted to give this question a miss. The variations in timings are much greater than could be caused by the uncertainties given. I wouldn't like to guess exactly what the question setter intended!

You may be expected to ignore the actual results, but that seems absurd to me.
 

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