# Acceleration Due to Gravity

1. May 19, 2015

### Ruturaj Vaidya

1. The problem statement, all variables and given/known data

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

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

3. 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 :)

2. May 19, 2015

### CWatters

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. May 19, 2015

### Ruturaj Vaidya

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. May 19, 2015

### jackwhirl

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].

Last edited by a moderator: May 7, 2017
5. May 19, 2015

### PeroK

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.