Physics Report 2

8/12/2019 Physics Report 2

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Wassen Mohammad

201205555

Physics 192- Lab Report 2:

Finding Acceleration of an Object in Free-fall

Introduction:

An object falling downwards experiences free-fall acceleration which is the acceleration due to gravity.This acceleration has a value of 9.81 m/s. In this experiment, we are to measure the time it takes a

small ball to fall from one point to another. The values obtained will be plotted on a graph as velocity vs.

time, and the following equation will be used.

( )Where

, is the slope of the best-fitted line.Objectives:

Measure the free fall acceleration (acceleration due to gravity) of a ball falling downwards Verify that the acceleration due to gravity is 9.81 m/s

The variables of this experiment:

The graph of the velocity vs. time will have the independent variable time (measured in seconds, andthe dependent variable velocity ( with the units (cm/s).Equipment:

Two photo-light sensors Digital timer A small ball A Computer

Procedure:

Using the sensors and the digital timer, measure the time it takes a small ball to get from thefirst sensor to the next

Increase the distance by 10cm each time youre done with a trial Repeat each trial three times and find the average Using the average time, find the velocity Find the uncertainty in distance, time and velocity Plot velocity vs. time using both Excel and manually Draw a best fit line and find the slope (acceleration)


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Wassen Mohammad

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Data obtained:

Table 1

Note: within this table we tried to be consistent with our significant figures and therefore chose 3

significant figures for all our results.

Uncertainties:

Table 2

Note: Uncertainty analysis can be found on page 6.

Standard

Deviation

Uncert. in

time

Uncert.

in X

Fractional Uncert.

in x

Fractional Uncert. in

time uncert. V

Uncert.

In V

0.00058 0.0003333 0.1 0.005000 0.00334 0.00004 1.207

0.00058 0.0003333 0.1 0.003333 0.00242 0.00002 0.898

0.00115 0.0006667 0.1 0.002500 0.00396 0.00002 1.113

0.00173 0.0010000 0.1 0.002000 0.00500 0.00003 1.346

0.00100 0.0005774 0.1 0.001667 0.00253 0.00001 0.798

0.00173 0.0010000 0.1 0.001429 0.00397 0.00002 1.172

Time (s)Distance x (cm) (s) (s) (s) Average Time ( (

20 0.100 0.099 0.100 0.100 201

30 0.138 0.138 0.137 0.138 218

40 0.167 0.169 0.169 0.168 238

50 0.201 0.201 0.198 0.200 250

60 0.229 0.227 0.228 0.228 263

70 0.253 0.253 0.250 0.252 278


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Wassen Mohammad

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Data obtained from the Linest function:

Slope 500.911 Intercept 150.554

Uncertainty in slopes 14.797 Uncertainty in intercept 2.78607

R 0.99652 Uncertainty in y 1.88709

Data Analysis:

Recalling that the equation of this line is:

( )To find the slope, we use the formula

, but since we are using excel, from the graph we can easilyfind the slope. In this case it is equal to 500.93. Since the slope is

, it means we need to multiply thisvalue by 2 to get. If we do that we find out that the value of the slope (acceleration) is 1002 cm/s, or10.02 m/s.

Final Result:

Acceleration due to gravity based on our experiment, is equal to 10.0 m/s 0.295m/s.(Please refer to the Uncertainty Analysis page 6).

Accuracy in the final result:

It appears that we were able to obtain a very close value to the true value, however it is not

accurate since the true value is 9.81m/s. To calculate the percentage error we use the following

equation: If we do that, we find that the percentage error is: 2.0% (calculated to 2 significant figures.)


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Wassen Mohammad

201205555

Sources of error in the experiment:

We might have some random errors because the student who was dropping the ball was trying to drop

the ball from the same point and at the same time they were trying to get the ball to pass through the

sensors in a proper way. Getting that done had proved to be a little difficult since the ball sometimes

passed without being sensed at all. Moreover, some errors may have occurred when we were trying to

measure the distances between both of the sensors.

Uncertainty Analysis:

Please refer to Table 2 (page 2) for the uncertainty values. To start off, we found the standard deviation

of the time. We did this using this equation:

( ((( = 0.00057735 or 0.0058 to 2 significant figures.After this, in order for us to find the uncertainty of the time, we found the standard deviation of the

mean using the following equation:

= = 0.000334863. or 0.0033(s) to 2 significant figuresThus with this result we are able to find the fractional uncertainty of the time, we use this equation;

by dividing the standard deviation of the mean by the actual value of time we get the value: 0.0033 to 2

significant figures.

As for the uncertainty in x, it is simply the smallest division of the devicewe used, which was a ruler.That is, 0.1cm. And the fraction uncertainty of that would be: = 0.0050 to 2 significantfigures.

Finally to find the uncertainty in velocity, we used this equation:


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Wassen Mohammad

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( ( all that multiplied by thevalue of velocity. Thus if we do that, we arrive at the conclusion that the uncertainty in velocity is equal

to: 1.207 m/s.

Continuing on, we still needed the uncertainty in the acceleration. And in order for me to find that, I

used the graph that I had drawn manually. After I plotted the values I drew the line of best fit. I

calculated the slope of this line using this equation:. Next I drew the worst lines of fit, as in, the

minimum slope and the maximum slope. Eventually I had three valued for the slope.

From the graph done manually, the slopes that I calculated were:

Minimum: 488.5 Best fit line: 504.9 Maximum: 518.0

To calculate the uncertainty in my slopes, I used the following equation:

( ( Once I did that I got the result as: 14.75. After that I multiplied this by 2, since the slope is

Therefore, the uncertainty in the slopes is 29.5 cm/s, or 0.295 m/s.

Physics Report 2

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