The purpose of this investigation is to determine the acceleration due to gravity for an object near the surface of the Earth. In physics this value is known as ÒgÓ and it has many important uses.
Set up a spark timer on its side clamped to a ring stand so that it extends over the edge of a lab table. Set the timer to 60 Hz operation, which means that it sparks 60 times every second (60 pairs of dots are made on the strip every second). Place a landing pad directly below the timer. Prepare a paper strip about 0.5 m long. Feed the paper through the timer in the direction indicated, making sure that the metallic treated side of the timer paper is facing the top of the timer. Attach the paper to a suitable mass. Make sure that the paper strip is not kinked and hold the strip at a point well above the timer so that it hangs straight down through the guide. First turn on the timer and then release the mass and strip. As soon as the mass hits the landing pad, turn off the timer.
There should be a ÒblurÓ of dots near the beginning of the strip (created as you held the object). Find a set of ten distinct pairs of dots near the beginning (but after the blur) that clearly illustrates the objectÕs accelerating motion in freefall and label A through J. Measure the distance of each labeled pair from pair A and enter in the table column for position, r. Measure to the nearest 0.0001 m (0.01 cm). Complete the data table as shown in the example below. Position is the only measured value – all other values can be calculated. Note how the table cascades; it takes three measured position values to obtain one calculated value for acceleration.
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Point |
t (s) |
r (m) |
d (m) |
v (m/s) |
Δv (m/s) |
a (m/s2) |
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A |
0.0000 |
0.0000 |
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0.0083 |
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0.0123 |
0.738 |
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B |
0.0167 |
0.0123 |
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0.132 |
7.92 |
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0.0250 |
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0.0145 |
0.870 |
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C |
0.0333 |
0.0268 |
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0.168 |
10.1 |
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0.0417 |
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0.0173 |
1.038 |
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D |
0.0500 |
0.0441 |
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etc. |
etc. |
Time, t, is the total elapsed time from the initial point A. Calculate using 1/60ths of a second.
Position, r, is distance from point A.
Displacement, d, is the change in position values shown in the previous column.
Velocity, v, is displacement divided by the corresponding interval of time (which is 1/60 s).
Change in velocity, Δv, is difference in velocity values shown in the previous column.
Acceleration, a, is change in velocity divided by the corresponding interval of time (1/60 s).
Deviation, dev, is absolute deviation of each acceleration value.
Note: t, r, v, dev should be all be positive; Δv and a may be positive or negative.
Interpretations
1. Make a position versus time graph. Before drawing a best fit curve, use your calculator to determine an equation. Choose a quadratic regression of the form y = ax2 + bx +c. Then use this equation to plot a few points and draw your best fit curve. Write the equation on the graph and label as Òregression equationÓ. Include the correlation coefficient, r, if this is available. Be sure to include appropriate variables and units for your written equation.
2. Make a velocity versus time graph. Determine the best fit and find the equation. For this graph you have the option of using your calculator or doing it Òthe old fashioned wayÓ. If you use your calculator to find equation you must choose an appropriate form and then actually plot that equation for your best fit curve or line. Doing it the old fashioned way means eyeballing the line or curve and then determining the equation as you learned in class.
3. Make an acceleration versus time graph but do not draw a best fit or find an equation. Usually this graph is quite sporadic with no clear pattern. Instead of finding a relation based on the data, draw a dashed line which shows what the results should look like theoretically. Label this dashed line as Òtheoretical valueÓ. This is a useful technique for this graph since it is known what the result should be based on the theory in question (and also because the pattern shown by the data is usually quite ÒnoisyÓ or scattered).
1. Examine your equation for the position versus time graph and compare it to the displacement equation for constant acceleration. These two equations should be essentially the same. Use this fact to determine the value of the acceleration. Hint: equate the coefficients in the regression equation with the corresponding values in the displacement equation.
2. According to the results of your velocity versus time graph what is the acceleration rate indicated by your data? Hint: consider the coefficients in the equation you found.
3. Calculate the relative (i.e. percent) error for the mean value of acceleration from the table.
4. Calculate the relative error for the acceleration found from the position graph.
5. Calculate the relative error for the acceleration found from the velocity graph.
6. Of the three graphs you made, which one most clearly shows that your test object had a constant rate of acceleration (which is what the theory of freefall predicts)? Explain specifically how this is evident.
7. Write a concise paragraph or two, free from errors in grammar and spelling, in which you discuss error in this experiment. Any complete discussion of error will address the errors that are apparent in your results and it will address the most probable causes of those apparent errors. In other words, you should describe how your results are less than perfect and attempt to reasonably explain why the results are less than perfect. Remember to consider both random and systematic error.
Your report (50 pts.) shall consist of the following material – neatly labeled and in this order:
q Completed data/calculations table (9)
q Position versus time graph with regression equation and best fit (9)
q Velocity versus time graph with equation and best fit (9)
q Acceleration versus time graph with theoretical curve or line (9)
q Answers to questions 1 – 7 (14)
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Mass of object dropped: |
Timer frequency setting: |
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Point |
t (s) |
r (m) |
d (m) |
v (m/s) |
Δv (m/s) |
a (m/s2) |
dev(m/s2) |
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B |
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C |
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D |
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E |
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F |
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G |
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H |
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I |
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J |
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Mean Value for Acceleration: |
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Average Absolute Deviation for Acceleration: |
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Note: for all vector quantities in the table, a positive value indicates a downward direction.