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Lab 4: Newton’s Second Law Newton’s second law of motion defines the relationship between the forces acting on an object and the

resulting acceleration of the object. For Lab 4, we will measure forces and acceleration and attempt to

validate Newton’s Second Law.

Setting up your Excel sheet

I have started your Excel sheet with an outline of one data table in cells B4 to J18. Complete this table to

make it look like this:

???

???

t1 (s) t2 (s) t3 (s) a (cm/s2)

Average of acceleration values:

Cart on an Airtrack

m =

L = cm

g

Enter the equations to allow Excel to calculate the acceleration for each set of t1 t2 and t3 measurements. Be

sure to use the value of L in your data table. Then use the AVERAGE function to allow Excel to calculate

the average of your acceleration values.

You will need a total of six of these data tables, so you will need to make five “copies”. To accomplish this:

Highlight rows 4 through 19, at the left of the screen; press Ctrl and C to “copy”.

Click row 20 so it is highlighted; then press Ctrl and V to “paste”.

Highlight columns B through K and press Ctrl and C to “copy”.

Click on column L, at the top, so the entire column is highlighted.

Press Ctrl and V to “paste”; there should now be a copy of your data table to the right of the original.

Click on column V, at the top; press Ctrl and V to “paste”.

You should now have six identical data tables, arranged two down and three across. Change the value of m

in these tables to show 20, 30, 40, 50, 60, and 70 grams.

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Setting up your equipment and measuring data

The equipment you will use for this lab is:

airtrack, two photogates, cart, weights, air source, black box, string

Setting up the equipment: Connect the air source to the track, the photogates to the black box and the black box to a laptop (as shown.)

Plug the air source into the wall; plug the black box into the wall.

Evenly distribute approximately 150 grams of weights on the cart.

Turn on the black box, then turn on the laptop. Double click on the DataStudio icon on the desktop.

Choose Create Experiment from the options provided. You should see this screen:

Click the picture of the black box where your first photogate is plugged in. Select Photogate from the menu.

On the Measurements menu, leave only Time in Gate checked.

Repeat for the second photogate, but leave only Time in Gate and Time Between Any Gates clicked.

Click on Digits in the menu at the lower left. Choose Time in Gate #1.

Repeat to create digital displays for Time Between Any Gates and Time in Gate #2.

Adjust the height of the photogates so the tab on the cart blocks the beam when passing through.

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Preliminary measurements: Place the cart, with all its additional weights, and the mass hanger, on the scale together to get M.

Measure L, the horizontal length of the tab on the cart, in centimeters.

Leveling the airtrack: Turn on the airtrack; gently push the cart through the photogates in the direction toward the center of the room.

DO NOT ALLOW THE CART TO HIT THE END OF THE AIRTRACK!

Note the values on the screen of Time in Gate #1 and Time in Gate #2.

If the times are different, adjust the level of the track by screwing the track legs in or out.

Repeat the above steps until the cart shows the same times in both photogates. Retest this to ensure the two

photogate times remain consistent for several passes of the cart.

Collecting data: Once the track is level, I will place a string around the cart.

Place the mass hanger on the other end of the string.

With m = 20 grams (including mass hanger), allow the cart to accelerate through both photogates.

Record t1 t2 and t3 where:

t1 is the time in Gate #1 t2 is the time between the gates t3 is the time in Gate #2

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Enter the three times in the appropriate data table; Excel will calculate the corresponding acceleration.

Repeat four more times for a total of five sets of measurements of these three times.

Verify that your five values of acceleration are close to each other. If they are not, you should continue to

measure until you are reasonably certain that you have five accurate trials.

Excel with calculate the average of the individual acceleration values.

After your first data table, with m = 20.0 grams, is complete:

Move 10 grams from the cart to the hanger, so that m = 30 grams and repeat the process above to measure

the corresponding acceleration.

Repeat the process, moving masses from the cart to the hanger, for m = 40, 50, 60, 70 grams.

You will have six data tables, each with a value of m and the average of the corresponding acceleration.

Create a summary data table that lists just two columns: m and the corresponding acceleration.

DO NOT type the values into this table; just tell Excel where to get them from your other tables.

Graphs: Using the summarized data, create a graph of a vs m and find the best fit line to your data.

Calculations: Measure the total mass of your cart and weights by putting all of it... cart, weights, hanger... on the scale

together.

We expect that the slope of the graph should equal g divided by the total mass (Refer to the derivation on the

board.)

Using this idea:

Calculate the expected value of the slope. Remember to:

o briefly explain what you are calculating,

o show the expression,

o show the numbers of the calculation with units,

o show the final result.

WATCH YOUR UNITS! The units of your expected value should match those of your measured slope.

Calculate the percent difference between the measured and expected values for the slope of your graph.

The slope of your graph serves as a summary of all your data, much like an average of all your measurements

combined. How close did your measured slope match to the expected? I will collect results from around the room

and we will discuss whether we find evidence of random error, systematic error, or both.