A group of students, performing the same Uniformly Accelerated Motion experiment

Question

A group of students, performing the same Uniformly Accelerated Motion experiment that you did in lab, dropped a picket fence through a photogate and obtained the following data from the computer.

Blocking Times (s) 0.06793 0.11019 0.14344 0.17203 0.19762 0.22069 0.24198 A group of students, performing the same Uniformly Accelerated Motion experiment that you did in lab, dropped a picket fence through a photogate and obtained the following data from the computer. The band spacing is 0.06 m. Use Excel to do the following. Calculate the accelerations. Calculate the average of the accelerations. Create a graph of velocity versus time. Use the trendline option to determine the slope. Report your results below. What is the average acceleration? What is the average acceleration a average as determined from the slope? What is the percent difference between the values of the acceleration you obtained in (b) and (c) above? Suppose you are an astronaut and you have been stationed on a distant planet. You would like to find the acceleration due to the gravitational force on this planet so you devise an experiment. You throw a rock up in the air with an initial velocity of 12 m/s and use a stopwatch to record the time it takes to hit the ground. If it takes 6.8 s for the rock to return to the same location from which it was released, what is the acceleration due to gravity on the planet?

Explanation / Answer

) Under Excel you need to make 5 column headings: Time, Distance, Average Time, Average Velocity, and Average Acceleration. Both Times and Distance should have 8 boxes rows of info, Average time and Average Velocity should have 7, and then Average Acceleration will have 6. Here is how to fill the columns out:

Times: the numbers you have above
Distance: increments of 0.06, so 0 up to 0.42
Average Time: (T1+T2)/2, (T2+T3)/2...
Average Velocity: 0.6/(T2-T1), 0.6/(T3-T2), ...
Average Acceleration: (V2-V1)/(Tavg2-Tavg1), (V3-V2)/(Tavg3-Tavg2), ...

Then take all 6 of your Average Accelerations and add them up then divide by 6 to get the answer.

2) Make another Excel sheet and in Column 1 put the Average Times, and in Column 2 put the Average Velocities. Then highlight both columns and click on insert --> Chart, from the tool bar up top. Then click on scatter plot, select the one with no line between the plots and a graph comes up. Next, click on anyone of the points to select it, and then right click on it, and choose add treadline. Make the line linear and select "show line equation." Use the slope (the # in front of the x).

3) Percent difference is (x1-x2)/(x1).

step by step procedure:

Times: Blocking times
Distance: increments of 0.06, so 0 up to 0.42
Average Time: (T1+T2)/2=T12, (T2+T3)/2=T23...
Average Velocity: (V2-V1)/(T2-T1)=V12, (V3-V2)/(T3-T2)=V23, ...
Average Acceleration: (V23-V12)/(T23-T12)...

Then take all of your Average Accelerations and add them up then divide by 6 to get the answer.

Next open excel
in excel make % columns labeled time(s),Distance,Average Time, Average Velocity, Acceleration
fill in the time (0.0000 to 0.1981)and distance (0 to .42) should have 8 rows of numbers and two columns filled in at this time.
(I started my time 0.000 in column B2 keep that in mind when I give formulas)
Next in Cell D3 type in the formula =((C3-C2)/(B3-B2)) , a number should appear. In the bottom right of that cell there should be a dot click and drag it down until cell D9. You should have numbers appearing.
Then in the the column average time type the formula =(B3-B2)/2 into cell E3. Then drag dot to E9.
Finally for the column acceleration type formula =((D4-D3)/(E4-E3)) into cell F4 then drag dot to F9.

For the graph you highlight data then click scatter plot.. create graph.Right click- select data. click to remove distance, average time, and acceleration. Then make the trendline which is linear and it should be the slope. hope this helps:)

for astronaut problem:

The formula is h = 1/2 a t^2 + vo t + ho
where h = final height, ho = initial height, vo = initial velocity, a = acceleration due to gravity, and t = time. So you'd have (assuming you let go of the rock when it is 2 m above the ground)

2 = 1/2 a (6.8^2) + 12(6.8) + 2
2 =23.12a + 81.6 + 2
0 = 23.13a + 81.6
-81.6 = 23.12a
-81.6/23.12= a = -3.529 m/sec

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