Lab 2--Free Fall to test g
PURPOSE: Today we are going to examine that in the absence of all other external forces except gravity, a falling body will accelerate at 9.8 m/s^2.
To begin with this lab, we need set up all equipment.
A heavy tripod base with leveling screws, a free- fall body, a weighted clip to anchor the spark paper, an electromagnet with power supply.
Here is picture when you set up all equipment.
To use the apparatus:
1. Turn the dial hooked up to the electromagnet up a bit.
2. Hang the wooden cylinder with the metal ring around it on electromagnet.
3. Turn on the power on the sparker thing.
4. Hold down the spark button on the sparker box.
5. Turn the electromagnet off so that the thing fall.
6. Turn off power to the sparker thing.
This free fall equipment will give a accurate 1.5 m falling distance, and the spark generator will record the fall clearly. The marks made at intervals on the spark-sensitive tape so that we can give a distance- time graph and a velocity graph.
The Marks will be made at every 1/60 of a second.
Set first mark as 0 and measure the distance from the first mark to next mark, and the time between each marks are 1/60 s.
Open a Excel so you can put all date in.
A3 = A2 +1/60
Distance: is every marks distance from 0.
△x: the distance between two points such 1 to 2, 2 to 3.C2 = (B3-B2)
Mid-interval time: is the mid time in 1/60, so it's 1/120
D2 = A2 + 1/120
Mid interval speed: we know the distance in between two points and the time which is 1/60, we can get the speed in middle.
E2 = C2 /(1/60)
When you input all the data.
Now we need to make this data more readable is to make a velocity- time graph and a position - time graph, so we can get g.
Here are the velocity vs time graph and position vs time.
As we know, when acceleration is constant, the graph of velocity vs time graph should a straight line, and the slope of that line is acceleration.
If t2 - t1 = t3 - t2
the velocity in the middle of a time interval is the same as the average velocity for that time interval.
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Using a differential equation, we know different v with respect t, we will get acceleration.
According to the velocity vs time graph we can get that acceleration a = 9.6 m/s^2.
According to the position graph, we got a = 8.1062 m/s^2
(This acceleration is not a very good result, and the reason may cause that is error we made during experiment, and that error we called systematic error.)
systematic error: errors that are caused by people or tools which can be reduced by mutiple test.
Assumption:
For every lab experiment, we all assume that our condition is perfect, but real world is not.
Let's assume that:
1. there is no any friction(such as air friction).
2. Sparks are exactly 1/60 second apart.
The patterns of my data is that all of my accelerations are smaller that gravity g = 9.81 m/s^2, and that's what I expected because there should have air friction in my experiment.
Differences between expected and experimental values:
In this lab, we expected that our data is different than the real gravity g, so we have to find how much different they are.
One way to do this is find the relative difference.
First one is -2.04%
second one is - 0.959%
Therefore, those result are very close to the real one.
Errors and Uncertainty
We need to figure out the uncertainty of our result, so we use standard deviation of the mean to do all the job.(standard deviation is to find out how big fluctuations your results are and how much your results are away from the original result. Standard deviation we get is small, that's mean our results are good; otherwise, results are bad.)
The reason why we use standard deviation is to find out our group results error and uncertainty.
Here is the graph of my teammates data and my data.
Average g = 9.56m/s^2.
and which is smaller too.
average deviation of the mean is = 20.123
The reasons why our g are different from each other are our measurements, air friction, accuracy of our data.
We can see that most of them are close to 9.81 m/s^2, some of them are not.
9.629, 9.6, 9.92, 9.62, or 9.77 are caused by random error.
9.397, 9.305, and 9.267 are caused by systematic errors.
Conclusion
After we did all the work, we can get our acceleration in a free-fall is not that accurate because all the uncertainty such as errors made by people, friction, accuracy of our data. The idea is that for every experiment, errors are very common things, so we need to do is to face that error and calculate how much difference that we make and know why it's different.
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