1-March-2017 : Lab 2: Free Fall Lab – determination of g and some statistics for analyzing data

Lab 2: Free Fall Lab – determination of g and some statistics for analyzing data

Author: Tiancih Jiao

Lab Partners: Weisheng Zhang, Kitarou

Date: March 1, 2017

Purpose: To examine the validity of the statement: In the absence of all other external forces except gravity, a falling body will accelerate at 9.8 m/s^2

Theory/Introduction:

This lab is to demonstrate the motion of a freely falling body. When the free-fall body, held at the top by an electromagnet, is released, its fall is precisely recorded by a spark generator. We will pull a piece of paper tape to record the points. Then we use the data to make a distance-time graph and a velocity-time graph. We can use them to calculate acceleration.

The spark box is 60 Hz which is 60 points in one sec.

Summary of apparatus/experimental procedure:  

We use laptop's Excel to calculate ∆x, Mid-interval time and speed. Based on these data, graphs are plotted.

Deviations using mathematical equations:

∆x1 = x1 – x0 (for example, follow the pattern for the remaining ∆x)

Mid-interval time = corresponding time + 1/120 (s)

Mid-interval speed = ∆x / (1/60)

Measured data:

Calculated Data and graph:

Average deviation of the mean =

Standard deviation of the mean =

Analysis:

From the graph, we can see that it's not constantly increasing, which is caused by some random errors. It is because when we read the rule of these points, we might read some point bigger or smaller, so it is random error. Since there are more points of the slope, the derived acceleration of gravity may be larger than the exact value in that situation.

Questions:

Part 1: 

1. Show that, for constant acceleration, the velocity in the middle of a time interval is the same as the average velocity for that time interval.

The velocity in the middle of a time interval: V0 + a(T2 – T1)/2

The average velocity for that time interval: [V0 + (V0+ a(T2 – T1))] / 2

They are the same.

2. Describe how you can get the acceleration due to gravity from your velocity/time graph. Compare your result with the accepted value.

From the graph, we can get a from the equation: V= V0 + at.

Then we can calculate that a = 9.853 which is very close to g = 9.8.

3. Describe how you can get the acceleration due to gravity from your position/time graph. Compare your result with the accepted value.

From the position graph, we can get g from the equation: y = y0 + 1/2 * g * t^2,

Then we can get g = 9.327 which is less than 9.8.

Part 2:

1. What pattern (if any) is there the values of our values of g?

The first is closer than the second one because there is random error with second one. 

2. How does our average value compare with the accepted value of g?

We can get average g is 9.6256. We will probably do this experimental steps more times to get the result closer to 9.8.

3. What pattern (if any) is there in the class’ values of g?

It is close to 9.6, because air resistance and some other factors will decrease the accelerate.

4. What might account with any difference between the average value of your measurements and those of the class? Which of these are systematic errors? Which are random errors?

Reading on the rule will cause the random errors, air resistance can be the systematic errors.

5. Write a paragraph summarizing the point of this part of the lab. What were the key ideas? What were you supposed to get out of it?

In the lab, we will never get the most accurate data because there are too many invisible errors that we cannot avoid. What we should do is to use better method and repeat the experiment then get average result to find the final accurate data.

Conclusions:

For the first part, we use free-fall body, spark box and tape to record the points on the tape and make two graphs to find the g.

For the second part, we learn how to minimize the error and factors in experiment, and compare our result with errors to the accurate value of g.