Rohan Joshi

Mr. Kilpatrick

IB1 Physics B3

28 January 2015

Mass v. Acceleration

In the experiment that I conducted, I wanted to find the relation between the mass of an

object and its acceleration. If I were to change the mass in any way, would the acceleration

increase or decrease? In order to find these results, I set up a lab that included the use of 2 carts,

both with an elastic rubber band in between them. I stretched the rubber band to a certain

position, let go, and calculated the results of the values. One cart had a changing mass, the other

stayed constant (had no masses added onto it). I took results through the use of video analysis on

Logger Pro, and through it found the results of acceleration as the mass continually increased.

These results told me the exact relationship between mass and acceleration. My research

question is:

“Would changing the mass of an object change the acceleration of the object?”

I wanted to do this lab as I wanted to find the raw relationship between mass and

acceleration. Normally, this is only hinted on and Newton’s second law is immediately shown.

But the relationship between both of the variables is what I have always been fascinated by.

When this opportunity arose, I had to seize it and attempt to find out what the exact relationship

between both were. After I found the results, it helped me understand acceleration and mass

more. It showed me that although the acceleration can stay constant, if the mass of the block

becomes larger and larger, the multiple forces that are applied on the block are not balanced and

will make the block move at a very slow pace. This experiment helped me compile all of the

things I knew about forces, motion, mass, and acceleration.

Variables:

Independent Variable: The masses of the carts. I changed the masses in order to see what effect

these changes would have on the acceleration of the cart. I measured this using a balance, and

added more and more massive weights.

Dependent Variable: The acceleration of the car. I measured through the use of video analysis on

Logger Pro after taking videos of each trial. The averages are presented in a table below with

appropriate uncertainties.

Constants: The amount of rubber bands used in order to stretch the carts back. Also, the distance

which we stretched them back also remained constant.

Controls: Simply do the procedure without putting any weights on the carts. This will give one

the unchanged, original data to compare the collected data to.

Materials

2 Carts of Equal Mass (w/o any added weights)

Weights of 0.5 kg, 1 kg, 1.5 kg, and 2 kg

1 Rubber Band

A video recording device

Laptop equipped with logger pro

2 Meter sticks

Procedure

1. Put 2 Meter Sticks down on the ground, end to end

2. Put both carts down, and attach the rubber band to the clips at the end. It should loosely

sit on them.

3. Align video capture device above the situation, making sure to capture both meter sticks

in the frame to later use in Logger Pro for scale

4. Have someone pull both carts back to -30cm and 30cm on each respective side.

5. Begin capturing video from device

6. Let go, and allow the carts to collide.

7. Take as many trials with multiple masses for a range of data.

8. Analyze in Logger Pro through Video Analysis, using only points from when the carts

acceleration began till the point just before the crash

9. The line should be linear (if needed linearize using log-log transformation)

10. The slope of the linearized function is the value of acceleration

11. Repeat 8-10 for all videos to complete all data

Uncertainty

The uncertainty for the masses is based on the fact that the weights were not solid

weights, and instead were the weights which contain beads in order to make the weight proper.

The uncertainty must be put on it to account for any of the errors in the weight itself. The

acceleration must have an uncertainty put on it for a number of reasons. The first, most obvious,

reason is the meter sticks. They may not be exactly a meter, and therefore may not provide

accurate results for the velocity on the graphing software. Also, the video recorder may have

been on a slight angle or been moving while capturing the videos for analysis, this could have led

to the values being slightly skewed due to the angle of how the videos were captured. Also, the

starting points for the carts may have been slightly different on each point and may not have

stayed constant, as a human hand was pulling them back to the same point each time. However,

this pullback may have been a centimeter or so off. The camera also comes in here, as if it is on a

tilt, the initial point may have been marked differently and all the other points may be off by a

bit. The crash also may have shook the lab a bit as well. Since the carts collided at the end of the

experiments, the crash may have disturbed the other objects in the area and made the rubber band

a bit weaker.

Data

Acceleration (m/s^2) Mass = cart with

changing mass

No mass = cart with no

mass changes

Mass (kg

± .1)

Trial 1 Trial 2 Trial 3

Mass No

Mass

Mass No

Mass

Mass No

Mass

Avg. for mass Avg. no mass

0.0 2.318 2.318 2.861 2.861 2.749 2.749 2.642±.590 2.642±.590

.5 1.188 4.449 1.340 4.594 1.380 4.593 1.307±.290 4.545±.522

1.0 1.168 4.119 1.411 4.405 1.313 4.369 1.297±.290 4.300±.262

1.5 0.905 4.178 1.051 4.289 1.048 4.288 1.001±.050 4.251±.234

2.0 0.696 4.642 .713 4.532 .683 4.728 .695±.700 4.634±.630

These are all the values for the acceleration of both carts. The seconds cart acceleration is also included.

This is an example graph for the control for Trial One.

This is another example graph for Trial 1 of the .5kg cart. The slope is the average acceleration

of the cart.

Conclusion

Through the data that I have collected, a clearly linear relationship can be seen. As the

mass of the object increased, the velocity of the object decreased by decent amounts. The

relationship would be written as:

M∝ 1a

This is an inverse relationship and is evident through the data. Since Fnet is equivalent to mass

times the acceleration, it is highly probable that a majority of the force turned into force normal.

This reduced the value of Fnet, and lowered the value of acceleration since the mass of the cart

was consistent (relatively) for all of the trials done.

The lab itself had many strengths and weaknesses. The first strength I saw was its

simplicity in the setup. It did not take much to make the lab set up to attain data. Also, the data

given from it is very simple to analyze. The first standout that you need to calculate is velocity,

and from their all of the other data can be derived. In my opinion, the experiment is also very

unique in the fact that it uses elastic energy in order to make 2 carts move. This adds a more

different kind of starting speed, and adds another force which may have been responsible for the

reduction in acceleration. Weaknesses in the lab were how the data was taken. It was very clear

that setting up my phone to take the videos for the lab was in itself a problem, as it was very

difficult to hold steady. This causes mild problems while analyzing the videos, and may have

changed the scale of the meter sticks. Also, while I had previously stated that the rubber band

was helpful, at times it was a little too unpredictable in how far it stretched. Both of these issues

may have been fixable if a tripod of some sort was used to steady the camera, and if a more

reliable rubber band was used. Overall, this lab was extremely helpful in determining how mass

and acceleration were related, and if I were to do it again, I may pick some more reliable data

taking devices.