Purpose
The purpose of this lab is to accurately find the acceleration of a mass falling on the Atwood's device. The falling mass is slightly heavier than the mass on the other side in order for acceleration to happen.
Theory
The Atwood's device was created in 1784 as a laboratory experiment by a English mathematician to verify the laws of mechanical motion with constant acceleration.
We have to find derive an equation for acceleration and then use the values we get from the experiment to calculate acceleration. We have to place objects of different masses on each side of the device and the side that is heavier will accelerate towards the ground.
In this lab we start with the equation, F1=ma
We can change the force into tension - weight, so we end up with, T1-w=m1a1
Weight can be changed to mass x gravity, the equation becomes, T1-m1g=m1a1
We can then sum the forces on the other side of the device, starting with, F2=ma
Force can be changed into tension - mass x gravity to leave you with, FT-m2g=m2a2
These two equation are then set equal to each other for to get, (m1-m2)g=(m1+m2)a
This can be then solved for acceleration for a final equation of, a=((m1-m2)/(m1+m2))g
We have to find derive an equation for acceleration and then use the values we get from the experiment to calculate acceleration. We have to place objects of different masses on each side of the device and the side that is heavier will accelerate towards the ground.
In this lab we start with the equation, F1=ma
We can change the force into tension - weight, so we end up with, T1-w=m1a1
Weight can be changed to mass x gravity, the equation becomes, T1-m1g=m1a1
We can then sum the forces on the other side of the device, starting with, F2=ma
Force can be changed into tension - mass x gravity to leave you with, FT-m2g=m2a2
These two equation are then set equal to each other for to get, (m1-m2)g=(m1+m2)a
This can be then solved for acceleration for a final equation of, a=((m1-m2)/(m1+m2))g
This is the free body diagram of the atwood's device
Experimental Technique
This picture shows where the photogate is recording the actual acceleration of the mass falling by measuring how many times the spokes of the wheel pass through the sensor.
This is a picture of the heavier mass falling toward the ground at a constant acceleration.
Data and Analysis
Acceleration of the first masses
a=((m1-m2)/(m1+m2))g
a = ((110g-112g)/(110g+112g))9.8m/s^2
a= -0.088m/s^2
What data studio measured:
a = -0.10m/s^2
Acceleration of the second masses
a=((m1-m2)/(m1+m2))g
a = ((107g-109g)/(107g+109g))9.8m/s^2
a= -0.091m/s^2
What data studio measured:
a = -0.12m/s^2
Acceleration of third masses
a=((m1-m2)/(m1+m2))g
a=((105g-107g)/(105g+107g))9.8m/s^2
a= -0.092m/s^2
What data studio measured:
a = -.10m/s^2
Percent difference between measured and actual:
|measurement 1 - measurement 2| / |measurement 1 + measurement 2| / 2 x 100
First masses
|-0.088m/s^2--0.1m/s^2| / |-0.088m/s^2+-0.10m/s^2| /2 x 100
Percent difference = 12.8%
Second masses
|-0.091m/s^2--0.12m/s^2| / |-0.091m/s^2+-0.12m/s^2| /2 x 100
Percent difference = 27.5%
Third masses
|-0.092m/s^2--0.1m/s^2| / |-0.092m/s^2+-0.10m/s^2| /2 x 100
Percent difference = 8.3%
a=((m1-m2)/(m1+m2))g
a = ((110g-112g)/(110g+112g))9.8m/s^2
a= -0.088m/s^2
What data studio measured:
a = -0.10m/s^2
Acceleration of the second masses
a=((m1-m2)/(m1+m2))g
a = ((107g-109g)/(107g+109g))9.8m/s^2
a= -0.091m/s^2
What data studio measured:
a = -0.12m/s^2
Acceleration of third masses
a=((m1-m2)/(m1+m2))g
a=((105g-107g)/(105g+107g))9.8m/s^2
a= -0.092m/s^2
What data studio measured:
a = -.10m/s^2
Percent difference between measured and actual:
|measurement 1 - measurement 2| / |measurement 1 + measurement 2| / 2 x 100
First masses
|-0.088m/s^2--0.1m/s^2| / |-0.088m/s^2+-0.10m/s^2| /2 x 100
Percent difference = 12.8%
Second masses
|-0.091m/s^2--0.12m/s^2| / |-0.091m/s^2+-0.12m/s^2| /2 x 100
Percent difference = 27.5%
Third masses
|-0.092m/s^2--0.1m/s^2| / |-0.092m/s^2+-0.10m/s^2| /2 x 100
Percent difference = 8.3%
Conclusion
The goal of this lab was to find the acceleration of three sets of masses on the Atwood's device. The equation was derived to calculate acceleration and then we could compare that to the actual acceleration recorded by data studio. Our first set of masses were 12.8% off from the actual acceleration. The second set of masses was 27.5% off from actual, which was the data that was the most inaccurate. The final set of masses had a percent difference of 8.3%, which was the most accurate data set. Overall, the Atwood's device is excellent from proving the laws of mechanical motion that acceleration will be constant when one mass is slightly heavier than the other. Our predictions for calculating the acceleration were fairly close to the measured accelerations. The first set of masses had an acceleration of -0.10 m/s^2 according to data studio while we calculated the acceleration to be -0.088m/s^2 with our derived equation. The second set of masses had a measured acceleration of -0.12m/s^2 while the calculated acceleration was -0.092m/s^2. The last set of masses had a measured acceleration of -0.10m/s^2 and a calculated acceleration of -0.091m/s^2. The contributor to the percent difference was possibly from not releasing the masses perfectly so there is no interference with the acceleration.
References
Atwood machine. (n.d.). Retrieved November 12, 2015, from https://en.m.wikipedia.org/wiki/Atwood_machine
Boyle, J., & Giancoli, D. (1998). Study guide: Physics, principles with applications, fifth edition. Englewood Cliffs, N.J.: Prentice Hall.
Our History. (n.d.). Retrieved November 13, 2015, from http://axusutajyx.comeze.com/slope-of-atwood-machine.php
Boyle, J., & Giancoli, D. (1998). Study guide: Physics, principles with applications, fifth edition. Englewood Cliffs, N.J.: Prentice Hall.
Our History. (n.d.). Retrieved November 13, 2015, from http://axusutajyx.comeze.com/slope-of-atwood-machine.php