Physics Lab Homework Statement: Calculating G Using Equations | AP Central

[ThisIsActual]

Homework Statement

http://apcentral.collegeboard.com/apc/public/repository/ap05_phys_laboneerror_47485.pdf

The above link is an updated version of the lab that I'm currently typing up. I have already gathered all data necessary:

Time taken to travel 50 meters:
@ 1.089 degree downward slope:
2.513 seconds
@ 2.178 degree downward slope:
1.600 seconds
@ 3.269 degree downward slope:
1.169 seconds

Time taken to travel 100 meters:
@ 1.089 degree downward slope:
2.870 seconds
@ 2.178 degree downward slope:
2.173 seconds
@ 3.269 degree downward slope:
1.633 seconds

Homework Equations

I am given the following equations:

(1-1)x=x0 + vt + at^2
(1-2)v=v0 + at
(1-3)a=g sin(theta)
(1-4)X=1/2(g sin theta)t^2
(1-5)v= (g sin theta)
(1-6)S=1/2 (g sin theta)t^2 [This is in a graph of S vs. t^2)

The Attempt at a Solution

My question is:
How do I use all these equations to work out a value of G? It states in my lab handout that "... a plot of t^2 versus S should yield a straight line with a slope equal to the reciprocal of 1/2g sin(theta). This may be used to calculate a local value of g."

 

[jbsteele]

I am not sure how I would go about doing this. Any guidance or help would be greatly appreciated. Thank you!

 

[tomcue]

To calculate a value for G, you can use the equation (1-6) S=1/2 (g sin theta)t^2. Rearrange this equation to solve for g, which will give you a value for the local acceleration due to gravity. Then, use this value in the equation (1-5) v= (g sin theta) to solve for G.

Alternatively, you can plot a graph of t^2 versus S and use the slope of the line to calculate g. Then, use this value of g in equation (1-5) to solve for G. It is important to note that the value of g will vary depending on the slope of the surface, so you will need to repeat this experiment for different slopes to get an accurate value for G. Additionally, make sure to include any sources of error in your calculations and analysis. Good luck with your lab!