# Finding g from 2 graphs

## Homework Statement

I am doing a lab report in which I am supposed to plot 2 graphs from which to approximate g. One is Delta X vs t and one is delta X vs t^2. The data represents the time it takes for an object to travel a certain distance interval (in my case a cart going down an inclined plane, and the time being measured by 2 photo-gates) I have SciDAVIs opened and have the data inside 2 tables, but I have no clue how to graph these two tables so that I get the necessary equations for approximating g. All i have right now is scattered data points.

## Homework Equations

a=.5gsin(theta) -> g=(2a)/sin(theta) (for graph x-t)

m=.5gsin(theta); g=(2m)/sin(theta) (for graph x-t^2)

## The Attempt at a Solution

Im not sure how these equations and graphs will help me get the experimental value of g. Does the computer just spit out some models and I plug them into each other? The lab just says to find the local value of g from both graphs, extremely helpful -_-. Someone please explain me how this is supposed to work. Thank you.

gneill
Mentor
What are the expressions for the theoretical curves that you expect? In other words, given an inclined plane at angle Θ to the horizontal, what is the function expressing x versus t?

What are the expressions for the theoretical curves that you expect? In other words, given an inclined plane at angle Θ to the horizontal, what is the function expressing x versus t?

that would be y= a+ ax + ax^2 and y= bx+c

I figured out the fit for my data points, with the x-t being a polynomial and x-tt being a linear fit. Now what am I supposed to do with them? How do these and my initial equations relate?

gneill
Mentor
A cart with frictionless wheel bearings is released from rest on an inclined plane that makes an angle Θ to the horizontal. Derive an expression for the distance x that the cart travels down slope with respect to time t.

Your expression should contain the constant g, the acceleration due to gravity.

A cart with frictionless wheel bearings is released from rest on an inclined plane that makes an angle Θ to the horizontal. Derive an expression for the distance x that the cart travels down slope with respect to time t.

Your expression should contain the constant g, the acceleration due to gravity.

general form:
x= x-node + v-node (t) + .5(a-x)t^2

in which case a-x is -g

gneill
Mentor
What is "node"? How can I calculate x(t) from "node"?

What is the specific equation for x versus t in this particular case? Have you not studied blocks sliding down frictionless slopes? There is a function x(t) = ??? which gives the distance that the cart has covered in time t.

What is "node"? How can I calculate x(t) from "node"?

What is the specific equation for x versus t in this particular case? Have you not studied blocks sliding down frictionless slopes? There is a function x(t) = ??? which gives the distance that the cart has covered in time t.

well i guess that would be Δx=.5 (g sin(θ)) t^2

gneill
Mentor
Okay! So you would expect your x versus t graph of your data to follow the form

$$x(t) = \frac{1}{2}a t^2$$

where a = g sin(θ). If you can find a from your graph, you can find g, right?

What is the slope of the function at some time t = t1? (hint: take the derivative). So pick suitable points along your plotted data and determine the local slope. Use the slope information at point t1 to find g using what you've derived.

For your second graph, where you're plotting x versus t2, essentially what you are doing is replacing t2 with a new variable τ. That is, τ = t2.

$$x(\tau) = \frac{1}{2}a \tau$$