What is the relationship between angle and gpe with a cart and a ramp. Also if it isn't linear find away to graph it in a linear fashion.

Answer 1

gpe depends on the sine of the angle times height

Graphing linearlily?
GPE=mgh=mg*distance*sinTheta

for a given distance on a ramp, you can plot it this way:
y axis: GPE, and height
x axis: distance.

Now, for the given ramp distance, draw a circle about the origin, of radius r laid out on the x axis, and on the y axis, the same scale for height. You can also label the y axis as GPE, orresponding to heights on the y scale.
Now, you measure any angle theta from the x axis, where it hits the y axis, you have an x,y intercept, and you can read the GPE directly from the intercept for any angle theta