Background info: We did a lab where we had an air track on an incline, creating

Question

Background info: We did a lab where we had an air track on an incline, creating a frictionless ramp. It was set at a 4 degree angle. There were two carts that we placed at the top and let go, and one was about 3 times bigger in mass than the other. It passed through four photogates that measured the velocity as it passed through, and we took the heights of the track where the photogates were.

I'm trying to find out the relation between mass, the incline, and velocity.. From looking at my data, it appears that mass doesn't affect the velocity?

I also had to graph height versus velocity squared for both carts. The graphs look nearly identical- which makes me think that mass does not affect the velocity.

1. Does the mass affect the velocity? But why? I thought F=m/a would apply in this situation, so wouldn't force be related to mass?

2. What is the physical property that the slope represents (height vs. velocity squared)? The slope for both graphs is about ~ -.05. I'm not sure what this could be..

3. And finally, what physical property does the vertical intercept represent? I have no idea what this is asking. I'm guessing the vertical intercept is when y=0, but that is just when the cart has not been let go of yet.

Thank you. I'm stumped on this lab.

Explanation / Answer

mass doesnt effect velocity

you will understand this if you try to find a relation for velocity

Only the gravitational force acts on the carts right now. So, the force acting on the carts if mgcos(x).

x is the angle
So, constant accelartion(a)=gcos(x),

v2=2aS (S is distance)

as we can see v is dependant on a (which is constant) and S the distance.. it doesnt depend on mass..

velocity of both carts will be same..

height vs veloicty squared = S/V^2 = 1/2a

so the physical property is inverse of acceleration..

vertical intercept is when x=0. vertical intercept represents height.

remember distance S is along the incline.

height is vertical height.

sin(x) = h/S

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