So in physics lab we did an experiment with a cart with two different masses on a air track (practically eliminating kinetic friction). The track was tilted at 4 degrees. Using 4 photo-gates I got the speed of both gliders and the height at each point. I made two graphs making height my x and velocity squared y. Both slopes are negative. Does that seem correct?

Question

Also these questions I need assistance in. Could someone please help me?

1) How does mass affect height and velocity squared relationship?
Since there is no kinetic friction this question confuses me.

2)What physical property does the slope of the height vs. v^2 graph represent? Should slope be positive or negative?
I got a negative slope for both hopefully I have assumed correctly to put height in x and velocity in y. But I don't understand what they mean by physical property?

c) What physical property does the vertical intercept represent?
yet again with the physical property thing..

Any sort of help would be appreciated! Thank you for taking the time to read this.

Answer 1

Im starting to guess that for question one would velocity be independent of mass
I asked someone else about two and they said the slopes should be neg because dv/dt = -g and since gravity is always downward then slope is neg.
As for the property I'm still not sure.

Answer 2

sliding down from height 1 to height 2- conservation of energy gives:

(1/2) m v2^2 - (1/2) m v1^2 = m g( h1-h2)

Mass cancels out
so

v2^2 - v1^2 = -2 g (h2 - h1)

v2^2 = v1^2 - 2g(h2-h1)
note
negative slope, as height goes down, speed goes up
if you start out at h1 = h2, then v2 = v1 .
for an object simply dropped through height h, v = sqrt(2 g h)
at t = 0 when h2 = h1

Answer 3

at t = 0 when h2 = h1
v2 = v1
usually v1 is zero but maybe not in your experiment which means the zero of velocity is the height the puck would have been dropped from at zero speed down

Answer 4

Okay its starting to make sense to me now. Thanks for taking the time to explain this to me!