So in physics lab we did an experiment with carts, with two different masses on

Question

So in physics lab we did an experiment with carts, with two different masses on each and they were 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. I got that both slopes are negative. Does that seem correct?
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 dont 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.

Explanation / Answer

From energy conservation law

mgh = 0.5mv^2

v^2 =2gh

v = -sqrt(2gh)

where g = 9.8 m/s^2 and h is height

the velocity expression is independent on mass

The next thing is your slope is negative because slope =dv/dt

=-g

so we can say that gravity always downward ,so slope is negative

Graph V^2 vs h slope should be +ve,because v^2 =2gh=+ve quantity

But v =-sqrt(2gh)

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