Lab investigating angle of descent and velocity help

[maturk]

Homework Statement

I have to do a high school report investigating the relationship between the angle of descent and the velocity of a ball rolling across a horizontal surface after it has gone through a ramp. I have collected the data already with the use of photo gates that measured the velocity of a ball that rolled down a ramp. The ramp angle was of coarse the independent variable and the velocity was the dependent variable. I have trouble analysing the results of my experiment now.

Homework Equations

1. Is the theoretical velocity of the ball calculated by mgh = 0.5 mv^2, which by simplifying gives v=sqrt(2gh)? Where, h is the height of my ramp which is a constant variable that I know.
2. When comparing the experimental velocities and the theoretical velocities, is it possible to deduce the force of friction that slowed down the experimental velocities from the data I have gathered?
3. What are some other things I could attempt to analyse regarding the horizontal velocities of a ball rolling down a ramp?

The Attempt at a Solution

1. I used this method and I did get results that were quite close to the experimental results. I graphed the experimental velocities and the theoretical velocities against the angle of descent and received curves that look like they are linear in the beginning but then begin to level out at the top, like a downwards opening parabola.
2. If I find the change in velocity, v(theoretical) - v(final), and divide this by the time taken for ball to go through the ramp and photo gates, and then multiply this result by the mass of the ball, will this give me the net force of friction that slowed down my experimental results? I have no idea, I'm just going by the equation f=ma.

 

[SteamKing]

This thread topic didn't seem to have any obvious connection to the Calculus HW forum, so it has been moved to the Introductory Physics HW forum.

In the future, please try to post threads in the HW forum where it will be most relevant. Thanks.

 

[haruspex]

I assume the length of ramp is constant, so the greater the angle the greater the height.
Did you really plot velocity against angle, or was it velocity against height?
What relationship do you expect between velocity and angle?
With regard to your energy equation, don't forget rotational energy.

You mention friction as slowing the ball. A rolling ball is subject to static friction, not kinetic. Static friction does no net work. What it can do is convert between rotational KE and linear KE. The ball rolling on the level surface eventually stops because of rolling resistance, not friction.

Please derive and post an equation for the speed of the ball in terms of your variables (height, angle, mass, radius...).