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## Homework Statement

I have an almost-frictionless air-hockey style ramp and i place it horizontally on a table. A little cart goes on top and on one end of the cart, i attach a string which connects to a pulley and then connected to a weight, thus pulling the cart to one side with the force of gravity. The other side is connected to a spring that is attached to the end of the ramp. I put a motion detector on the end with the spring attached and i can record the motion of the cart. The experiment starts with me pulling the cart back toward the detector until the spring is fully unstretched and the detector reads zero. The cart moves back and forth in a sinusoidal pattern, but the motion dies down because of friction. I have my graph with me with values. I also have the velocity graph. This is all in logger pro. I can upload that if its needed.

Sorry that was really long. I've been going about this lab for ages. I can't seem to figure out how to do it. The point is to find the coefficient of friction.

Heres some extra data that is def needed:

mass of cart: 168g

mass of weight: 150g

location where the force of spring = force of gravity of the weight (IE the middle): 51cm

And that is where the max speed is too i think.

## Homework Equations

Fspring = -kx

PE Spring= -0.5 k x^2 (also work Spring)

PE gravity = mgh

KE = 0.5 m v^2

## The Attempt at a Solution

I've calculated the K to be 2.94 N/m

by -1.5N = -k x 0.51m

because in the middle, the force of the weight (1.5N) = the force of the spring (-k x 0.51)

Also, since gravity and spring are conservative, and friction is not...ill need to calculate total distance that my cart has moved...

That is the definite integral of the square root of (1 + (dx/dt)^2) with respect to t.

Thanks!