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I am trying to calculate the coefficient of kinetic friction in two ways. One using energy and one using the principal of linear impulse and momentum. Not getting the same answer!

The system is a wheeled cart oscillating on a flat metal track between two springs. The motion of the cart was recorded using a motion detector into LoggerPro which calculates the velocity automatically. The mass of the cart and the spring constants are known.

Method 1: using energy/work concepts. Two points on the position graph where the velocity was zero are chosen. All the energy at those points is in the potential energy of the springs. That is calculated using 1/2kx^2 where x is the displacement from the equilibrium point (centered between the two springs). So, then I took subtracted the initial energy from the final energy to determine the amount of work done on the cart. The work in this case we are attributing solely to friction for simplicities sake. Force due to friction acting perpendicular to the motion: mu(normal force)(distance traveled). Normal force is mg. Distance traveled was found by determining the distance between each end of all the oscillations that occurred during the time in question and summing those up.

Method 2: using linear impulse/momentum. Two points 1/4 of an oscillation away from the two points previously chosen were selected. At these two new points, the velocity is at a local max and the potential energy is zero (ie the cart is at the equilibrium point). mv1 + impulse = mv2. Took the final momentum and subtracted the initial momentum from that. The impulse is the integral from time 1 to time 2 of (muN)dt. Again attributing all dampening to friction.

So, the problem is that the result I get from Method 2 is almost exactly twice that of Method 1. Is there something about the oscillatory motion that causes this? Why would I need to divide Method 2 by 2?

Thanks for any insight.

Chris