Calculating Rolling Friction Coefficient u_r

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To calculate the coefficient of rolling friction (u_r), a car was rolled down an 18.8 cm ramp and stopped on different materials. The car traveled 181 cm in 2 seconds, leading to an initial velocity of 1.92 m/s and an acceleration of -0.960 m/s². The calculated u_r is 0.098, derived from the formula u_r = a/g. The discussion seeks confirmation on the accuracy of this calculation and guidance on how to verify the result. The calculations and methodology appear sound based on the provided physics principles.
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Homework Statement


Need to calculate the coefficient of rolling friction u_r. A car was set atop a ramp at a height of 18.8 cm and then rolled (not pushed) down the ramp. There is a strip of material, 3 different types including rug, sandpaper, and plexiglass, where the car is eventually stopped. The timer was started once the car reached the bottom of the ramp and went up until the car stopped. Distance was also measured. Assumptions are that frictional force is 0 up until it hits the bottom of the ramp once the time is started and that friction on the bearings is also 0.

For this specific case, the car went for 2 seconds and for a total distance of 181 cm.

Homework Equations


mgh = 1/2 mv^2
v= sqrt(2gh)

F_f = u_r*F_n
F_n = mg
F = ma
so, u_r = a/g

a = v/t

The Attempt at a Solution


Being that the height of the ramp is 18.8cm I got that the initial velocity at time 0 is 1.92m/s. I then took that velocity divided by the time to reach an acceleration of -.960m/s^2. Taking that divided by g I get that u_r = .098. Is this correct? Where would I plug in .098 to check my answer?
 
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