This question gives practice using error propagation formulas. A cart of mass m

Question

This question gives practice using error propagation formulas. A cart of mass m = 0.90 kg on a track undergoes a collision with another cart. It's velocity before and after the collision, vi, and vf is measured and found to be vi = 2.02 0.06 m/s and vf = 0.34 0.04 m/s. Calculate the following quantities including their uncertainty. Uncertainties must be stated to correct number of sigfigs, but you should keep more figures for intermediate calculations, rounding only at the end. The momentum of the cart before, pi = mvi, and after, pf = mvf the collision: pi = pf = The change in momentum deltap = pf - pi of the cart deltaP= If the collision lasts a time interval deltat = 0.200 0.012 s, calculate the average force Fave = deltap/deltat. Fave =

Explanation / Answer

a)

pi = mvi = 0.90*(2.02±0.06) = 1.818±0.054

pf = mvf = 0.90*(0.34±0.04) = 0.306±0.036

b)

p = pf - pi = 1.818±0.054 - 0.306±0.036 = 1.512±0.09

c)

F = p/t = 1.512±0.09/(0.200±0.012) = 7.61±0.906

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