A cart of mass m = 1.30 kg on a track undergoes a collision with another cart. I

Question

A cart of mass m = 1.30 kg on a track undergoes a collision with another cart. It's velocity before and after the collision, v, and Vf is measured and found to be v, = 1.20 plusminus 0.04 m/s and Vf = 0.62 plusminus 0.08 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 = mvj, and after, pf = mvf the collision: Pj =1.56 plusminus 0 05 kg*m/s pf = 0.81 plusminus 0.10 kg*m/s The change in momentum Delta p = pf - pi of the cart Delta p = 0.75 plusminus 0.12 kg*m/s If the collision lasts a time interval Delta t = 0.060 plusminus 0.004 s, calculate the average force Fave = Ap/At. Fave=-12.5 plusminus 0.004 N

Explanation / Answer

change in momentum is impulse J, Jx since it is in the x axis (F_av)x = Jx/?t Jx= pf-pi Jx= .98-.75 = .23 ± .104 uncertainties v (.03)^2 + (.10)^2= .104 (F_av)x= .23 ± .104 / .160 ± .010 (F_av)x=.23/.160 ± .21/1.60 v (.104/.23)^2 + ( .010/.160)^2 (F_av)x = 1.44 ± .101

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