In a laboratory model of cars skidding to a stop, data are measuredfor six trial

Question

In a laboratory model of cars skidding to a stop, data are measuredfor six trials. Each of three blocks is launched at two differentinitial speeds vi and slides across alevel table as it comes to rest. The blocks have equal masses butdiffer in roughness and so have different coefficients of kineticfriction µk with the table.Rank the following cases (a) through (f) according to the stoppingdistance, from largest to smallest. If the stopping distance is thesame in two cases, give them equal rank and list themalphabetically. (Use only the symbols > or =, for examplea>b=c.) (a) vi = 2 m/s, µk = 0.1
(b) vi = 2 m/s, µk = 0.2
(c) vi = 2 m/s, µk = 0.4
(d) vi = 4 m/s, µk = 0.1
(e) vi = 4 m/s, µk = 0.2
(f) vi = 4 m/s, µk = 0.4 (a) vi = 2 m/s, µk = 0.1
(b) vi = 2 m/s, µk = 0.2
(c) vi = 2 m/s, µk = 0.4
(d) vi = 4 m/s, µk = 0.1
(e) vi = 4 m/s, µk = 0.2
(f) vi = 4 m/s, µk = 0.4

Explanation / Answer

In kinetic friction, -g = a Also, from kinematics, vf2 =vi2 + 2ad At the stopping point, v = 0. Therefore, 0 = vi2 + 2ad vi2 = -2ad (vi2)/(-2a) = d (vi2)/(2g) = d This will apply for all the cases.

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