In a laboratory model of cars skidding to a stop, data are measured for four tri

Question

In a laboratory model of cars skidding to a stop, data are measured for four trials using two blocks. The blocks have identical masses but different coefficients of kinetic friction with a table: mu_k = 0.2 and 0.8. Each block is launched with speed upsilon_i = 1 m/s and slides across the level table as the block comes to rest. This process represents the first two trials. For the next two trials, the procedure is repeated but the blocks are launched with speed upsilon_i = 2 m/s. Rank the four trials (a) through (d) according to the stopping distance from largest to smallest. If the stopping distance is the same in two cases, give them equal rank, (a) upsilon_i = 1 m/s, mu_k = 0.2 (b) upsilon_i = 1 m/s, mu_k = 0.8 (c) upsilon_i = 2 m/s, mu_k = 0.2 (d) upsilon_i = 2 m/s, mu_k = 0.8

Explanation / Answer

at the end, kinetic energy is equal to the work done by the frictional force in stopping the object. Assume block has a

mass M, in which case, its weight is mu*M*g and the work it does in stopping in a distance d is

mu*M*g*d = 1/2*M*v^2

The M cancels,

d = v^2 / (2*mu*g)

a) d = 1^2 / (2*0.2*9.81) = 0.2548 m

b) d = 1^2 / (2*0.8*9.81) = 0.0637 m

c) d = 2^2 / (2*0.2*9.81) = 1.019 m

d) d = 2^2 / (2*0.8*9.81) = 0.2548 m

Rank :- c),a) and d) are equal,b)

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