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Question

A small box resting on one edge of the table is struck in such a way that it slides off the other edge, 1m away, after 2 seconds. The coeeficient of kinetic friction between the box and the table
a. must be less than 0.05
b. must be exactly zero
c. must be more than 0.05
d. must be exactly 0.05

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Answer 1 · 2016-10-03T16:05:55

The answer is (a) Coefficient of kinetic friction must be less than 0.05

Refer the image

For limiting case,

# F = μ_s * m g #

now using,

# S= 1/2 at^2#

#implies 1 = 1/2 *a *2^2 #

#implies 1 = 2*a #

#implies a = 1/2 m/s^2#

#implies a = 0.5 m/s^2 #

For sliding friction,

# F >mu_k *mg #

#implies ma>mu_k *mg #

#implies mu_k < a/g #

taking # g = 10 m/s^2 #

#implies mu_k<0.5/10 #

#implies mu_k < 0.05 #