A horizontal force is applied to the textbook. Find the force of friction the desk exerts on the textbook, if the applied force is: 0N, 12.9N[S], 39[W], 45[E]?

A 6.7 kg book is on a desk, both of which are in an elevator. The coefficient of static friction between the textbook and the desk is 0.46, while the coefficient of kinetic friction between the textbook and the desk is 0.29. The elevator is accelerating upwards at 3.2m/s^2.

1 Answer
Ananda Dasgupta
Apr 16, 2018

0N, 12.9N[N], 39N[E], 25N[W]?

Explanation:

The normal force on the book #N# is given by

#N-mg=ma implies N=m(g+a)#

So

#N = 6.7" Kg" times (9.8+3.2)" ms"^-2=87.1" N"#

Thus, the limiting value of static friction is

#mu_s N =l~~40" N" #

Thus, in the first three cases, the force of friction will be equal to the applied force and directed opposite to it(since friction self adjusts to ensure that there is no relative motion between the surfaces, as long as the force it has to supply for this is within the limiting value.

When the applied force is 45 N, the book slips and the force of friction is now kinetic friction, given by

#mu_k N ~~ 25" N"#

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