Question

A car starts from rest at time t = 0 and its a-t graph is shown in figure. A coin is initially at rest on the floor of the car. At t= 1 s the coin begins to slip and it
stops slipping at t= 3 s. The coefficient of static friction between the floor and the coin is (g = 10 m/s?)
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Answer 1

Given :

The car starts at time , t= 0 .

The time when the coin placed on its floor starts slipping is :

t = 1 sec

The time when it stops slipping is :

t = 3 sec

To Find :

What is the coefficient of static friction between the floor and the coin ?

Solution :

The free body diagram is shown in the attached fig .

A Pseudo force will be acting on the coin and it will be given as :

$F_P=ma$   , here m is mass of the coin and a is acceleration of the car .

Now for the coin to just slip w.r.t. car :

ma = f     ; f is force of friction

∴$f = \mu N$   ; N is normal force

So, $ma = \mu mg$        - (1)

From the graph we get that when the coin slips  :

a = $4 m/s^2$

So , on putting value of a in equation 1 :

$a = \mu g$

Or, $4 = \mu 10$

Or, $\mu = \frac{4}{10}$

So , $\mu = 0.4$

Hence , the coefficient of friction between the floor and the coin is 0.4 .