Question

1) An 8.9-kg box that has a uniform density and is twice as tall as it is wide rests on the floor of a truck. What is the maximum coefficient of static friction between the box and floor so that the box will slide toward the rear of the truck rather than tip when the truck accelerates forward on a level road?
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2) Repeat the problem if the truck accelerates up a hill that makes an angle of 9.5

Answer 1

1:- Frictional force,f(s) will be equal to N*s where, N-Normal contact force & s-cofficient of friction.

Now,N=m*g(Since box is on horizental plane)= 8.9*10=89N (g=10m/s^2 has been assumed).

So, f(s)=89*s
Now, for getting maximum s, f(s) has to be maximum but it can't be greater then 89N. So,Maximum cofficient of friction,s=1.

2:- cofficient of friction s= f(s)/N=m*g*sin(9.5)/m*g*cos(9.5)=tan(9.5 degree)= 0.167