A platform that rolls on wheels and has inertia mp is attached to a wall by a ho

Question

A platform that rolls on wheels and has inertia mp is attached to a wall by a horizontal spring of spring constant k. A load of inertia ml sits on the platform, and the coefficient of static friction between platform and load is s. If you pull the platform away from the wall so that the spring is stretched a distance x from its relaxed length and then let go, the platform-spring combination bounces back and forth. If you want the load to stay in place held only by friction, what is the maximum distance xmax you can stretch the spring from its relaxed length and have the load stay on when you release the platform-spring combination?

Express your answer in terms of some or all of the variables mp, ml, s, and k.

Explanation / Answer

Force on Platform due to stretched string , F = K*x
Friction Force on Load = us*N
Normal Force on Load, N = ml * g

For load to stay in it's position, Friction Force = Spring Force

Therefore, Maximum Strech is given by -

F = k*x = m*a
k*x = us *N

k*xmax = us * ml *g
xmax =  (us * ml *g) / k

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