Answer to Question #130917 in Classical Mechanics for Arsh

Question

A cart of mass M is being pulled by a force of magnitude F; the friction between the cart and the ground is negligible. On the flat top of the cart lies a block of wood of mass m; the coefficient of static friction between the cart and the block is u = 0.2. What is the maximal possible value for F before the block starts to slip?

Answer 1

Sliding Force = Normal Reaction - Friction Force

Sliding Force(F) =(Mass of cart +mass of block)times gravity(g) -(u  times R) where R = mass (m) times gravity (g)

F = (M +m)g - (0.2 times R)

F =Mg +mg - (0.2 times mass of block times gravity)

F = Mg +mg -(0.2 times m times g)

F =Mg +mg - 0.2 mg

F= Mg +0.8 mg