Correct Answer to Question 7

If the force F is just enough the block moving, then the block is still in equilibrium and the force situation must be that shown in the vector diagram:

F is just equal and opposite to Fs, the maximum static frictional force.

The normal force R due to the floor is equal and oppisite to the weight W = M g, since there is no vertical acceleration.

So, R = W = M g.

Now Fs is related to R by

Fs = R = M g = 0.4*M*10 = 4*M.

Now we know the magnitude of F in terms of M.

As soon as the block moves, the force situation changes: the friction force Fk is now a force of kinetic friction. Its value is

Fk = R = M g = 0.15*M*10 = 1.5*M.

F remains 4M, so we now have a resultant force directed horizontally to the right: = F - Fk. Its value is 4 M - 1.5 M = 2.5 M. Now we use Newton's law

= M a

so that a = 2.5 m/s^2.

Notice we did not need the value of the mass M, since all forces are proportional to M.

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