A block of mass M is kept on as rough horizontal surface. The coefficient of static frictionbetween the block and the surface is `mu`. The block is to be pulled by applying a force to it. What minimum force is needed to slide the block? In which direction should this force act?

Explanation

To solve the problem of determining the minimum force needed to slide a block of mass \( M \) on a rough horizontal surface with a coefficient of static friction \( \mu \), we can follow these steps:

### Step 1: Understand the Forces Acting on the Block
The block experiences several forces:
- The gravitational force \( Mg \) acting downwards.
- The normal force \( N \) acting upwards from the surface.
- The applied force \( F \) that we want to determine, which will act at an angle \( \theta \) to the horizontal.
- The frictional force \( f \) acting opposite to the direction of the applied force.
...