A block of mass M is kept on as rough horizontal surface. The coefficient of static friction between 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 forces acting on the block include:
- The gravitational force \( mg \) acting downward.
- The normal force \( N \) acting upward.
- The applied force \( F \) which can be applied at an angle \( \theta \) with the horizontal.
- The frictional force \( f \) acting opposite to the direction of the applied force.
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