A 10-kg block is pushed against a vertical wall by a horizontal force of 100 N. What is the coefficient of static friction between the block and the wall if the block is about to slide down?

100*mu=10g

mu=0.98

To find the coefficient of static friction between the block and the wall, we need to use the concept of equilibrium. When an object is about to slide down a vertical wall, the force of static friction must be equal to or greater than the force pulling the object downward.

1. Identify the forces acting on the block:
- The weight of the block (mg), where m = mass of the block (10 kg) and g = acceleration due to gravity (approximately 9.8 m/s^2).
- The normal force exerted by the wall on the block (equal to the weight of the block, since it's not moving vertically).

2. Determine the force pulling the block downward:
- In this case, the horizontal force of 100 N does not contribute to the downward motion, so we only need to consider the weight of the block (mg).

3. Calculate the maximum static friction force:
- The maximum static friction force (F(max)) is given by the equation F(max) = static friction coefficient (μ) × normal force.
- Since the block is about to slide down, the static friction force and the weight of the object must balance each other, so F(max) = mg.

4. Substitute the values into the equation to find the coefficient of static friction:
mg = μ × normal force
mg = μ × mg
1 = μ

Therefore, the coefficient of static friction (μ) between the block and the wall is 1.