A 20 kg block is initially at rest on a rough horizontal surface. A horizontal force of 75 N is required to set the block in motion. After it is in motion, a horizontal force of 60 N is required to keep the block moving with constant speed. The coefficient of static friction is

The correct answer is 0.38.

We are given the following information:

Mass of block: m = 20 kg
Force required to set the block in motion (overcomes static friction): F_s = 75 N
Force required to keep the block moving at constant speed (overcomes kinetic friction): F_k = 60 N

Step 1: Find the Normal Force

Since the surface is horizontal and the block is not accelerating vertically, the normal force N is equal to the weight of the block:

N=mg=20\times 9.8=196\text{N}

Step 2: Understand Static vs Kinetic Friction

The coefficient of static friction (μ_s) governs the maximum friction force that must be overcome to start moving the block from rest. This is why a larger force (75 N) is needed to initiate motion compared to the force needed to maintain motion.

The relationship is:

F_s={\mu }_s\times N

Step 3: Calculate the Coefficient of Static Friction

At the moment the block is just about to move, the applied force (75 N) equals the maximum static friction force. Therefore:

{\mu }_s=\frac{F_s}{N}=\frac{75}{196}=\mathrm{0.3826...}

Rounding to two decimal places:

{\mu }_s\approx 0.38

Step 4: Verify with Kinetic Friction (for completeness)

The coefficient of kinetic friction would be:

{\mu }_k=\frac{F_k}{N}=\frac{60}{196}\approx 0.31

This confirms our result is physically consistent: μ_s > μ_k, which is always true in nature — it is always harder to start moving an object than to keep it moving.

Therefore, the coefficient of static friction is μ_s ≈ 0.38.