A 4 kg block on a rough horizontal surface is pulled with F = 11.8 N and μ_k = 0.25. What is the resulting acceleration if it is already sliding?

A 4 kg block on a rough horizontal surface is pulled with F = 11.8 N and μ_k = 0.25. What is the resulting acceleration if it is already sliding?

• A. ≈ 0.5 m/s^2
• B. ≈ 1.0 m/s^2
• C. ≈ −0.5 m/s^2
• D. ≈ 2.0 m/s^2

Answer: (A)

When an object is sliding on a horizontal surface, the friction force that opposes the motion is the kinetic friction, with magnitude f_k = μ_k N. The normal force on a horizontal plane is the weight, N = mg. Here, m = 4 kg, g ≈ 9.8 m/s^2, so N = 4 × 9.8 = 39.2 N. The kinetic friction is f_k = 0.25 × 39.2 = 9.8 N, acting opposite the pull. The net force along the direction of the pull is F_net = 11.8 N − 9.8 N = 2.0 N. The acceleration follows from Newton’s second law: a = F_net / m = 2.0 / 4 = 0.5 m/s^2. Thus the block accelerates in the direction of the pull at about 0.5 m/s^2.

When an object is sliding on a horizontal surface, the friction force that opposes the motion is the kinetic friction, with magnitude f_k = μ_k N. The normal force on a horizontal plane is the weight, N = mg.

Here, m = 4 kg, g ≈ 9.8 m/s^2, so N = 4 × 9.8 = 39.2 N. The kinetic friction is f_k = 0.25 × 39.2 = 9.8 N, acting opposite the pull.

The net force along the direction of the pull is F_net = 11.8 N − 9.8 N = 2.0 N. The acceleration follows from Newton’s second law: a = F_net / m = 2.0 / 4 = 0.5 m/s^2.

Thus the block accelerates in the direction of the pull at about 0.5 m/s^2.