A mass m on a horizontal surface experiences gravity mg downward, normal N upward, an applied force F to the right, and kinetic friction f_k to the left with f_k = μ_k N. If F > f_k, what is the acceleration?

A mass m on a horizontal surface experiences gravity mg downward, normal N upward, an applied force F to the right, and kinetic friction f_k to the left with f_k = μ_k N. If F > f_k, what is the acceleration?

• A. a = (f_k − F) / m.
• B. a = F / m.
• C. a = (N − mg) / m.
• D. a = (F − f_k) / m.

Answer: (D)

Net horizontal force determines the horizontal acceleration. On a horizontal surface the vertical forces balance (N = mg, since there’s no vertical acceleration), so friction has magnitude f_k = μ_k N and acts to the left, opposite the motion. The applied force F pushes to the right, and because F > f_k there is a net force to the right: F_net = F − f_k. Newton’s second law gives a = F_net / m, so the acceleration is a = (F − f_k) / m. This is the correct expression because it accounts for the opposing friction and the resulting net force along the direction of the applied push. The other forms either ignore friction, mix up the direction of the net force, or use vertical forces that cancel out on a horizontal surface.

Net horizontal force determines the horizontal acceleration. On a horizontal surface the vertical forces balance (N = mg, since there’s no vertical acceleration), so friction has magnitude f_k = μ_k N and acts to the left, opposite the motion. The applied force F pushes to the right, and because F > f_k there is a net force to the right: F_net = F − f_k. Newton’s second law gives a = F_net / m, so the acceleration is a = (F − f_k) / m. This is the correct expression because it accounts for the opposing friction and the resulting net force along the direction of the applied push. The other forms either ignore friction, mix up the direction of the net force, or use vertical forces that cancel out on a horizontal surface.