A block of mass m on a horizontal surface is being pulled with force F and experiences kinetic friction μ_k. Which expression gives the acceleration?

A block of mass m on a horizontal surface is being pulled with force F and experiences kinetic friction μ_k. Which expression gives the acceleration?

• A. a = (F − μ_k N) / m
• B. a = (F + μ_k N) / m
• C. a = F / m
• D. a = μ_k N / m

Answer: (A)

The key idea is Newton’s second law with friction: the acceleration comes from the net horizontal force. The pulling force tries to move the block, while kinetic friction μ_k N resists that motion and acts in the opposite direction. So the net horizontal force is F minus μ_k N, and the acceleration is a = (F − μ_k N) / m. If the pull is horizontal with no vertical component, the normal force is N = mg, so the friction term is μ_k mg and you could write a = (F − μ_k mg) / m. The other possibilities either add friction (which would oppose the idea of friction slowing things) or omit friction entirely, or give only the friction term, none of which describe the actual net acceleration.

The key idea is Newton’s second law with friction: the acceleration comes from the net horizontal force. The pulling force tries to move the block, while kinetic friction μ_k N resists that motion and acts in the opposite direction. So the net horizontal force is F minus μ_k N, and the acceleration is a = (F − μ_k N) / m. If the pull is horizontal with no vertical component, the normal force is N = mg, so the friction term is μ_k mg and you could write a = (F − μ_k mg) / m. The other possibilities either add friction (which would oppose the idea of friction slowing things) or omit friction entirely, or give only the friction term, none of which describe the actual net acceleration.