If a horizontal force is applied to a block on a rough surface and the force is less than the maximum static friction, what happens?

If a horizontal force is applied to a block on a rough surface and the force is less than the maximum static friction, what happens?

• A. The block remains at rest because static friction balances the applied force up to its maximum.
• B. The block accelerates with acceleration a = F/m.
• C. The normal force increases to match the applied force.
• D. The surface becomes slippery and kinetic friction engages immediately.

Answer: (B)

When a horizontal push on a block on a rough surface is not large enough to overcome friction, static friction does the job of balancing the push. The normal force on a horizontal surface is N = mg, so the maximum static friction is μ_s N = μ_s mg. If the applied force F is less than this limit, static friction adjusts to a value equal in magnitude to F but opposite in direction, yielding zero net horizontal force. With no net force, the block stays at rest and its acceleration is zero. The normal force remains mg (the horizontal push doesn’t change the vertical load in this setup), and no kinetic friction comes into play because the block does not slip. Only if F exceeded μ_s mg would the block start to slip and kinetic friction would govern the motion, leading to a nonzero acceleration given by a = (F − μ_k mg)/m. In this scenario, since F < μ_s mg, the block remains unmoved and the acceleration is zero.

When a horizontal push on a block on a rough surface is not large enough to overcome friction, static friction does the job of balancing the push. The normal force on a horizontal surface is N = mg, so the maximum static friction is μ_s N = μ_s mg. If the applied force F is less than this limit, static friction adjusts to a value equal in magnitude to F but opposite in direction, yielding zero net horizontal force. With no net force, the block stays at rest and its acceleration is zero. The normal force remains mg (the horizontal push doesn’t change the vertical load in this setup), and no kinetic friction comes into play because the block does not slip. Only if F exceeded μ_s mg would the block start to slip and kinetic friction would govern the motion, leading to a nonzero acceleration given by a = (F − μ_k mg)/m. In this scenario, since F < μ_s mg, the block remains unmoved and the acceleration is zero.