FRICTION ON FLAT SURFACE

On a flat horizontal surface, the floor pushes up on the crate with a normal force equal in magnitude to the crate's weight. Weight = mg = 12 × 9.807 ≈ 117.68 N, so the normal force is also 117.68 N. This is a direct consequence of Newton's first law applied vertically: there is no vertical acceleration, so the vertical forces must balance. Kinetic friction acts horizontally, opposing the direction of motion. Its magnitude is F_friction = μk × N = 0.35 × 117.68 ≈ 41.19 N. This force acts backward on the crate while the applied force acts forward. The net horizontal force is the vector sum: F_net = 80 − 41.19 ≈ 38.81 N in the forward direction. Newton's second law then gives the acceleration: a = F_net / m = 38.81 / 12 ≈ 3.23 m/s². The most common mistake is treating the applied force directly as the net force, which would give a = 80/12 ≈ 6.67 m/s² — nearly double the correct answer. Friction is real and takes nearly half the applied force away from accelerating the crate. Another error is using the applied force (80 N) as the normal force when computing friction, which would be wrong on a horizontal surface where the normal force comes from the weight.