Acceleration of a Crate with Friction

Equations: kinetic friction F_f = μ_k·N; Newton's second law along the floor, ΣF_x = m·a. Values: m = 20 kg and μ_k = 0.25 are given. The floor is level and P is horizontal, so the normal force equals the weight: N = mg = 20 × 9.81 = 196.2 N. P = 100 N pulls to the right; friction acts to the left, against the motion. Step 1: F_f = 0.25 × 196.2 = 49.05 N. Step 2: net horizontal force, ΣF_x = 100 − 49.05 = 50.95 N. Step 3: a = 50.95/20 = 2.55 m/s². 5.00 m/s² ignores friction. 4.75 m/s² computes friction from the mass (0.25 × 20) instead of the weight. 7.45 m/s² adds friction instead of subtracting it.