Final answer:
The minimum force required to move the crate, fm, is greater than the maximum static friction force of 440 N, calculated using the coefficient of static friction (0.45) and the normal force (980 N).
Step-by-step explanation:
The expression for fm, the minimum force required to produce movement of the crate on the surface of the counter, is based on the maximum static friction force (fs(max)) that must be overcome to initiate movement. The static friction force is calculated as fs(max) = μs N, where μs is the coefficient of static friction and N is the normal force. According to the provided information, if the coefficient of static friction is 0.45 and the normal force is 980 N, the maximum static friction force is fs(max) = (0.45)(980 N) = 440 N. Therefore, any applied force greater than 440 N will move the crate. Once the crate is in motion, the coefficient of kinetic friction comes into play, which might be 0.30, and to keep the crate moving at a constant velocity, a force of = μk N = (0.30)(980 N) = 290 N is required.