If the coefficient of kinetic friction between a 22-kg crate and the floor is 0.30, what horizontal force is required to move the crate at a steady speed across the floor? What horizontal force is required if $\mu_k$ is zero?

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Here's a free body diagram of all the forces that are on the crate. Since it's not accelerating vertically, that means the sum of all the forces in the y direction are zero and there's gravity down in the normal force up. And since they add up to zero that means the size of these two forces has to be equal and so, the normal force is mg 22 kilograms times 9.8 Newtons per kilogram which gives 215.6 Newtons. And the reason that's important is because when we want to find the force needed to pull the crate at constant speed, we have to calculate the friction force which is found using the normal force multiplied by the coefficient of friction. So, the applied force is going to be 0.3 coefficient of kinetic friction times 215.6 Newton normal force which is about 65 Newtons. And if there was no coefficient of kinetic friction, no force would be needed to move the crate at constant speed. And if this was the case of no friction, any force would result in acceleration.