Question

You are trying to drag a heavy sleeper-sofa across your floor. The sofa has a mass of 150 kg and the coefficient of static friction between the couch and the floor is 1.08. Being a bright physics student, you realize that you can make this easier by pulling upwards and forwards at the same time rather that just pulling the sofa forwards. If you pull on the sofa at an angle 32? above the horizontal how much force does it take to move the sofa?

Being an extremely clever physics student, while doing the last problem you realize that there must be some angle which allows you to move the sofa with the minimum amount of force. Write the magnitude of the pulling force need to make the sofa move as a function on angle. Making clever use of a derivative find the angle that allows you to move the sofa with the minimum amount of force, then plug that back into the function to find an algebraic expression for the minimum force needed.

Answer 1