Question

The motor exerts a constant force on the cable pulling the crate to the right on a smooth floor. as a result, the crate is moving at constant acceleration
a. if the motor force doubles and the mass of the crate decreases by half, what is the crate's acceleration in this situation?

Answer 1

This is a job for Newton's 2nd Law! F = ma. We want to know the acceleration, so let's solve it for a, and get a = F/m. Now if we double the force, we'll have a' = 2F/m (where a' is the modified acceleration), and then if we decrease the mass by a half, we'd get a'' = 2F/(1/2*m) = 4F/m. We know the original acceleration was a = F/m, so let's sub that into the a'' equation and get: a'' = 4a, so a'' is 4 times the magnitude of our starting a.