Question

A crate pushed along the floor with velocity vâ i slides a distance d after the pushing force is removed. if the mass of the crate is doubled but the initial velocity is not changed, what distance does the crate slide before stopping?

Answer 1

d The mass is doubled which means that both the momentum and kinetic energy are also doubled. Also the normal force that's acting along with the coefficient of kinetic friction is also doubled. So the friction that's working to slow down the crate is doubled. So the crate will have double the kinetic energy that needs to be dissipated, but the rate of dissipation is also doubled, so the total time required to dissipate the kinetic energy is the same. And since both crates start out with the same velocity and since they'll lose energy (and velocity) at the same proportional rate, they'll take the same distance to slide to a stop.