Final answer:
The distance covered by the crate after the pushing force is removed and before coming to a stop remains the same even if the mass of the crate is doubled, assuming the initial velocity and the coefficient of friction remain unchanged.
Step-by-step explanation:
The phenomena described in the student's question relates to the laws of physics, specifically the concepts of kinetic energy and friction. When the mass of the crate is doubled, while maintaining the initial velocity constant, the kinetic energy of the crate also doubles. However, the force of friction (which is presumed to be constant in both cases) acts over a distance to convert all of the kinetic energy into thermal energy or other forms of energy until the crate stops. This scenario is governed by the work-energy principle.
According to this principle, the work done by friction can be expressed as the change in kinetic energy. If the coefficient of friction and the initial velocity remain constant, and the mass is doubled, the work done by friction will still be the same since it is dependent on the distance the crate slides and the constant frictional force. As a result, the crate will slide the same distance, d, even after the mass is doubled. This is because the increased mass will have increased inertia, but it will also have proportionally more kinetic energy to dissipate.