The stopping distance of two masses with the same kinetic energy and the same magnitude of friction applied will not necessarily be the same due to the difference in their masses and resulting forces acting on them.
The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this scenario, both masses have the same initial kinetic energy, which means the work done by friction to bring them to rest is the same. However, the distance over which this work is done can vary.
The work done by friction is given by the equation:
Work = Force * Distance
While the force of friction is the same for both masses, the distance over which this force acts will differ because the force required to bring a larger mass to a stop is greater than that required for a smaller mass.
Let's assume the larger mass requires a longer distance to stop. In this case, the force of friction acting on it will remain constant, but the larger mass will require a greater distance to decelerate to zero velocity due to its greater inertia. The smaller mass, on the other hand, will require a shorter distance to come to rest because it has less inertia.
In summary, even though the work done by friction is the same for both masses, their stopping distances will differ because the forces required to decelerate them to zero velocity depend on their masses.