Final answer:
A ball rolled up a ramp without slipping will reach a higher point than a sliding ball because rolling combines translational and rotational kinetic energy, reducing the energy available for climbing, hence reaching a greater height.
Step-by-step explanation:
When a ball slides up a frictionless ramp and then rolled without slipping with the same initial velocity up another frictionless ramp with the same slope angle, the scenario involving rolling will result in the ball reaching a higher point.
This is because rolling combines translational and rotational kinetic energy, whereas sliding only involves translational kinetic energy. Upon rolling, some of the ball's kinetic energy is converted into rotational kinetic energy, which doesn't contribute to climbing higher on the ramp. Therefore, for a rolling ball, less energy is available for upward motion, allowing it to reach a greater height compared to when it slides.
The inclined plane, a simple machine demonstrated by ramps, lowers the required force to move an object upward by extending the distance over which that force must act. While both sliding and rolling involve the conversion of kinetic energy to potential energy as the ball moves up the ramp, the presence of rotational kinetic energy in the rolling scenario introduces a difference.
A ball that is sliding has all of its kinetic energy in translational form, which is entirely converted to potential energy. In contrast, the rolling ball's rotational kinetic energy is an additional form of energy that is not converted to potential energy