When a ball rolls with slipping down a ramp, the presence of both translational and rotational motion affects the effective distance over which friction acts. While the ball is slipping, the frictional force is acting at the point of contact between the ball and the surface. However, due to the rolling motion, the ball rotates as it moves.
When calculating work using the formula W = Force * distance, it's important to consider that the distance in this context refers to the distance over which the force is applied. In the case of rolling with slipping, the effective distance over which the friction force acts is reduced due to the rotational motion.
To understand this concept, imagine a ball rolling down a ramp. As it rolls, the bottom point of the ball is in contact with the surface, experiencing friction. However, as the ball moves forward, the point of contact changes due to rotation. The bottom point loses contact with the surface, and a new point comes into contact. This means that the force of friction is not acting over the full distance traveled by the ball.
In essence, the effective distance over which friction acts is reduced because the contact point keeps changing due to the rolling and slipping motion. As a result, the work done by friction is also reduced compared to a scenario where the ball rolls without slipping.
It's worth noting that in the case of pure rolling, where there is no slipping, the effective distance over which friction acts would be equal to the total distance traveled by the ball. In that scenario, the rotational motion does not reduce the effective distance. However, when slipping occurs, the effective distance is reduced due to the changing contact point.