- #1

avi

- 6

- 1

- TL;DR Summary
- How should the conversation of energy principle be applied to determining the distance that a ball would travel on a flat path if the only thing known is the distance the ball traveled on a flat path and up a ramp where it stopped at the top of the ramp.

Question: A ball is hit with a certain force and it starts with an initial velocity of V m/sec decelerating due to friction along a flat path and then up an inclined ramp coming to stop at the top of the ramp where the ramp becomes flat again (as per diagram A). The total distance traveled along the horizontal direction is R meters, is it correct to say that the additional distance the ball would have traveled (F- R) had there been no ramp as seen in diagram B can be determined by rolling the ball from a stationary position on top of the ramp down the ramp until it stops as seen in diagram C?

Here are my calculations. As energy is conserved in any closed system, one could argue that in Diagram A, the initial kinetic energy is equal to the potential energy when the ball stops on the top + the loss in energy to friction. So, 0.5mv^2 = mgh + loss1 . For Diagram B, the entire kinetic energy is lost to friction by the time the ball stops, so the equation would be 0.5mv^2 = loss . For Diagram C, as the potential energy is lost to friction, so the equation is mgh = loss2 . From equations of Diagrams A and C, 0.5mv^2 = loss2 + loss1 . As loss1 + loss2 = loss , so one could write equation as 0.5mv^2 = loss, which is the equation for Diagram B. Thus I would argue that it is correct to say that the additional distance the ball would have traveled would be (F- R) had there been no ramp as seen in diagram B.

Here are my calculations. As energy is conserved in any closed system, one could argue that in Diagram A, the initial kinetic energy is equal to the potential energy when the ball stops on the top + the loss in energy to friction. So, 0.5mv^2 = mgh + loss1 . For Diagram B, the entire kinetic energy is lost to friction by the time the ball stops, so the equation would be 0.5mv^2 = loss . For Diagram C, as the potential energy is lost to friction, so the equation is mgh = loss2 . From equations of Diagrams A and C, 0.5mv^2 = loss2 + loss1 . As loss1 + loss2 = loss , so one could write equation as 0.5mv^2 = loss, which is the equation for Diagram B. Thus I would argue that it is correct to say that the additional distance the ball would have traveled would be (F- R) had there been no ramp as seen in diagram B.