Question

Consider two slides, both of the same height. One is long and the other is short. From which slide will a child have a greater final speed when sliding off? Assume that there is no friction acting.

Answer 1

Answer:

The final speed will be the same for the children on the shorter side and on the longer side.

Explanation:

This is because since the they are the same distance above the ground, their potential energy which is a function of mass, acceleration due to gravity and vertical height are the same.

PE = Mass × gravity × vertical height

At this point, we can deduce that the horizontal length of the slide has no effect on the potential energy. Only the vertical height does.

All this potential energy is converted to kinetic energy at the end of the slide. Since the potential energy is the same, then the kinetic energy will be the same and thus their velocity is the same.

Mathematically, consider that PE = mgh and KE = $\frac{1}{2}$m$v^{2}$

at the bottom of the slide, since energy has to be conserved, PE must be equal to KE.

mgh = $\frac{1}{2}$m$v^{2}$

final velocity of the child , v = $\sqrt{2gh}$

It shows the final velocity is only a function f acceleration due to gravity and height.

Thus, making their velocities equal.