Answer to Question #78153 in Mechanics | Relativity for Prerana

Question

Define conservative force. Give an example.
A child of mass 20 kg climbs a slide (of
height 2.0 m from the ground) and slides
down from top. What is her speed when she
reaches the ground ? Neglect friction.

Answer 1

Conservative force is the force where curl of the force is zero.
Gravitational force is conservative force.

When a child climbs a slide of height 2 m from the ground, the total energy is potential energy.
This potential energy = mgh [where, m = mass of child = 20 kg, g = acceleration due to gravity = 9.8 m/sec2, h = height = 2 m]
Again when a child slides down from top, the total energy is kinetic energy.
This kinetic energy = 1/2 mv^2 [where, m = mass of child = 20 kg, v = velocity when reaches the ground]
As energy is conserved, then kinetic energy = potential energy.
So, 1/2 mv^2 = mgh
Or, v = √2gh = √(2×9.8×2) = 6.26 m/sec.