Question

A frightened child is restrained by her mother as the child slides down a frictionless playground slide. If the force on the child from the mother is 116 N up the slide, the child's kinetic energy increases by 30 J as she moves down the slide a distance of 1.9 m.

(A) How much work is done on the child by the gravitational force during the 1.9 m descent?
(B) If the child is not restrained by her mother, how much will the child's kinetic energy increase as she comes down the slide that same distance of 1.9 m?

Answer 1

Explanation:

Given

Restrained Force
`F=116 N`

Increase in Kinetic Energy
`\Delta K.E.=30 J`

Distance moved d=1.9 m

Work done by all the forces is equal to change in Kinetic Energy of Object i.e. by gravity force, Normal force and Applied Force

`\Delta K.E.=W_g+W_f+W_N`

`30=W_g-F\cdot d`

`30=W_g-116\cdot 1.9`

`W_g=250.4 J`

(b)In absence of applied force thus

work done by gravity will be equal to change in kinetic Energy

change in Kinetic Energy
`=210 J`