A25 kg child slides down a playground slide at a constant speed. the slide has a height of 3.0 m and is 7.0 m long. using the law of conservation of energy, find the magnitude of the kinetic friction force acting on the child.

The magnitude of the kinetic friction force acting on the child is 105 Newton.

Given the following data:

We know that the acceleration due to gravity (g) of an object on planet Earth is equal to 9.8

To find the magnitude of the kinetic friction force acting on the child, we would apply the law of conservation of energy:

First of all, we would determine gravitational potential energy possessed by the child initially:

G.P.Ei = 735 Joules

At the bottom of the slide, gravitational potential energy possessed by the child would be equal to zero (0) Joules.

So, the change in energy is given by:

The work done is the energy required to move the child from the top to the bottom of the slide.

Since friction opposes the direction, the work done is negative:

Kinetic friction force, F = 105 Newton

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105 N

Explanation:

The initial gravitational potential energy of the child is given by:

The child slides down at constant speed, so we there is no change in kinetic energy (because the speed remains constant). However, there is a change in gravitational potential energy, because when the child arrives at the bottom of the slide, the height is h=0 and the gravitational potential energy is Uf=0. Therefore, the variation of energy is

So, there have been a loss of energy. This energy loss is equal to the work done by the friction, which is given by:

where

F is the magnitude of the force of friction

d=7.0 m is the length of the slide

the negative sign is due to the fact that the friction is opposite to the motion of the child

Substituting, we get:

e/c, where e is its total energy