Physics, 01.07.2019 23:00 shainaanderson24

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.

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Answer from: sindy35111

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

Given the following data:

Mass = 25 kgHeight = 3.0 metersLength (distance) = 7.0 meters

We know that the acceleration due to gravity (g) of an object on planet Earth is equal to 9.8 m/s^2

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:

$G.P.E_i = mgh\\\\G.P.E_i = 25 \times 9.8 \times 3$

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:

$\Delta E = 0 - G.P.E_i\\\\\Delta E = 0 - 735\\\\\Delta E = -735\;Joules$

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

$Work\;done = \Delta E=-735$

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

$Workdone = -Fd\\\\-735 = -F(7)\\\\7F = 735\\\\F = \frac{735}{7}$

Kinetic friction force, F = 105 Newton

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Answer from: lliaaaa

105 N

Explanation:

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

E_i = U_i = mgh_i = (25 kg)(9.8 m/s^2)(3.0 m)=735 J

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

$\Delta E= \Delta U=0-735 J=-735 J$

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

W=-Fd

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:

$-735 J=-Fd\\F=\frac{-735 J}{-7.0 m}=105 N$

Answer from: Quest

all of the answers are correct.

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A25 kg child slides down a playground slide at a constant speed. the slide has a height of 3.0 m and...