# What is the magnitude of the energy dissipated by the frictional force on the child in the following case. A child of mass 27 kg takes a ride on an irregularly curved slide of height 8.45 m. The...

What is the magnitude of the energy dissipated by the frictional force on the child in the following case.

A child of mass 27 kg takes a ride on an irregularly curved slide of height 8.45 m. The child starts from rest at the top.The acceleration of gravity is 9.8 m / s^2. The child at the bottom is 11 m/s.

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### 1 Answer

The height of the slide is 8.45 m and the child is starting at rest at the top. The mass of the child is 27 kg and acceleration due to gravity is 9.8 m/s^2.

The potential energy of the child at the top of the slide is equal to m*g*h, here m = 27, g = 9.8 and h = 8.45

m*g*h = 2235.87 J.

When the child reaches the bottom of the slide, if there were no friction the velocity would have been v with (1/2) m*v^2 = m*g*h

=> v^2 = g*h*2

=> v = sqrt (9.8 * 8.45 * 2)

=> v = 12.86 m/s

Instead, the velocity is 11 m/s.

The energy dissipated by the force of friction is (1/2)*27*(12.86 - 11)^2

=> 47.17 J

**The energy dissipated due to the force of friction is 47.17 J**