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...

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