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.
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