Question

A 35 kg child slides down a playground slide at a constant speed. The slide has a height of 3.8 m and is 8.0 m long. Find the magnitude of the kinetic friction force acting on the child.

Answer 1

The magnitude of the kinetic frictional force acting on the child is 162.93 N

Step-by-step explanation:

Given;

mass of the child, m = 35 kg

height of the slide, h = 3.8 m

length of the slide, d = 8.0 m

The change in thermal energy associated with the kinetic frictional force is calculated as follows;

`\Delta E_(th) + \Delta K.E + \Delta U = 0\\\\\Delta E_(th) + ((1)/(2) mv_f^2 - (1)/(2) mv_i^2) + (mgh_f - mgh_i) =0\\\\since \ the \ speed \ is \ constant, \ v_f = v_i \ and \ \Delta K.E = 0\\\\Also, \ final \ height \ , h _f= 0\\\\\Delta E_(th) - mgh_i = 0\\\\\Delta E_(th) = mgh_i\\\\\Delta E_(th) = 35 *9.8 * 3.8\\\\\Delta E_(th) = 1303.4 \ J`

The magnitude of the kinetic frictional force that produced this thermal energy is calculated from the work done by frictional force;

`\Delta E_(th) = F * d\\\\F = (\Delta E_(th) )/(d) \\\\F = (1303.4)/(8) \\\\F = 162.93 \ N`

Therefore, the magnitude of the kinetic frictional force acting on the child is 162.93 N