The coefficient of friction between a child and the surface of a slide is 0.5. What is the minimum slope required if he has to slide down?
Let the mass of the child be M. And the angle that the slide should make with the ground for him to be able to slide down be x.
When the child sits on the slide, there is a force equal to M*g with which he is pulled towards the ground. This force acts in a vertical direction. It can be divided into two components. One along the slide that is equal to M*g*sin x and one normal to the surface of the slide equal to M*g*cos x.
The coefficient of friction between the slide and the child is equal to 0.5. This gives the force of resistance due to friction as M*g*cos x*0.5.
For him to slide down M*g*sin x should be greater than M*g*cos x*0.5.
M*g*sin x > M*g*cos x*0.5
=> sin x > cos x*0.5
=> tan x > 0.5
=> x > 26.56 degrees.
The slide has to be inclined at an angle greater than 26.56 degrees with the ground for the child to slide down.