[dayah]

a child goees down a playground slide with an accelaration of 1.36m/s^2.find the coefficient of kinetic friction between the child and the slide if the slide is inclined at an angle of 31.0 below the horizontal.

[jcaron2]

This sounds like a homework problem. We can help, but we're not here to do your homework for you.

It will be much easier if you draw a picture. There are two forces acting on the child, gravity and friction. You know the force of gravity is mg directed straight down (where m is the mass of the child). You need to break that force into two components: one directed parallel to the slide and one normal to it. The parallel component will be the force pulling the child down the slide. The normal component will be the one contributing to the kinetic friction.

Ultimately, the problem tells you that the child is accelerating down the slide at 1.36m/s^2, so you know the net force (the sum of the gravitational and frictional forces, which act in opposite directions parallel to the slide) is 1.36m (again, where m is the mass of the child).

So there's your equation: 1.36m = F_gravity + F_friction

Note that both F_gravity and F_friction will also have an m in their values. Hence the m will cancel out of everything, and its value won't matter. The only unknown you'll be left with is the coefficient of kinetic friction. You'll just have to solve for it once you have the rest of the equation.

Can you take it from there? If not, post back with your attempts to find F_gravity and F_friction, and we'll proceed from there.

[ankita.g]

0.433 is the answer
its equation is like this
mg(sin(31)-Mu*cos(31))=m*1.36
=g*sin(31)-g*Mu*cos(31)=1.36
=0.433answer