# When can you assume dynamic equilibrium?

1. Sep 14, 2013

### Coop

SOLVED

1. The problem statement, all variables and given/known data

A 23 kg child goes down a straight slide inclined 38∘ above horizontal. The child is acted on by his weight, the normal force from the slide, and kinetic friction. Find the magnitude of the normal force.

2. Relevant equations

3. The attempt at a solution

ƩFy=(Fk)y + ny + wy

Where Fk is kinetic friction, n is normal force and w is weight

ƩFy=0+ny+(-178 N) <- 23 kg * 9.81 m/s^2 = 226 N, 226N * cos(38) = 178 N

Now I know the answer is 180 N (rounded), but for that to be true, ƩFy would have to equal 0, which means that the Fnet would equal 0, which would mean that the kid is in dynamic equilibrium and has an acceleration equal to 0. But why is this true? Wouldn't the kid be accelerating while going down the slide?

Thanks,
Coop

Last edited: Sep 14, 2013
2. Sep 14, 2013

### Coop

I figured it out. I forgot to to remember that the kid is on an incline, but how I drew it is having the X-axis horizontal, therefore there will not be any acceleration along the Y-axis.