Friction Problem with Pulley System: Determining Acceleration and Force

[groundhog92]

Homework Statement

There are 4 parts to this question. Two children are playing on a pulley system. A 65 kg child jumps of a platform pulling an 85 kg child horizontally across a platform. a) what is the maximum value for static friction to allow the larger child to begin sliding? b) Once sliding the coefficient of kinetic friction is .2 what will the acceleration of the children be? c) How much additional mass should the sliding child hold to maintain a constant speed? d) If their father comes and offers to pull them both, using the value of static friction from part a) how much force would he need to exert in order to start the children sliding?

Homework Equations

mg-umgcos(theta)=ma

The Attempt at a Solution

part a
650=u(850)
u=.76

part b
650-(.2)(850)=150a
a=3.2m/s^2

part c
650=(.2)(850+10x)
10x=2400
x=240kg

part d
1500(.76)=F
F=1140

Note: This is rounding gravity to 10 from 9.81 (My teacher says we need learn the process and he doesn't really care about us simplifying the math)

I think I have this right, but we have to do these up in front of the class on the board so I wanted to make sure.

 

[groundhog92]

sorry if it wasn't clear
I meant u to be the coefficient of friction