- #1
ual8658
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- 3
Homework Statement
Given Ma = Mb =Mc and muk between c and the surface is 0.30
Homework Equations
(rope length) = constant
Maaa = Mag - T
Mbab = Mbg - 2T
Mcac = T - (mu)Mcg
The Attempt at a Solution
The equations I came up on my own and the answer key did as well. The problem is I also need an equation relating the length of the rope as constant. My convention is to measure the length of the rope in the direction of positive motion as defined by my equations.
In this case I make the assumption mass A and mass B accelerate down (the answer later gives B as negative indicating it goes up) and made that the positive direction. I also made going to the left positive for mass C.
The problem is when I go to write the rope length equation I get
Xa + 2 Xb + (X - Xc) = constant
and obviously differentiate to get the acceleration equation. I measured X as the distance from the right side to the pulley nearest C and thus X - Xc is the rope length between that pulley and C. This is so that I measure positive distances in the direction of positive acceleration.
The answer key simply lists the equation as
Xa + 2 Xb + Xc) = constant
with all other equations I gave as true.
Where am I picturing this wrong?