- #1
irishrock724
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Homework Statement
A light cable passes over a frictionless pulley attached to the ceiling. A 10 kg block hangs at one end of the cable and an 8 kg block connected by a light cable to a 4 kg block hangs at the other end. a) Construct a force diagram for each block. b) Write Newton's second law for the vertical motion of each block (choose the axes so that positive acceleration is in the same direction for each block). c) Solve these equations to determine the acceleration of the blocks and the tension in the cables.
Homework Equations
F = ma
T - w = ma
Ab + Ac = -Aa
The Attempt at a Solution
Assume block a is 10 kg, block b is 8 kg, and block c is 4 kg
Force Diagrams:
^ ^ ^
| Ta | Tb | Tc
. . .
| w | w | w
v v v
I am fairly confident this is right
Newtons 2nd Law:
Fneta = Ta - Wa = Ta - MaG = MaAa
Fnetb = Tb - Wb = Tb - MbG = MbAb
Fnetc = Tc - Wc = Tc - McG = McAc
I am pretty sure these equations are right, it just seems that when applying them to part C, I continually get 0 for the acceleration.
Acceleration and Tension:
Ta = Tb + Tc
-Aa = Ab + Ac
Ta = MaG + MaAa
Tb = MbG + MbAb
Tc = McG + McAc
MaG + MaAa = MbG + MbAb + McG + McAc
And then I get stuck trying to substitute in acceleration. I know I am going about the problem wrong in someway, but after looking at countless examples, I can't figure out where my mistake is. Thanks