# Homework Help: Calculating Tension in a Two Pulley Atwood Machine

1. Oct 13, 2007

### rossel

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

Calculate the force of tension in the string of an Atwood machine with masses (1 - on right) 69.95 grams, (2 - middle) 80.11 grams, and (3 - on right) 60.28 grams. When this value is determined, verify that the net force in the atwood machine is equal to zero.

.........\........|......../
.....44º.\.46º.|.60º./.30º
----------------------------- (all angles are measured from this line, x components)
.......|..........|...........|
.......|..........|...........|
.....m1.......m2........m3

2. Relevant equations

Fg = mg
Fnet = Fg + Ft (Fnet should equal approx. 0)

3. The attempt at a solution

First, calculating the force of gravity on each of the masses:

Fg1 = (0.06995)(9.8)
= 0.68 N

Fg2 = (0.08011)(9.8)
= 0.79 N

Fg3 = (0.060280)(9.8)
= 0.59 N

Secondly, using the angles measured and the forces of gravity determined, solve for the x and y components.

y1 = 0.68 N
y2 = 0.59N

x1/sin 46 = 0.68/sin 44
x1 = 0.70 N

x2/sin 60 = 0.59/sin 30
x2 = 1.02 N

Writing Fnet statements for both x and y components produces:

Fnet(x) = 0.70 N + 1.02 N
= 1.72 N

Fnet(y) = 0.68 N + 0.79 N + 0.59
= 2.06 N

Finally:
Fnet = Fx + Fy
Fnet = 1.72 - 2.06
Fnet = 0.34 N

The sum of each of these Fnet statements is supposed to be approximately zero. I understand why this should be so (as it is a static equilibrium), however I do not not know how to achieve that answer, or what I am doing wrong. I do not believe that 0.34 N is a relatively close answer.

These angles were calculating in a lab, so is it possible that I have done everything right and simply measured the angles wrong?

I understand some of the values are to be negative, but I am unaware of which (I think it is gravity?). My teacher is no help, so I would really appreciate someone explaining how to fix this. Thank you.

Last edited: Oct 14, 2007