1. Tension is equally distributed in a rope and can be bidirectional
Draw FBD block Draw FBD hand
30N
Tension does not always equal weight:

2. Derive a general formula for the acceleration of the system and tension in the ropes

3. Derive a general formula for the acceleration of the system and tension in the ropes
Draw FBDs and set your sign conventions: Up is positive down is negative m1 m2 m1 m2

4. Derive a general formula for the acceleration of the system and tension in the ropes
Draw FBDs and set your sign conventions: If up is positive down is negative on the right, the opposite is happening on the other side of the pulley. -T
+m1g +T
-m2g m1 m2 m1 m2
Then, do ΣF= ma to solve for a if possible.

5. Derive a general formula for the acceleration of the system and tension in the ropes
+m1g +T
-m2g m1 m2 m1 m2
Σ F2 = T – m2g = m2 a
Σ F1 = - T + m1g = m1 a
To find acceleration I must eliminate T: so solve one equation for T and then substitute it into the other equation (This is called “solving simultaneous equations” )

6. Σ F1 = - T + m1g = m1 a
Solving this for T
T = m1g - m1 a
Σ F2 = T – m2g = m2 a
Σ F2 = m1g - m1 a – m2g = m2 a
Now get all the a variables on one side and solve for a.

7. m1g - m1 a – m2g = m2 a
m1g – m2g = m2 a + m1 a
Factor out g on left and a on right
g(m1– m2) = a (m2 + m1)
Divide this away
(m1– m2)
g = a
(m2 + m1)

8. Now you can find the tension formula by eliminating a
Now you can find the tension formula by eliminating a. Just plug the new a formula either one of the original force equations.
Σ F2 = T – m2g = m1 a
Σ F1 = - T + m1g = m1 a -T
+m1g m1 m1 m2

9. Problem #68 and 58 is just like Atwood’s machine. Use the same analysis. For #57, use the block & pully analysis on the “Forces Advanced B” presentation on my website

10. Problem #69: Dumbwaiter: a trickier Atwood’s machine
First analyze the forces on the man and do F=ma.
N + T –mg =ma
Then analyze the forces on the elevator and do F= ma.
2T – (M+m)g = (M +m)a
This will generate two equations and two unknowns. Solve simultaneously by solving the top equation for T and plugging into the bottom equation. This will yield
a = { 2N + (M-m)g} / ( m - M). Once you know a, find T.