1. Aim: How do we explain the behavior of two or more objects in a pulley system?

2. Tension
Assumption 1: T = T’ (The tension in a string is constant)

3. Pulley System
Are there any other forces acting on the rope?

4. Normal Force

5. Freebody Diagrams of Atwood Machine
Assume M2 >M1

6. Atwood Machine
An Atwood machine uses a cable drawn over a pulley to connect two or more masses. One of the masses acts as a counterbalance or counterweight to reduce acceleration because of gravity.

7. Thought Question
Assumption 2: The acceleration of both masses is equal. Why is the acceleration the same for each mass in an Atwood Machine?

8. Example 1
Find the acceleration and tension of an Atwood Machine in which m1 = 2kg and m2 = 4kg.

9. Example 1

10. Example 2
In an Atwood's machine, the larger mass is 1.8 kg and the smaller mass is 1.2 kg. a. Ignoring friction, what is the acceleration of the masses? b. What is the tension in the string?

11. Example 2

12. General Equations for Atwood Machines
Let us assume M is the bigger mass and m is the smaller mass. Then a = ((M-m)/(M+m))g T = (2Mm/(M+m))g We will prove this.
a = 3.27 m/s2 T=26.1N

13. Example 3
A 10.0 kg mass, m1, on a frictionless table is accelerated by a 5.0 kg mass, m2, hanging over the edge of the table. What is the acceleration of the mass along the table?

14. Example 3

15. Example 4
Calculate the force read by the scale.

16. Example 4
50 N
100 N
25 N

17. Example 5
If angle ϴ=30 degrees, calculate the acceleration of the masses.

18. Example 5