This course article contains videos that can only be accessed once enrolled in the Learn AP Physics from Scratch Course.

### Unit 2 Breakdown

You are on Lesson 7 of 8:

- Unit 2.1 | Understanding and Applying Newton’s Law in Depth
- Unit 2.2 | Common Linear Forces, Equations, and Misconceptions
- Unit 2.3 | Drawing and Understanding Force Body Diagrams
- Unit 2.4 | Deriving Equations to Solve Linear Force Problems
- Unit 2.5 | Advanced Force Problems – Tension and Elevators
- Unit 2.6 | Advanced Force Problems – Ramps (Inclines)
- Unit 2.7 | Advanced Force Problems – Pulley System [Current Lesson]
- Unit 2.8 | Advanced Force Problems – Multi-Body System

#### In this lesson you will learn:

- Understanding simple pulley systems (called an Atwood Machine)
- Solving pulley problems (the long way)
- Solving pulley problems (the easy way)

### The basics

The most basic pulley system, also referred to as an Atwood’s machine, consists of 2 masses connected by a rope. The tension is the same throughout the entire rope. The rope goes around a massless pulley as shown below.

And what if the pulley had mass? Then the mass would create a force called “Torque” which we will cover much later in Unit 6.

#### The direction of acceleration

The pulley system will always accelerate in the direction of the heavier mass.

### Solving Pulley Problems

There are two ways we can solve pulley problems.

- Using our force frame worked covered in previous sections (the long way)
- Solving as a system (the easy way)

I will explain how to do method one in the video below and cover method two in the next lesson (Lesson 2.8)

[Video for course members only]

### PQ – Pulleys (Intermediate)

- Two objects (49.0 and 24.0 kg) are connected by a massless string that passes over a massless, frictionless pulley. The pulley hangs from the ceiling. Find the acceleration of the objects and the tension in the string.
- A window washer pulls herself upward using the bucket–pulley system. She sits in the bucket, and when she pulls down on the rope the bucket moves up.
- How hard must she pull downward to raise herself slowly at constant speed?
- If she increases this force by 15%, what will her acceleration be? The mass of the person plus the bucket is 72 kg.

### PQ – Pulleys (Advanced)

- Block A (m
_{A}) of mass 13kg is held in place on a frictionless table. It is connected by a massless rope to Block B (m_{B}) of mass 5kg, that is hanging off the table.- Find the acceleration of each block when the system is released from rest.
- Now if Block A is released from rest 1.25m from the edge of the table. How long does it take to get there?

- Let’s replicate the situation above. This time, however, the table has a coefficient of static friction of .4 (µ
_{s}= .4) and a kinetic friction of .2 (µ_{k}= .4).- What minimum value of m
_{A}will keep the system from starting to move? - What value of ma will keep the system moving at constant speed?

- What minimum value of m

- A block of mass m
_{1}(5kg) is on a ramp (µ_{k}= .22) that is inclined at 20° above the horizontal. It is connected by a massless string to a block of mass m_{2}(8kg) that hangs over the top edge of the ramp.- What is the acceleration of the masses and the tension in the string?
- If m
_{1}= 8 kg, and the coefficient of static friction between m_{1}and the incline is 0.300, find the maximum value of m_{2}that will not make m_{1}slide up the incline.

### Lesson 2.7 Recap

In this lesson you learned how to solve pulley problems in two different way.

### Lesson 2.8 Preview

In the next lesson, we will take “solving problems as a system” to the next step. We will cover how to solve problems where there are 2 or more objects — similar to what we did with the pulley system.