**Simple Machines**

Learn how simple machines give a mechanical advantage. Levers, pulleys, and incline planes an simple machines that can help lift or move an object. You may not be able to lift a heavy refrigerator alone but with a simple machine you can.

**Types of Simple Machines**

**Lever**: A bar that turns around a fulcrum (pivot point) used to lift an object when a force is applied on the other side.**Incline Plane**: A sloped surface used to raise an object.**Pulley**: Used to change the direction of force and or multiply it.

**Simple Machine Variables**

Name |
Variable |
Unit |
Unit Abbreviation |

Work |
W | Joules | J |

Input Work |
W_{in} |
Joules | J |

Output Work |
W_{out} |
Joules | J |

Force |
F | Newton | N |

Input Force |
F_{in} |
Newton | N |

Output Force |
F_{out} |
Newton | N |

Distance |
d | Meters | m |

Input Distance |
d_{in} |
Meters | m |

Output Distance |
d_{out} |
Meters | m |

Ideal Mechanical Advantage |
IMA | (No unit) | |

Actual Mechanical Advantage |
AMA | (No Unit) | |

Percent Efficiency |
% Eff | Percent | % |

Heat |
Q | Joules | J |

### Work and Energy Can't Be Created

A machine **can’t create work or energy.** People use simple machines to **multiply force at the expense of distance** or **multiply distance at the expense of force**. See what this means below and in our animations.

When you use a simple machine, you and the machine does work.

Work in equals work out (W_{in} = W_{out}) and work equals force time distance (W = Fd). I**n the work equation, force and distance are inversely related**. So the **lower the force** you need to apply the **greater the distance** you need to do it for.

Observe the stickman applying less force but also how much further he must push.

### Input and Output

**Input** in these equations is the work "you do" while using a **simple machine. **Your work includes your **input force (F _{in})** and the

**distance**

**(d**you apply the force.

_{in})**Output** is what the machine does as a result of your input. A simple machine does work by outputting a force **(F _{out}) **over a distance

**(d**. The

_{out})**weight (F**the machine provides.

_{w}) of an object you lift is the (F_{out}), the output force,Remember **output** as the job you'd do with**out** the machine. This incline is used by the stickman to **lift the weight of the fridge the height of the truck bed.** With the machine this stickman has to apply less force but over a greater distance.

### Simple Machine Basic Formulas (Ideal)

Most physics problems in this unit involve the ideal and ignore heat lost. Use these formulas unless noted otherwise.

The work put into the machine equals the work you get out of it

**W _{in} = W_{out}**

The force times distance you put into the machine equals the force times distance you get out.

**F _{in}d_{in }= F_{out}d_{out}**

### Example Problems

**1. What is the output force of an incline plane is used to lift a 61 kg refrigerator?**

**2. What length of ramp would have to be used to raise a 610 N box to a height of 1.1 m using a force of 180 N?**

**3. Which incline would require the most input force from you to raise a 15 kg mass? Why?**

### Mechanical Advantage (MA)

Mechanical Advantage represents how much a machine multiples your input force. For example an Actual Mechanical Advantage (AMA) of 2 means that I can lift a 100N box with 50N of applied force.

**IMA: Ideal mechanical advantage**

- Assumes 100% efficiency
- IMA is theoretical based on measurement distances (d
_{in & }d_{out}) - How long you push divided by how far the object actually moves the direction it would without the machine.

**AMA: Actual mechanical advantage**

- Assumes machine are inefficient and will loose some energy as heat
- This equations deals with actual force put into the machine and what force it actually outputs (F
_{in & }F_{out}) - How much weight you actually lift through the machine compared to what you must input.

### Determining a pulleys IMA

The IMA of a pulley system can also be determined by the number of supporting strands that suspend the object. The strands that suspend the object are the ones going up from the object lifted. Observe this in the picture.

### Example Problems

**4. What ****is the ****actual mechanical advantage if Sam pushed a 610N box up an incline plane with a force of 220N?**

**5. What is the ideal mechanical advantage of the pulley system lifting the couch here? (It would be the same as the one below)**

**6. What is the ideal mechanical advantage if Sam pushed a box 3.73 m up an incline plane to lift a box 1.1 ****m up on a truck bed?**

**Ideal vs. Actual and Efficiency**

**No machine is 100% efficient or ideal**. So in reality or "actual" some energy will be lost from the system at heat instead of output. Use these formulas when a problem provides or asks about heat.

**W _{in} = W_{out + Heat}**

**F _{in}d_{in}=F_{out}d_{out + Heat}**

**Percent Efficiency Equation**

Percent efficiency related to how efficient a machine is. In other words, how much of the energy is lost using a machine that became heat instead of work output.

Percent efficiency of a machine can be determined many ways. The first equation below takes the work you get out of a machine compared to what is put in to find efficiency. The second takes the actual mechanical advantage you get from a machine and compares it to the perfect or ideal mechanical advantage.

**Example Problems**

**You attempt to push a 3500 N washing machine up a 5.0 m ramp into your truck bed that stands 0.50 m above the ground.**

**7 a) What is the ideal mechanical advantage of the ramp?**

**7 b) If you need to exert a 450 N force to push the washing machine up the ramp with constant speed, ****what is the actual mechanical advantage?**

**7 c) What is the efficiency of the ramp?**

**(Click here to See All the Simple Machine Example Problems and Solutions)**

**Simple Machines Quiz**

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