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 Machines

Simple Machine Variables

Name Variable Unit Unit Abbreviation
Work W Joules J
Input Work Win Joules J
Output Work Wout Joules J
Force F Newton N
Input Force Fin Newton N
Output Force Fout Newton N
Distance d Meters m
Input Distance din Meters m
Output Distance dout 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 (Win = Wout) and work equals force time distance (W = Fd).  In 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 (Fin) and the distance (din) you apply the force.

lever simple machine

Output is what the machine does as a result of your input.  A simple machine does work by outputting a force (Fout) over a distance (dout).  The weight (Fw) of an object you lift is the (Fout), the output force, the machine provides.

Remember output as the job you'd do without 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.

incline plane simple machine

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

Win = Wout

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

Findin = Foutdout

Example Problems

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


Problem 1 Solution

(Click on the image for a larger picture)

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?


Problem 2 Solution

(Click on the image for a larger picture)

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

different inclines


Problem 3 Solution

(Click on the image for a larger picture)

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 (din & dout)
  • How long you push divided by how far the object actually moves the direction it would without the machine.

ideal mechanical advantage

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 (Fin & Fout)
  • How much weight you actually lift through the machine compared to what you must input.

actual mechanical advantage

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.

pulley-ma

Example Problems

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


Problem 4 Solution

(Click on the image for a larger picture)

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

pulley


Problem 5 Solution

(Click on the image for a larger picture)

pulley simple machine

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?


Problem 6 Solution

(Click on the image for a larger picture)

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.

Win = Wout + Heat

Findin=Foutdout + 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.

Percent Efficiency

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?


Question 7a

(Click on the image for a larger picture)

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?


Question 7b

(Click on the image for a larger picture)

7 c) What is the efficiency of the ramp?


question 7c

(Click on the image for a larger picture)

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

Simple Machines Quiz

Simple Machines Quiz

Do you know your simple machines?

incline plane simple machine

Take our quiz to find out

1 / 14

Simple machines can't be used to multiply _________________.

2 / 14

When energy is lost from a simple machine which of the following must be less

3 / 14

When energy is lost from a system it is most likely ________________.

4 / 14

Which is a simple machine consisting of a bar or plank that turns around a pivot point?

5 / 14

Simple Machine

The picture above is of a(n) ___________________.

6 / 14

John pushes a box up a ramp using a 10 m plank.  The box moves a vertical distance of 2 m and weighs 500 N, ideally with how much force must he push?

7 / 14

A 460 N box is hoisted above a truck by John who applies 60 N of force.  What is the actual mechanical advantage of the pulley system?

8 / 14

A 460 N box is hoisted above a truck by John who applies 60 N of force.  What is the actual mechanical advantage of the pulley system?

9 / 14

Joe is attempting to lift a 3000 N motorcycle into a trailer 1.5 meters off the ground using a pulley system.  If Joe applies 300 N of force, what is the ideal distance he would pull on his side of the rope?

10 / 14

What is the Actual Mechanical Advantage when 300 N of force is required to lift a 3000 N object?

11 / 14

What length of ramp would you ideally have to use to raise an 815 N box a height of 2.10 m using a force of 165 N?

12 / 14

What is the ideal mechanical advantage when a ramp of 4 meters is used to lift a 1400 N sled full of toys 1 meter off the ground pushing with a force of 500 N?

13 / 14

What is the efficiency of 4 meters ramp used to lift a 1400 N sled full of toys 1 meter off the ground pushing with a force of 500 N?

14 / 14

Tom pushes a 50 kg box up a 15 meter incline plane by pushing with a force of 100 N.  The end result is that the box was lifted 2 meters.  What was the efficiency of this simple machine?

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