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
Force	F	Newton	N
Distance	d	Meter	m
Ideal Mechanical Advantage	IMA	None	None
Actual Mechanical Advantage	AMA	None	None

Force and Distance Tradeoff with Simple Machines

People use simple machines to:

Multiply force at the expense of distance
- You can lift more weight but you need to push for a greater distance
Multiply distance at the expense of force.
- You don’t need to push as far but you need to apply more force
Change the direction of force applied

Q1: Which stickman, A or B in the animation, would have to push the lever with more force?

Stickman B is pushing less distance but will have to apply a much greater force.

Q2: Why would you want to use something like a lever if a simple machine?

Simple machines can help you multiply your input force (less force required to lift something) or change the direction you have to apply a force

Input and Output

Input (also called effort) in these equations is the work "you do" while using a simple machine.
Output is the work the simple machine does because of your work.

What is the simple machines usual purpose: To lift the weight of the object a certain distance. The output force is equal to weight of the object.

When you use a simple machine

You do input work (W_in= F_ind_in)
The machine does output work (W_out=F_outd_out)

In an ideal (perfect) situation, the work done by person and machine would be equal

W_in=W_out

F_ind_in=F_outd_out

Output force will be equal to weight of the object we are trying to lift with a simple machine.

Q3: What is the weight of a 100 kg fridge?

F_W = mg

F_W = (100)(10)= 1000 N

Q4: How much work would you do to lift a 1000 N fridge 0.50 m?

W=Fd

W = (1000)(0.50)= 500 J

Q5: How much work would a lever do lifting a 1000 N fridge 0.50 m, under ideal conditions?

W = (1000)(0.50)= 500 J

Same as you

Q6: How much distance must you apply a 200 N force to lift a 1000 N fridge 0.50 m using a lever?

Mechanical Advantage (MA)

Mechanical Advantage represents how much a machine multiples your input force.
Actual Mechanical Advantage (AMA) of 2 means that you could lift a 100 N box with 50 N of input force.
Ideal Mechanical Advantage (IMA) of 2 means is a simple machine was 100% efficient you would be able to lift a 100 N box with 50 N of input force.

IMA: Ideal mechanical advantage

Assumes 100% efficiency
IMA is theoretical based on measurement distances
How long you push (d_in) divided by how far the object actually moves in the direction of the output force (d_out)

Q7: What is the ideal mechanical advantage of an incline that you apply a force of 65 N for 10 m and lift a 150 N couch 3 m?

AMA: Actual mechanical advantage

Assumes machine are inefficient and will lose some energy as heat
This equations deals with input and output forces
How much weight the machine lifts (F_out) divided by the force you apply (F_in)

Q8: What is the Actual mechanical advantage of an incline that you apply a force of 65 N for 10 m and lift a 150 N couch 3 m?

Determining a pulleys IMA

The IMA of a pulley system can be estimated 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.

Ideal Mechanical Advantage (IMA) of three pulleys

Q9: What is the ideal mechanical advantage of the pulley system in the animation?

Question 9

A simple machine cannot create work or energy

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_ind_in=F_outd_{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.

Q10: What is the percent efficiency of a machine with an AMA of 2.31 and an IMA of 3.33?

Q11: A person does 1000 J of work with a machine with an AMA of 2.31 and an IMA of 3.33. How much energy would be would turn into work output? (Use the percent efficiency solved for in Q10)

Q12: A person does 1000 J of work with a machine with an AMA of 2.31 and an IMA of 3.33. How much energy would be would be lost as heat?

Simple Machines Problem Set

Click check answer to see the answer for any of the problems after you completed your work. To see the work you will have to watch the end of our video for this lesson.

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

610 N

2. What “ideal” 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?

3.73 m

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

C, because it has the least input distance so the most input force

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

AMA 2.77

5. 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?

IMA 3.39

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.

6A. What is the ideal mechanical advantage of the ramp?

IMA 10

6B. 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?

AMA 7.78

6C. What is the efficiency of the ramp?

77.8%

7. What would the ideal mechanical advantage of this pulley system be?

IMA 4

8. What would the IMA of this incline plane be?

IMA 3.1

9. In an ideal situation, how much force would you have to apply to lift a 50 kg box with this incline?

161.29 N

Simple Machines Quiz

Do you know your simple machines?

Take our quiz to find out

1 / 14

Simple machines can't be used to multiply _________________.

Energy

Force

Distance

2 / 14

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

work output

force output

distance output

work input

3 / 14

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

converted to heat

converted to mechanical energy

destroyed

4 / 14

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

pulley

lever

incline plane

5 / 14

The picture above is of a(n) ___________________.

lever

incline plane

pulley

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?

250 N

10000 N

100 N

0.01 N

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?

7.67

2760

27600

0.13

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?

27600

2760

0.13

7.67

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?

450

15 m

0.0005 m

10 m

10 / 14

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

0.1

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?

13.22 m

0.43 m

10.37 m

9.81 m

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?

350

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?

62 %

110 %

45 %

70 %

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?

32.1%

32 %

66.7%

73.1 %

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