Simple Machines

Mechanical Advantage

Ideal Mechanical Advantage: Is the mechanical advantage of an “ideal

machine” Theoretical value

The IMA for a pulley is equal to the number of supporting ropes.

R

E

d

dIMA

A lever is used to move a rock. The resistance distance if 20cm and the effort distance is 120cm. What is the IMA?

R

E

d

dIMA

20

120IMA 6IMA

A lever has an IMA of 5. Find the distance the effort arm must be pushed down in order to lift a 5kg mass 25cm up.

R

E

d

dIMA

25

5 Ed cmdE 125

3IMA 1IMA

Calculate the IMA for each simple machine.

R

E

d

dIMA

1

3IMA

3IMA2

6IMA

3IMA 4IMA

Actual Mechanical Advantage: Is the mechanical advantage of a real

machine Actual value

IMA will always be higher than AMA due to friction.

E

R

F

FAMA

Lifting an object, AMA will always be less than IMA because working against gravity

But if you are lowering an object, AMA will be greater than IMA because gravity (friction) is helping

To move a rock with a weight of 100N, an effort force of 18N is needed. If a lever is used, calculate the AMA.

E

R

F

FAMA

18

100AMA 56.5AMA

A lever with an AMA of 4 is used to lift mass of 5kg. How much effort force is needed?

E

R

F

FAMA

EF

)8.9)(5(4 NFE 25.12

For a machine to be 100% efficient: IMA = AMA So…

E

R

R

E

F

F

d

d

RREE dFdF

A ramp is used to slide a 350kg piano onto the back of a pickup truck.

a) Calculate the IMA

b) Calculate the AMA

c)Is this 100% efficient?

R

E

d

dIMA

8.0

3IMA 75.3IMA

E

R

F

FAMA

1500

)8.9)(350(AMA 29.2AMA

Not 100% efficient b/c IMA = AMA

A crowbar is used as a lever to pry a board loose. A boy applies an effort force at a distance of 0.8m from the fulcrum. The resistance force acts 0.2m from the fulcrum.

a) Calculate the IMA.

b) Assuming friction is negligible, what is the resistance force if the boy pushes

with a force of 225N?

R

E

d

dIMA

2.0

8.0IMA 4IMA

IMA = AMA

RREE dFdF )2.0)(()8.0)(225( RF

NFR 900

You need to lift a 100kg load by applying a force less than 980N. Ignoring friction, which of the following machines should NOT be chosen?

RREE dFdF

)2)(980()5.1)(( EF1. NFE 67.1306

2. )2)(980()6)(( EF NFE 67.326

3. )1)(980()1)(( EF NFE 980

4. )20)(980()40)(( EF NFE 490

The great pyramid of Cheops is 146m high. Workers used large stones to build this structure, each with a mass of 900kg.

Egyptologists believe that ramps were used to raise the stones to the height needed. It is thought that 6 workers, each pushing with 400N of force, could accomplish this task.

Neglecting friction, what would be the length of the ramp needed to get each stone to the top of the pyramid?

RREE dFdF

)146)(8.9900())(4006( Ed

mdE 55.536