Simple Machines A machine is a device for multiplying forces or simply changing the direction of forces. Many machines can increase the speed with which work is done.
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Simple Machines
A machine is a device for multiplying forces or simply changing the direction of forces.
Many machines can increase the speed with which work is done.
The Lever
The law of conservation of energy applies to all machines!
At the same time we do work on one end of the lever, the other end does work on the load.
The LeverWe see that the direction of the force is changed.
If we push down, the load is lifted up.
More importantly, the small force we use has been multiplied into a much larger force.
The LeverIn this example, the small force this person
exerts on the car jack handle has been multiplied so much it can lift the weight of the car.
The price you pay for this is that you have to exert your force over a much larger distance.
When the handle moves down 25 cm,
the car moves up only 0.25 cm.
Energy Conservation
Input work = output work
input force x input distance = output force x output distance
F x d = F x d
A machine can multiply force but never energy! NO WAY!
1st class leverThe first class lever places the pivot point
(fulcrum) in the middle.
FR
FE
Examples: the playground see-saw, the pry bar, scissors, and car jack
2nd class lever
The second class lever places the load (resistance force) in the middle.
FR
FE
An example would be a wheelbarrow.
3rd class leverIn the third class lever, the input force (effort
force) is in the middle.
FE
FR
An example would be a tennis racket.
What advantages and disadvantages can you identify for each class of lever?
Pulleys
Another type of simple machine is the pulley.
Like the lever, pulleys can also
multiply force and change its direction.
REMEMBER: No simple machine can
multiply energy!
PulleysCan you see that a pulley is just a lever in disguise?
This is a single fixed pulley. It
acts like a lever with equal arms. It changes only the direction of the input force.
When the person pulls down on the rope, the load is lifted up.
PulleysThis is a single movable pulley.
The advantage here is that the
load can be lifted with an input
force that is only half of the load's
true weight.
Why is the “fulcrum” pictured on the left?
Mechanical AdvantageMany people say that simple machines make
work seem easier to do.
Physicists can actually quantify the term “mechanical advantage.”
Ideal Mechanical Advantage (IMA) stands for the number of times your input force is multiplied under ideal conditions, i.e. no friction.
Actual Mechanical Advantage (AMA) stands for the number of times your input force is multiplied under real world conditions. (friction is present)
Single Fixed Pulley
In this case, the IMA = 1.This pulley does not multiply
the input force. It does change the direction of the force from
up to down, and for many people, that is an advantage.
Win = Wout
Fin din = Fout dout
(100 N)(10 cm) = (100 N)(10 cm)
One Fixed, One Movable Pulley
In this case, the IMA = 2.Not only does this pulley
change the direction of the force, but it also multiplies it. The 50 newton input force is
able to lift 100 N of load.
Win = Wout
Fin din = Fout dout
(50 N)(20 cm) = (100 N)(10 cm)
Two Fixed, One Movable Pulley
In this case, the IMA = 3.Again, this pulley change the direction of the force, and it
also multiplies it. The 33⅓ N input force is able to lift 100 N
of load.
Win = Wout
Fin din = Fout dout
(33⅓ N)(30 cm) = (100 N)(10 cm)
Two Fixed, Two Movable Pulleys
In this case, the IMA = 4.Again, this pulley change the direction of the force, and it also multiplies it. The 25 N
input force is able to lift 100 N of load.
Win = Wout
Fin din = Fout dout
(25 N)(40 cm) = (100 N)(10 cm)
Actual Mechanical Advantage
The actual input force in this case would be a little greater than the ideal value of 25 N.
It might be 30 newtons. (The extra 5 newtons is used to
overcome friction).
Win > Wout
Fin din > Fout dout
(30 N)(40 cm) > (100 N)(10 cm)
Actual Mechanical Advantage
The actual mechanical advantage (AMA) would be the ratio of the output force to the
input force.
AMA=F R
F E
=100 N30 N
=3.33
FE = 30 N
The AMA will always be less than the IMA.
How Large is the IMA?
There is an easy way to tell, just by looking at the picture.
This method works even if there are no numerical values
labeled on the diagram.
Just count the number of strands of rope that directly
support the load.
In this case it is 4. Therefore, the IMA is 4.
Let's try another one!
There's move than one way to wind the cord around two fixed
and two movable pulleys.
Again, to find the IMA, we count the number of strands that lead directly to the load.
In this case, there are 5. Therefore, the IMA is 5.
The effort force is only 20 N.
What's the IMA here?
If you said 4, you were correct!
Remember not to count the strand
where the input force is applied when it doesn't lead directly to the load, as in this
case.
Other Kinds of Simple MachinesBesides the lever and pulley, there are four other
simples machines.
the screw the inclined plane
the wedge
What Can Machines Do?All complex machines can be seen as
combinations of simple machines.
Machines can change the direction of forces.They can multiply forces or multiply distances.
No machine can create energy; it can only transfer energy or transform it
from one form to another.
1
Simple Machines
A machine is a device for multiplying forces or simply changing the direction of forces.
Many machines can increase the speed with which work is done.
2
The Lever
The law of conservation of energy applies to all machines!
At the same time we do work on one end of the lever, the other end does work on the load.
3
The LeverWe see that the direction of the force is changed.
If we push down, the load is lifted up.
More importantly, the small force we use has been multiplied into a much larger force.
4
The LeverIn this example, the small force this person
exerts on the car jack handle has been multiplied so much it can lift the weight of the car.
The price you pay for this is that you have to exert your force over a much larger distance.
When the handle moves down 25 cm,
the car moves up only 0.25 cm.
5
Energy Conservation
Input work = output work
input force x input distance = output force x output distance
F x d = F x d
A machine can multiply force but never energy! NO WAY!
input work = output work only when there is no friction. In the real world, input work is greater than output work. The difference is the energy dissipated away due to friction. Nevertheless, the input force is less than the output force and the advantage of using the machine is still there.
6
1st class leverThe first class lever places the pivot point
(fulcrum) in the middle.
FR
FE
Examples: the playground see-saw, the pry bar, scissors, and car jack
7
2nd class lever
The second class lever places the load (resistance force) in the middle.
FR
FE
An example would be a wheelbarrow.
The advantage of this arrangement is that the input force (effort force) is much farther from the fulcrum than the resistance force. That means that the effort force is multiplied by how many times it is farther from the fulcrum than the resistance force.
8
3rd class leverIn the third class lever, the input force (effort
force) is in the middle.
FE
FR
An example would be a tennis racket.
What advantages and disadvantages can you identify for each class of lever?
9
Pulleys
Another type of simple machine is the pulley.
Like the lever, pulleys can also
multiply force and change its direction.
REMEMBER: No simple machine can
multiply energy!
10
PulleysCan you see that a pulley is just a lever in disguise?
This is a single fixed pulley. It
acts like a lever with equal arms. It changes only the direction of the input force.
When the person pulls down on the rope, the load is lifted up.
11
PulleysThis is a single movable pulley.
The advantage here is that the
load can be lifted with an input
force that is only half of the load's
true weight.
Why is the “fulcrum” pictured on the left?
12
Mechanical AdvantageMany people say that simple machines make
work seem easier to do.
Physicists can actually quantify the term “mechanical advantage.”
Ideal Mechanical Advantage (IMA) stands for the number of times your input force is multiplied under ideal conditions, i.e. no friction.
Actual Mechanical Advantage (AMA) stands for the number of times your input force is multiplied under real world conditions. (friction is present)
13
Single Fixed Pulley
In this case, the IMA = 1.This pulley does not multiply
the input force. It does change the direction of the force from
up to down, and for many people, that is an advantage.
Win = Wout
Fin din = Fout dout
(100 N)(10 cm) = (100 N)(10 cm)
14
One Fixed, One Movable Pulley
In this case, the IMA = 2.Not only does this pulley
change the direction of the force, but it also multiplies it. The 50 newton input force is
able to lift 100 N of load.
Win = Wout
Fin din = Fout dout
(50 N)(20 cm) = (100 N)(10 cm)
Notice here that you have traded off distance for force. You have to pull down 20 cm of rope for every 10 cm you wish the load to rise up in the air.
15
Two Fixed, One Movable Pulley
In this case, the IMA = 3.Again, this pulley change the direction of the force, and it
also multiplies it. The 33⅓ N input force is able to lift 100 N
of load.
Win = Wout
Fin din = Fout dout
(33⅓ N)(30 cm) = (100 N)(10 cm)
Notice here that you have traded off distance for force. You have to pull down 20 cm of rope for every 10 cm you wish the load to rise up in the air.
16
Two Fixed, Two Movable Pulleys
In this case, the IMA = 4.Again, this pulley change the direction of the force, and it also multiplies it. The 25 N
input force is able to lift 100 N of load.
Win = Wout
Fin din = Fout dout
(25 N)(40 cm) = (100 N)(10 cm)
Notice here that you have traded off distance for force. You have to pull down 20 cm of rope for every 10 cm you wish the load to rise up in the air.
17
Actual Mechanical Advantage
The actual input force in this case would be a little greater than the ideal value of 25 N.
It might be 30 newtons. (The extra 5 newtons is used to
overcome friction).
Win > Wout
Fin din > Fout dout
(30 N)(40 cm) > (100 N)(10 cm)
Notice here that you have traded off distance for force. You have to pull down 20 cm of rope for every 10 cm you wish the load to rise up in the air.
18
Actual Mechanical Advantage
The actual mechanical advantage (AMA) would be the ratio of the output force to the
input force.
AMA=F R
F E
=100 N30 N
=3.33
FE = 30 N
The AMA will always be less than the IMA.
Notice that the effort distance is still 4 times longer than the distance the load moves up. The ratio of the distance is always equal to the IMA, even when a lot of friction is present.
19
How Large is the IMA?
There is an easy way to tell, just by looking at the picture.
This method works even if there are no numerical values
labeled on the diagram.
Just count the number of strands of rope that directly
support the load.
In this case it is 4. Therefore, the IMA is 4.
20
Let's try another one!
There's move than one way to wind the cord around two fixed
and two movable pulleys.
Again, to find the IMA, we count the number of strands that lead directly to the load.
In this case, there are 5. Therefore, the IMA is 5.
The effort force is only 20 N.
21
What's the IMA here?
If you said 4, you were correct!
Remember not to count the strand
where the input force is applied when it doesn't lead directly to the load, as in this
case.
22
Other Kinds of Simple MachinesBesides the lever and pulley, there are four other
simples machines.
the screw the inclined plane
the wedge
23
What Can Machines Do?All complex machines can be seen as
combinations of simple machines.
Machines can change the direction of forces.They can multiply forces or multiply distances.
No machine can create energy; it can only transfer energy or transform it
from one form to another.
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