Download simple machines.

Simple Machines &
Mechanical Advantage
Simple Machines
• A machine is any device that transmits or
modifies force, usually by changing the force
applied to an object.
• All machines are combinations or
modifications of six fundamental types of
machines, called simple machines.
• These six simple machines are the lever,
pulley, inclined plane, wheel and axle,
wedge, and screw.
Mechanical Advantage
• Because the purpose of a simple machine is to change the
direction or magnitude of an input force, a useful way of
characterizing a simple machine is to compare the output
and input force.
• This ratio is called mechanical advantage.
• If friction is disregarded, mechanical advantage can
also be expressed in terms of input and output distance.
Fout
din
MA 

Fin dout
The diagrams show two examples of a trunk
being loaded onto a truck.
• In the first example, a force (F1) of
360 N moves the trunk through a
distance (d1) of 1.0 m. This requires
360 N•m of work. (Work = Fxd)
• In the second example, a lesser
force (F2) of only 120 N would be
needed (ignoring friction), but the
trunk must be pushed a greater
distance (d2) of 3.0 m. This also
requires 360 N•m of work.
A machine uses an input force of 200
newtons to produce an output force of 800
newtons. What is the mechanical advantage
of this machine?
Fout = 800 N
Fin = 200 N
MA = 800N/200N = 4
Another machine uses an input force of 200
newtons to produce an output force of 80
newtons. What is the mechanical advantage
of this machine?
Fout = 80 N
Fin = 200 N
MA = 80N/200N = 0.4
A machine is required to produce an output
force of 600 newtons. If the machine has a
mechanical advantage of 6, what input force
must be applied to the machine?
Fout = 600 N
MA = 6
Fin = Fout/MA = 600N/6 = 100N
An input force of 35 newtons is applied to a
machine with a mechanical advantage of
0.75. What is the size of the load this
machine could lift (how large is the output
force)?
Fin = 35 N
MA = 0.75
Fout = MA x Fin = (0.75)(35N) = 26.25N
A person lifts a 950 N box by
pushing it up an incline. If the
person exerts a force of 350 N along
the incline, what is the mechanical
advantage of the incline?
What is the mechanical advantage
of a lever that allows Jorge to lift a
24-newton box with a force of 4
newtons?
A machine with a mechanical
advantage of 2.5 requires an input
force of 120 newtons. What output
force is produced by this machine?
Levers
Example of a lever
A lever can be made by balancing a
board on a log. Pushing down on one
end of the board lifts a load on the other
end of the board. The downward force
you apply is the input force. The upward
force the board exerts on the load is the
output force.
Parts of the lever
All levers include a stiff structure that rotates around a fixed point
called the fulcrum. The side of the lever where the input force is
applied is called the input arm. The output arm is the end of the
lever that applies the output force. Levers are useful because you can
arrange the fulcrum and the input and output arms to make almost
any mechanical advantage you need.
A construction worker uses a board and
log as a lever to lift a heavy rock. If the
input arm is 3 meters long and the output
arm is 0.75 meters long, what is the
mechanical advantage of the lever?
Lin = 3 m
Lout = 0.75 m
MA = 3m/0.75m = 4
A child’s toy rake is held so that its
output arm is 0.75 meters. If the
mechanical advantage is 0.33, what is
the input arm length?
A lever has a mechanical advantage of 4. Its input
arm is 60 centimeters long. How long is its output
arm?
Lin = 60 cm
MA = 4
Lout = Lin / MA = 60cm/4 = 15 cm
A lever used to lift a heavy box has an
input arm of 4 meters and an output arm
of 0.8 meters. What is the mechanical
advantage of the lever?
What is the mechanical advantage of a
lever that has an input arm of 3 meters
and an output arm of 2 meters?
Sometimes levers are used to
multiply distance. For a broom, your
upper hand is the fulcrum and your
lower hand provides the input force:
Notice the input arm is shorter than
the output arm. The
mechanical advantage
of this broom is:
Ramps
A ramp is another type of simple machine. Using a
ramp allows you to push a heavy car to a higher
location with less force than is needed to lift the car
straight up. Ramps reduce the input force needed by
increasing the distance over which the input force
acts. For example, suppose a 10-meter ramp is used to
lift a car one meter. The output work is work done
against gravity. If the weight of the car is 500
newtons, then the output work is 500 joules
Mechanical advantage of a ramp
The input work is the input force
multiplied by the length of the
ramp (10 meters). If you set the
input work equal to the output
work, you quickly find that the
input force is 50 newtons (Fd = F
× 10 m = 500 J). The input force
is one-tenth of the output force.
For a frictionless ramp, the
mechanical advantage is the
length of the ramp divided by the
height.
A 5-meter ramp lifts objects to a height
of 0.75 meters. What is the mechanical
advantage of the ramp?
A ramp with a mechanical advantage of
6 is used to move a 36-newton load.
What input force is needed to push the
load up the ramp?
MA Solutions
1. 5
2. 1.5
3. 0.5 meters
4. 4.8 meters
5. 0.4
6. 0.8 meters
7. 0.25 meters
8. 6.7
9. 2 meters
10.12 meters
11. 2.4
12. 6 newtons
13. 560 newtons
Honors Mixed MA Worksheet
1. 26 N
2. 3
3. 150 N
4. 1.5
5. 4.8 meters
6. 0.4
7. 0.8 meters
8. 0.25 meters
9. 2.4
10. 6 N
11. 560 N
12. 4 meters
Mixed MA Worksheet
1. 26 N
2. 3
3. 4.8 meters
4. 0.4
5. 0.8 meters
6. 0.25 meters
7. 2.4
8. 6 N
9. 560 N
10. 4 meters