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Simple Machines – Devices that help do work by changing
the direction or magnitude of the force applied.
Examples: pulley, lever, wheel and axle, inclined plane….
The pulley
- changes the direction of the force or
changes the force supporting the load.
- the mechanical advantage is equal to the
number of ropes supporting the load
What is the Mechanical
Advantage of this system?
With what force does the
person pull down in order
To lift the 400 N weight?
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Example Problem:
A crate of bananas weighing 3000 N is lifted using a pulley.
If 500 N of force is applied (the effort force), what is the
mechanical advantage of the pulley?
M.A. (mechanical advantage) = Force out / Force in
So, M.A. = 3000 N / 500 N = 6
This means that the force needed to lift the crate is reduced
by 6 times the weight of the crate.
Or that the machine multiplies the effort force 6 times.
The Lever
- can change the direction of the force
- can multiply the force of the effort
Three types of levers based on the position of the fulcrum (or
pivot point).
Mechanical Advantage can be calculated using the distances
from the fulcrum or by comparing the forces on each end.
MA = de / dr or MA = Fr / Fe
Example :
A screwdriver is used to open a can of paint. The distance
that the arm is moved downward is 4 cm, while the lid moves
0.5 cm before popping open.
M.A. = distance in / distance out
M.A. = 4 cm / .5 cm = 8
The work on each side of the
lever will also be equal.
force x distance (side 1) = force x distance (side 2)
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The Inclined Plane (Ramp or screw)
- reduces the effort force needed by increasing
the distance through which the force is applied.
10 m
2m
The ideal mechanical advantage is equal to the length
of the run divided by the height of the rise.
M.A. = 10 m / 2 m = 5
Another way to calculate the mechanical advantage:
M.A. = Force out / Force in
Example: A 3500 N piano is moved up a small fight of stairs
by using a ramp. If the piano movers only push with a force
of 500 N, what is the mechanical advantage?
M.A. = 3500 N / 500 N = 7
The Screw is a type of inclined plane.
M.A. = distance in / distance out
Here, the handle is turned through a radius
of 15 cm. For each turn the drill bit enters
.5 cm.
M.A = 2r / h
= 2 (3.14)(15 cm) / .5 cm
= 186
More inclined planes
Wedge
The wheel and axle
- multiplies the effort distance or force
The captain uses a large wheel to apply
a greater force to a small axle which
controls the steering of the ship.
This shows that a small axle (handle)
attached to the grind stone, increase
the distance that the stone wheel moves.
The mechanical advantage is the ratio of the distance the outer
wheel rotates to the inner axle.
MA = de / dr
Here a smaller wheel (or gear)
is used to turn a larger wheel.
More wheels and axles
Example
Jack and Jill go up the hill to fetch a pail of water. When they
get to the well, Jill turns a handle which spins an axle attached
to a wheel. The wheel brings up the water bucket. If Jill applies
a force of 20 N to bring up a 50 N bucket, what is the
mechanical advantage?
M.A. = Force out / Force in = 50 N / 20 N = 2.5
P.S. – Jack fell down…and you know what happened then.
Most machines are a combination of more than one simple
machine. They are called complex machines.
Name 2 machines
this man is using?
A VERY complex machine!
Efficiency
The efficiency of a machine will always be less than 100%.
More work will be put in than we can ever get out.
Efficiency = Work Output / Work Input
Efficiency = Actual M.A. / Theoretical M.A.
Example: If 200 J of energy is expended to get out 150 J of
work, the efficiency is 75%.
This means that 25 % of the energy expended was
lost to the environment as heat energy (because
of friction).