Work  Machines  efficiency  lever
 Calculating work  AMA  simple machines   Pulley
 Power  IMA Inclined plane  wheel and axle

Work

Work - A force acting through a distance.

The force must cause motion in the direction of the force for work to be done.

Ex: If a student pushes a wall with all of his strength - he has done no work on the wall (if the wall does not move)

Also a student carrying a book does NO work on the book because the force and motion are NOT in the same direction.

Any time a mass is lifted upward work is done. The force is the weight of the object.

If a person goes up a ladder or a flight of stairs, the force is the weight of the person and the distance is the vertical distance when calculating work

Work is calculated:

W = Fd - remember the d must be in the same direction as the force.

The unit for work is the newton -meter. This is called the Joule named after James Prescott Joule.

Ex 1. What is the work when a force of 10 N pulls a 80 N box a distance of 5.0 m across the floor?

W = Fd = (10N)(5m) = 50 J

Ex 2: What is the work done if the same box is lifted 5 m?

W = (80 n)(5 m) = 400 J

 

Ex 3: What is the work done on the box if a 10 N force applied at an angle of 30 degrees pulls the box 5.0 m across the floor?

This time the force is not in the same direction as the movement. Therefore, you must find the horizontal component of the F (Fx) to determine the work.

Fx = (cos 30)(10 N) = 8.66 N

W = (8.66 N)(5.0m) = 43.3 J

 

 

 

Power

Power is the rate of doing work or how fast the work is done.

To calculate power

P = W/t

The unit of power is J/s which is renamed the watt after James Watt.

Ex. If a student weighing 70 N runs up a flight of steps 25 m high in 3.5 seconds, what is his power?

W = Fd = (70N)(25 m) = 1750 J

P = 1750 J/3.5 s = 500 W or .5 kW

Machines

Machines make jobs easier by:
1. changing the size of the force
2. changing the direction of the
force
3. Increase the speed or distance
an object is moved

Effort force (E) - the force a person
puts into a machine

Resistance force - the force that
must be overcome to do the work

Mechanical Advantage (MA) - the
number of times a machine
multiplies the effort force

Actual Mechanical Advantage (AMA)

AMA = R/E

If you have perfect machine then
you would have Ideal Mechanical
Advantage (IMA)

The efficiency of a machine can be
found in two ways

eff = AMA/IMA x 100%

eff = work out/work in x 100%

 

Work in = Effort X effort distance

Work out = Resistance X R distance


The Six Simple Machines

A simple machine do work with one
movement.

There are two groups of similar
machines

1. Inclined plane, wedge, screw

2. Lever, pulley, wheel and axle

 

Inclined Plane
The IMA of inclined plane is found
by dividing its length by height.

The longer it is the more MA you
get, but you have to do more work,
because your force acts through a
longer distance.

 

Example: An inclined plane 4 m
long is used to lift a piano weighing
1500 n onto the back of a truck 2 m
off the ground. A force of 900n was
needed to push the piano up the
inclined plane.
(A) What was the work in?

W in = 900n x 4 m = 3600 J


(B) What was the work out?

Wout = 1500 n x 2 m = 3000 J


(C) What was the IMA of the inclined
plane? IMA = length/height = 4/2=2
(D) What was the AMA of the
inclined plane?

AMA = R/E = 1500 n/900n = 1.67


(E) What was the efficiency?

eff = 1.67/2 = 83.5% or

eff = 3000 J/ 3600 J = 83.3 %

Lever
The IMA of a lever is determined by
dividing the effort arm by the
resistance arm.
The resistance arm is the distance
from the location of the resistance
to the fulcrum.

The effort arm is the distance from
the location of the effort to the
fulcrum

IMA = EA/RA


Pulley
The pulley is just a round lever with
a fixed fulcrum in the middle. The
effort arm and the resistance arm
are equal in length so the MA of a
round fixed pulley is always 1.
The fixed pulley does not increase
your MA but it does change the
direction of the force making it
easier to lift objects.
A movable pulley can give you a MA
of 2 because two ropes support the
resistance.

Pulley systems (Combinations of
pulleys)
The IMA of any pulley system can be
determined by counting the number
of ropes supporting the resistance.
You can also divide the distance the rope is pulled by the distance the resistance rises.


Wheel and Axle
A wheel and axle is similar to a
pulley but the resistance arm and
the effort arm are not equal lengths.
The radius of the wheel is the
effort arm.
The radius of the axle is the
resistance arm.
Since the radius of the wheel is
always larger than the radius of
the axle the MA is always greater
than 1.

The IMA of a wheel and axle is found
by dividing the radius of the
wheel by the radius of the axle.

IMA =r of wheel/r of axle

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