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Energy & Work
(Cont.)
4 Basic Simple Machines

Levers

Inclined planes

Pulleys

Wheel and axle
How much easier is it to do the work (1470J)
with the inclined plane than without?
Mechanical advantage = force without incline / force with incline
Force w/o
Force w
490 N
=
294 N
=
1.66
For inclined planes you get the same number by:
Length of plane
Height of plane
3m
5m
5m
=
3m
= 1.66
1st Class Lever
Effort arm
Fe
Resistance arm
Fr
dr
de
Fulcrum
The work done on one side of the lever must
equal or exceed the work performed by the other
side.

Fe*de ≥ Fr*dr
Resistance arm
Effort arm
Fe
Fr
de
dr
Fulcrum
If we have a 150 kg mass and we need to life it 1 m, and we have
a 1st class lever that is 3 m on the other end, what is the
minimum force necessary to lift the weight?
F = m*a = (150 kg)(9.8 m/s2)
= 1470 kg m / s2
W = F*d = (1470 kg m / s2)(1m) = 1470 kg m2 / s2 = 1470 Joules (J)
Recall : We ≥ Wr
F = W/d
F = (1470 kg*m2/s2)(3 m)
3m
1m
dr
de
= 490 kg*m/s2
= 490 N
Alternative way to look at the problem:
For all simple machines: Win = Wout
But W= F*d, so:
in = effort
out = resistance
Fin*din = Fout*dout
If you know any 3 of these, you can solve for the 4th
Fin =
Fin =
Fout*dout
But Fout=m*a;
din
m*a*dout
din
(150 kg*9.8m/s2)(1 m)
=
3m
= 490 kg*m/s2 = 490 N
Mechanical Advantage

It is a measure of how much easier or harder it is to do
work with a machine
F out / F in

In the previous example = 1470 N / 490 N = 3

For levers, a quick way to determine mechanical
advantage is:

 MA = Effort arm / Resistance arm
What is the mechanical advantage of
the lever system?
in = effort
out = resistance
5 kg
15 kg
R
E
de
15 kg * 9.8 m / s2
F out
=
F in
5 kg * 9.8 m / s2
2nd Class Lever
Resistance arm
Fr
dr
de Fe
Effort arm
Fulcrum
3rd Class Lever
Effort arm d
e
Fe
dr
Fr
Resistance arm
Fulcrum
Radius
Humerus
Ulna
Olecranon
Process
If I am lifting a 25 pound weight with my biceps, what
is the mechanical advantage, and how much force
(minimum) must the biceps apply?
Effort arm d
e
Fe
dr
Fr
What do we need to know?
Resistance arm
Fulcrum
Recall: mechanical advantage is effort
arm/resist. arm
It is about 5 cm from elbow to
point of attachment of muscle
and the whole bone is about
33 cm
Therefore, 5 cm/ 3 cm = 0.15
Recall We = Wr
Fede = Frdr
Fe = Frdr/de
Fe = 25lb.*33cm / 5 cm
= 165 lbs.
Pulleys
W=F*d
W=F*d
W=F*d
W=F*d

Fixed pulleys only change the
direction of a force

They provide no mechanical
advantage
Moveable pulleys supply mechanical advantage
to the number of lines attached to the mass
If the box weights 100 kg, how much force
is needed to lift it without the pulley?
F = ma = (100 kg)(9.8 m/s2) = 980 N
W=F*d
W=F*
d
W=F*d
W=F*d
How much force would you have to use
using the pulley?
For all simple machines: Win = Wout
But W= F*d, so:
Fin*din = Fout*dout
980N*d = F*2*d
980N / 2 = F
490 N = F
F = 490 N
The Wheel and Axle
rwheel

As in all simple machine, Fd = Fd

Circumference of axle = d = 2πraxle

Circumference of wheel = d = 2πrwheel

Therefore, Faxleraxle = Fwheelrwheel

A small force on the wheel translates
into a large force on the axle

A slow velocity on the axle becomes a
fast velocity on the wheel
raxle
Axle
Wheel