DEFINITION OF A MACHINE:
Machines
are
designed to make
your
life
_________. If
they didn’t, there
would be no point
in using them.
A machine is a device for either
multiplying forces or changing the
direction of forces. Machines cannot
multiply work. If they did they would
violate the ___________________
___________________________.
KINDS OF SIMPLE MACHINES:
In the blanks provided, label the seven simple machines shown below.
________________
________________
________________
________________
________________
________________
________________
The following items are examples of which kinds of simple machines?
________
________
________
________
THE MECHANICAL ADVANTAGE OF A MACHINE:
In ideal conditions, all the work you put in on one side of a machine (Win) comes
out the other side of the machine (Wout). In practice, however, some of the
energy (work) you put in is “lost” as ____________ energy.
Workin
Workout
This "loss" is a result of the presence of _______________________ between
the parts of the machine.
The MECHANICAL ADVANTAGE a machine gives to its user is the ratio of the
Output Force (Fout) to the Input Force (Fin).
OUTPUT FORCE : INPUT FORCE or
Fout
Fin
*** REMEMBER: The Input Force is the force the USER applies. The Output Force is what results at
the other end of the machine (what lifts, pulls, pushes the LOAD).
The THEORETICAL MECHANICAL ADVANTAGE is the benefit the machine gives to
a user in ideal conditions with no friction present. The ACTUAL MECHANICAL
ADVANTAGE is the benefit the machine gives you in the real world (where friction
exists). Obviously, the actual mechanical advantage is always __________________
than the theoretical mechanical advantage.
 PROBLEMS:
If you were using a machine that required only an INPUT force of 80 N to obtain
an OUTPUT force of 16,000 N, what would be that machine’s mechanical
advantage? __________________
If a machine could lift 80 N of weight with only 20 N of human effort on the other
end, what is the machine’s mechanical advantage? __________________
Fin = 10 N
Fout = ?
If a machine has a theoretical mechanical advantage
of 4, and the INPUT FORCE is 10 N, what OUTPUT
force is possible? __________________
If a machine has an actual mechanical advantage of 4, and the INPUT FORCE is
10 N, what OUTPUT force is possible? __________________
What is the ratio of OUTPUT distance to the INPUT distance if a machine has a
mechanical advantage of 10? __________________
HINT: The mechanical advantage interestingly enough can also be expressed
as the ratio of the INPUT DISTANCE TO THE OUTPUT DISTANCE (as
opposed to the OUTPUT FORCE : INPUT FORCE).
THE EFFICIENCY OF A MACHINE:
The efficiency of a machine is the ratio of useful work output to total work input
(or the actual mechanical advantage vs. theoretical mechanical advantage)
Efficiency

Wout MAactual

Win
MAtheor
No machine is 100% efficient. Gasoline powered
cars, for example, are at most 40% efficient. The
rest of the energy is dissipated through heat
losses due to friction, etc.
 PROBLEMS:
What is the efficiency of a machine that gives 1.85 Joules of useful work out for
every 3.25 J of work put in? __________________
If a machine is 60% efficient and has a theoretical mechanical advantage of 5:1,
what is the actual mechanical advantage it gives a person using it? __________
Which is more efficient: a machine that has an actual
mechanical advantage of 8 : 3 and a theoretical mechanical
advantage of 12 : 3, or a machine that yields 220 J of useful
work out for every 550 J of work put in ? _________________
THE LEVER
There are three kinds of levers. Name them below and draw each in terms of
the fulcrum’s location, the input force’s location, and the output force’s location.
The DISTANCES used to calculate the
WORK done using a lever are the arc
lengths through which the lever arms
move.
BUT…
If WORK is not necessary
to solve the problem, using the
distances from the forces to the
fulcrum are more convenient for
comparison purposes because
they are simple straight-line
distances so you don't have to
mess with curves.
dout
din
dout
din
EXAMPLE: If it requires 1000 N of input force to lift a load of 2550 N and the
load is 2 m away from the fulcrum, how far away from the fulcrum
should the input force be applied?
Ans. The Force/distance relationship is proportional.
d
Fin
1000N 2m
 out so…

Fout
din
2550N din  1000din = 5100  din = 5.1 m
but… the Work is NOT 1000 N X 5.1 m = 5100 Joules however, because the din
is not in the same direction as the FORCEin!!! As mentioned earlier, to calculate the
work, the arc lengths would have to be used for the distances.
 PROBLEMS:
A. Andres wants to lift a 120,000 N car
off the ground. The car is 0.2
meters from the fulcrum. If Andres
can exert a force of 1320 N on his
side of the lever, how far away from
the fulcrum should he apply the
force?
___________________
In each of the following lever arrangements, label the INPUT FORCE (Fin), the
OUTPUT FORCE (Fout), the INPUT DISTANCE (din) and the OUTPUT
DISTANCE (dout). Be sure that as the fulcrum’s position changes, the size of the
arrows you use to represent the forces change accordingly.
Label the fulcrum and the location
of the input and output forces in
the simple machines shown at
right. What kind of levers (Type I,
Type II, or Type III) are they?
__________________
_______________
dout
din
BillyBoBob wants to get a load of
fertilizer up to a height where he can
load it on his pickup.
_____________ a. Through what arc
length should BillyBoBob apply a force
of 2400 N if he wishes to raise a 5000
N load through an arc length of 0.4 m?
_____________ b. If the lever arm from the fulcrum to BillyBoBob is 5 m,
what part of the circle is the arc through which he must
apply the force of 2400 N?
_____________ c. If the distance from the fulcrum to BillyBoBob is 3 m,
through what angle did he apply the force? (Hint: s = r)
THE INCLINED PLANE
An inclined plane is a simple machine that connects a higher level to a lower
level. The inclined plane, as with all machines, makes it “easier” to move things
at the expense of the distance through which they must be moved.
Label the illustration above with the INPUT FORCE (Fin), the OUTPUT FORCE
(Fout), the INPUT DISTANCE (din) and the OUTPUT DISTANCE (dout).
 PROBLEMS:
If in the figure above, the large force (F) was 300 N, the small distance (d) was 2 m,
and the “small” force (f) was 80 N, how long would the ramp have to be?
_________.
The total work done in raising a box through a vertical distance of three meters
is 4000 J. With how much force would a person have to push the same box, if
he/she used a ramp that was 12 meters long? _____________________
It requires 4000 J of work to lift a box
from the ground to the top of the ramp
shown. If the weight of the box is 500 N
and the ramp is 15 meters long, what is
wrong with this problem?
________________________________
_______________________________.
A 35° inclined plane that is 3 meters long leads to the
incinerator. If it requires 400 N of force to move a
crate full of fake CD's up the inclined plane,
15 m
500 N
3m
400 N
_____________ a. how high is the incinerator off
the ground?
 = 35
_____________ b. how heavy is the box?
An inclined plane that is 2.5 meters long and 1
meter high leads to the incinerator. If it requires
800 N of force to move a box full of trash picked
up by JQM up the plane,
_____________ a. what is the angle  of the
inclined plane?
2.5 m
1m
800 N
=?
_____________ b. how heavy is the box?
An inclined plane that is 4 meters long and has a base of length 2.2 meters
leads to the incinerator. If it requires 200 N of force
to lift a crate full of used disciplinary action forms to
200 N
4m
the height of the incinerator,
_____________ a. how high is the incinerator off
the ground?
2.2 m
_____________ b. how much force would it take to move the crate to the
incinerator up the inclined plane?
THE WEDGE
The wedge is simply a moving ________________________.
Normally an inclined plane is stationary and objects (such as boxes) are moved
up its slope. A wedge, on the other hand, is jammed under, between, or into
objects. As with every machine, the wedge works to minimize the effort put in
by the user so as to maximize the output force on the other end but always at
the expense of _____________.
In the illustration of a wedge used as
a door jamb at right, draw and label
the input and output distances and
forces f (small force), F (big force), d
(small distance), D (big distance).
In the illustration of a wedge used
as an axe in the picture at left,
draw and label the input and
output forces f (small force), F (big
force). Make sure you draw the
input and output arrows to scale
with each other.
 PROBLEMS:
If a wedge is jammed under a door a distance of
0.1 m by a force of 200 N, how far up will the door
move considering that the upwards force is 980 N?
_______________ .
?
0.1 m
Which of the wedges shown at right are "easier" (require less input force) to use
(they are drawn to scale with each other)? Why?
__________________________________________
__________________________________________
__________________________________________
__________________________________________
__________________________________________
THE PULLEY
The pulley is just a modified lever. It is a very useful for two reasons. It can be
used to:
a. ______________________________________
b. ______________________________________
a. Change the direction of the force.
TYPE I LEVER
output
The single pulley in the following illustration
behaves as a type I lever. The axis of the
pulley acts as the fulcrum of the lever and
both lever distances (the radii of the pulley
are equal in length, so the pulley does not
magnify force, it simply changes its
direction (the person can pull down to get
the load to go up). Note that the input
distance and output distance will be the
same (the amount of rope that the person
pulls down will be the same as the amount
of distance the load rises)
input
axis or fulcrum
output
input
b. Multiply or Magnify the Force.
In the illustration to the right, the single
pulley acts as a type II lever. The fulcrum
in this case is the left edge of the lever
(where the rope that is tied to the ceiling
makes contact with the pulley wheel). The
load (which is where the output force is
being applied) is suspended half way
between the fulcrum and the input force
(the input force is located where the rope
that the user is holding makes contact with
the pulley wheel). By conservation of
output
input
input


TYPE II LEVER
output
axis or fulcrum
energy and the principles we learned
earlier about the lever, one need only apply
half as much force as input when the input
force is applied twice as far from the
fulcrum as the output force (fD = Fd). The
pay-off is that one will have to apply this
smaller force through twice the distance.
How a pulley multiplies a force can also be interpreted in terms of the tension in
a string and equilibrium of forces.
In the illustration of a pulley system at
right, the system is at rest. In order for
this to be true, what must be true about
the sum of the forces upward and the
sum of the forces downward?
_____________________________

In the illustration at right, draw the
arrows that represent where these
forces are acting (to scale with each
other).
The multiplication of force (the same thing as mechanical advantage) available
to a user of a pulley is easy to obtain. The user needs only to count the number
of ropes/rope segments that are holding up the load. So, as in the above
illustration, the ratio of the output force to the input force, is 2: 1 because the
user can lift 2 N of weight with only 1 N of applied force. The catch is of course,
that the user apply this 1 N of force over twice the distance that the load moves…
 PROBLEMS:
In the illustration shown at right, although there
are three rope segments present, only two
actually support weight. Which are they and
what is the third rope doing in this pulley
arrangement?
A
B
C
_________________________________________
_________________________________________
_________________________________________
In the illustration at right, draw the arrows
that represent where the forces are acting
(to scale with each other).
_______ What is the mechanical advantage of the pulley shown?
THE WHEEL AND AXLE
The wheel and axle can be thought of as a circular lever. The fulcrum is the
center of the axle. The input force is applied to the wheel’s outer rim. The
output force is applied to the axle’s outer rim… The distances in a wheel and
axle machine are the distances through which the wheel turn (input distance)
and the distance through which the axle turns (output distance).
NOTE: Once again, as with the lengths of the lever
arms in the lever, although the radius of the axle and
dout
the radius of the wheel cannot be used to calculate
the WORK done, they can be used to compare the
din
input and output forces!!!
Example: If the outer radius is twice as large as the
inner radius then the output force will be twice as
large as the input force. As mentioned before, to calculate work, the arc lengths
should be used for distance.
Din
dout
axle is fulcrum
 PROBLEMS:
.
output
FORCE
input
force
A screwdriver applies a force of 2978 N to the head of a screw and turns a
distance of 0.25 m.
_______________ a. Through what distance must the screwdriver handle have
turned if the input force is 168 N?
_______________ b. How many rotations of the screwdriver does that
distance correspond to if the screwdriver handle has a
radius of 0.04 m?
THE SCREW
The screw is simply an _____________ wrapped around a shaft or cylinder.
The screw just allows the user to apply the forces in a circular motion rather
than in a linear one.
As with all machines, the input force is smaller, but consequently, the screw
must be turned many times (through many revolutions and hence, a lot of
distance) to produce a considerable output force over just a short distance on
the other end (the distance into the wood that the screw penetrates).
In the illustration of a screw shown at
right, label the screw with an F (BIG
FORCE), D (BIG DISTANCE), f (small
force), d (small distance).
PITCH
Another way of comparing the amount of input force
that you have to apply to the screw is the PITCH of the
threads of the screw. The PITCH is the distance
between adjacent threads on a screw (as shown in the
illustration). If we compare how far a screw with a
large pitch goes into a piece of wood and how far a
screw of the same size, length, and shape but with a small pitch goes into
a wood, we will find that the larger pitched screw will penetrate _____________
into the wood after “x” number of turns of the screw head are applied to both.
But if what was just mentioned is true then what must be true of the input force
applied to a large-pitched screw vs. the input force applied to a small pitched
screw? ______________________________.
Compare hammering a nail into a piece
of wood and screwing in a screw of the
same mass, size, and shape into the
same piece of wood the same distance.
Which
of
the two
machines
requires greater input distance?
greater input force? Explain.
_______________________________
____________________________________
_______________________________
_______________________________
_______________________________
_______________________________
Which of the two machines has the
greater mechanical advantage (all other things being equal)?_______________
The spiral staircase is an example of the screw applied on a large scale.
What is the advantage of the spiral staircase in the following comparison of two
ladies climbing a tower? ___________________________________________
________________________________________________________________
What is the disadvantage of the spiral staircase? ________________________
________________________________________________________________
Can you identify the PITCH in the illustration of the spiral staircase (draw it in)?
Would it be easier or harder if the staircase had a smaller “PITCH”? ________
_______________________________________________________________.
THE GEAR
Gears are pairs on interlocking toothed wheels that transmit force and motion in
machines. Gears can do any one of the following three things:
a. _____________________________________________________
b. _____________________________________________________
c. _____________________________________________________
a. Gears change the direction of the applied (input) force.
In a gear train (a system of at least
two gears), one gear is the driving
gear or driver. One gear is the driven
gear. The driver is associated with
which force?
_____________The
driven gear is associated with which
force? ____________ Label the
driver and the driven gear in the
illustration to the right.
If the driving gear in the illustration is spinning clockwise, in what direction will
the driven gear spin? ___________________ Draw arrows on the illustration
above indicating the direction of motion of each gear.
In the following gear trains draw arrows indicating the direction of motion of the
gears given that the driven gear is moving…
a. Clockwise
b. Counter-clockwise
c. Clockwise
Driven
Gear
Driven
Gear
b. Multiplying force
The gear is subject to the same
relationship that the other machines
follow. The distance through which a
gear train turns can be interpreted several
ways for comparison purposes:
drivers
i. in terms of the number of times the driver
turns compared to the number of times
the driven gear turns
ii.
by comparing the number of teeth that
each gear has.
iii. by comparing the radii of the gears.
If the driver gear has twice as many teeth as the driven gear, then it will also
have twice the radius of the driven gear and will only turn once for every two
times the driven gear turns…
In the following illustrations a mark has been painted at the bottom point of each
gear. Draw the gears and label the new position of the marks after the driver
has gone through…a. …¼ turns,
b. …½ turns, c. …¾ turn, d. …one full turn
Do the above for the following two cases.
I. The driver has twice
as many teeth as
the driven gear
a.
b.
c.
d.
driver
II. The driver has half
as many teeth as the
driven gear
a.
b.
c.
d.
driver
As you can see, from the above examples, the larger the gear size (however
you may interpret that…”fewer turns,” “more teeth,” or “larger radius”), the less
distance the gear turns compared to a gear of smaller size (i. e. “smaller radius”,
“more turns”, “fewer teeth”).
If f D = Fd is to hold true, then the larger gear (which travels less distance)
must offer up ____________________ force.
Label the following illustrations
correctly with f (small force), F
(large force), d (small distance),
and D (large distance).
a.
b.
driver
driver
c. A real-life example of using gears.
The bicycle employs a gear train to adjust how much force the rider can
transfer from the front sprocket (the chain ring to which the pedal is attached)
to the rear wheel sprocket (which applies the force to the wheel for motion)
A chain is used to transfer the force between the gears (driver and driven
gears) and ideally does not affect the force transfer.
c
If you wanted to go down a hill on a multi.b
speed bicycle, which front chain ring would
a.
you want your chain to be on? Why?
_________________________________
.
__________________________________
___________________________________
_____________________________________
d. Do the following gear problems:
1. The driver gear has 14 teeth and provides a force of 300 N to the driven
gear. If the driven gear delivers 1200 N to a shaft attached to it, how many
teeth does it have?
2. A driven gear has a radius of 0.5 m and the driver gear has a radius of 2 m.
What is the mechanical advantage of this gear train?
3. What is the output force of a gear train if the input force is 220 N and the
driver gear turns ½ a turn for every turn of the driven gear?