FORMULA’S:
Name: ________________________________8___
LEARNING OUTCOME #3: Investigate and describe the transmission of force and energy between parts of
a mechanical system
3a) analyze mechanical devices to determine speed ratios and force ratios
3c) compare theoretical and actual values of force ratios, and propose explanations for discrepancies
Machines are used to make work easier.
CALCULATING MECHANICAL ADVANTAGE: The mechanical advantage is the amount
by which a machine can multiply a force.
Mechanical Advantage (MA) = output force
Input force
MA = OF
IF
Using the pulley system setup:
MA = OF
IF
MA = 180N
45N
MA = 4
What does this 4 mean? The Mechanical Advantage of 4 means:
that the pulley system will multiply the input force by four to get
the output force.
So if the input force to the pulley system was 100N the pulley
system would be able to lift (100N X 4) a 400N load.
CALCULATING SPEED RATIO: Speed Ratio is another way of analyzing how machines
work. Speed measures the distance an object travels compared to the distance the
input force travels.
Speed Ratio (SR) = input distance
output distance
SR = ID
OD
Using the same pulley system setup, but measuring distance
instead.
SR = ID
OD
SR = 4m
1m
SR = 4
What does this mean? The Speed Ratio means that the input
force has to travel four times farther than the input force.
So if the output force moved 5m the input force would have to move (5m X 4) 20m!
IF YOU NOTICED THE MA EQUALS THE SR FOR THE SAME DEVICE!!!
Calculate the following Mechanical Advantage and Speed Ratio for each device used!
MECHANICAL ADVANTAGE
SPEED RATIO
1 Calculate the mechanical advantage
This mechanical device has an input
when it takes 200N to move a 550N
distance of 45m and an output distance of
object.
15m.
2 Hans made a tree branch trimming
machine to help clean up his yard. The
input effort to the machine was 2.7N
but the output was 6N.
Hans’s tree branch trimming machine
needs to be moved 0.5m to cut a distance
of 0.2m.
3 Robert invented a machine that would
do his work for him. His machine used
5.6N and produced 11N.
Robert’s machine moves 2.3m when the
input force moves 5m.
4 Arnold built a machine to help deliver
the morning paper. He had to pull with
38N of force to move a stack of papers
that had a force of 92N.
Arnold’s machine moves the load 1.8m
when the input distance is 6.2m.
Does the MA = SR for the above devices? _______
What do you think accounts for the difference?
Speed Ratio is NOT effected by FRICTION but Mechanical Ratio is!
So Mechanical Advantage will always be lower than Speed Ratio!
5. Can the mechanical advantage of a device be less than one? _______
Think of a bicycle. It has a mechanical advantage of less than one! The output
force causes the bicycle to move much faster than a person can walk, thus a
bicycle is very useful machine.
6. Mechanical Advantage is always LESS THAN Speed Ratio because Mechanical
Advantage is affected by _____________________. Mechanical Advantage is more
realistic than Speed Ratio.
7. We now want to look at the EFFICIENCY of the device.
EFFICIENCY means: the measurement of how well a machine uses the input
energy. Efficiency is measured as a percentage!
EFFICIENCY = MECHANICAL ADVANTAGE
SPEED RATIO
X 100
Eff = MA X 100
SR
8. Calculate the efficiency of the machines in questions 1-4 (formula, substitute in,
answer with units)
#1
Eff = MA X 100
Eff = _____ X 100
SR
Hans
Robert
Arnold
9. THE MORE ENERGY THAT IS LOST BY A MACHINE DUE TO FRICTION
( AS __________) THE LESS EFFICIENT IT IS! Less input energy converted to
output energy!
10. Can a machine be 100% efficient? Explain.
2.2 The Science of WORK!!
LEARNING OUTCOME #3: Investigate and describe the transmission of force and energy between parts
of a mechanical system
3d) identify work input and work output in joules for a simple machine or mechanical system
1. Work is done: when a __________________ acts on an object to make it _____________.
If the object DOES NOT MOVE—no work is done!
WORK = FORCE x DISTANCE
Units for WORK: N·m
W=Fd
(1N·m = 1 JOULE)
2. If you used 50N to lift a chair 0.4m, what is the amount of work done?
W=Fd
W= ____N x ____m
W= ____N·m or ____Joules
3. You used a force of 40N to push a box of books 3.2m. How much work has been
done?
4. A pulley uses 1000N to lift a piano up 10m. How much work is being done?
5. a. Calculate the amount of work needed to lift the box up onto the loading dock.
800N
2m
b. Calculate the amount of work needed to push the box up onto the loading dock
using the incline plane.
c. Is there any difference in the amount of work done in (a) and (b) to get the box to
the top of the loading dock? Yes or No
d. Why would pushing the box up the loading dock seem easier?
FORMULA CALCULATIONS: FORMATIVE ASSESSMENT
Name: ____________________________ 8___
Date: ________________
LEARNING OUTCOME #3: Investigate and describe the transmission of force and energy between parts
of a mechanical system
3a) analyze mechanical devices to determine speed ratios and force ratios
3c) compare theoretical and actual values of force ratios, and propose explanations for discrepancies
3d) identify work input and work output in joules for a simple machine or mechanical system
a. Place the following data onto the simple machine diagram.
-input force: 70N
-output force: 200N
-input distance: 30m
-output distance: 10m
b. This simple machine is called a
____________________________
and the advantage you would get is
__________________________________.
c. Calculate mechanical advantage.
d. Calculate the speed ratio.
e. Why is the speed ratio and mechanical advantage different?
f. Calculate the efficiency for this simple machine.
g. Why is this machine not 100% efficient?
h. Calculate the work done by this simple machine. Be careful on what data you use!
Beginning
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Acceptable
Proficient
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application of the learning
 demonstrates strong academic
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Mastery
 demonstrates exemplary
academic achievement
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and insightful application of the
learning in a variety of situations