Balancing Forces
Topic
The principle of moments
Introduction
Many forces act to turn an object about a point, e.g., pulling open a door or
using a pair of scissors. Such a turning effect is known as the “moment” about a
point. A moment acts on an object to turn it in either a clockwise or
counterclockwise direction; for an object in equilibrium, these forces are
balanced. This leads to the law of moments, which states that when an object is
in equilibrium, the sum of the clockwise forces equals the sum of the
counterclockwise forces and there is no net turning effect. In this experiment,
you will demonstrate the law of moments using different masses to apply force
to a ruler supported on a fulcrum or pivot (the point on which the ruler is
supported and about which it can turn). The force exerted by such masses is
calculated using the formula:
force exerted by a mass = mass × g
where g is the acceleration due to gravity (its value is 9.8 meters per second
per second)
You will calculate the moment of the forces affecting the ruler when the ruler is
in equilibrium (it is considered to be in equilibrium when it is parallel to the
surface of a bench or table). The moment is calculated using the formula:
moment of a force = force × distance from the fulcrum (pivot)
= mass × g × distance.
Time required
30 minutes
Materials
ruler (between 30 and 60 cm long)
selection of “masses” such as coins, e.g., a nickel can
be used as a 5 gram mass; 4 dimes taped together
make a mass of 10 grams; 10 cents (pennies) taped
together makes a mass of 25 grams (you will need
about six different masses of different sizes)
fulcrum – a 60° prism makes an excellent fulcrum,
otherwise use a piece of cardboard 5 × 20 cm
folded into the shape shown in diagram 1 adjacent
and secured across the base with tape
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1
Cardboard folded to make
a prism-shape
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translucent tape
scissors
balance
calculator
Safety note
Please click the icon to view the general safety precautions.
Procedure
1. Make one of the participants responsible for deciding when the ruler is in
equilibrium (i.e., level).
2. Place the fulcrum at the ruler’s center of gravity (this point is at the center of
the ruler) as in diagram 2 below. You need to make sure the ruler balances by
making small adjustments to its position. When the ruler is balanced (in
equilibrium), a very small change in its position will change one end from
dipping down to going up.
2
ruler
center of gravity of ruler
A
B
fulcrum
Ruler balanced on the fulcrum at its center of gravity
3. Choose two masses of different sizes; these are mass 1 and mass 2 in diagram
3 below. Record the weight of the masses (m1 and m2, respectively) in the data
table on the next page.
4. Gently support the ruler at end B with a hand, while placing mass 1 between
end A and the fulcrum. The distance between this mass (measuring from the
center of the base of the mass) and the fulcrum is d1 and is measured in meters
(see diagram 3 below).
3
d1
mass 1
d2
mass 2
A
B
ruler
fulcrum
Masses at each end of the ruler
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5. While supporting end A, place a mass between end B and the fulcrum. Move
this mass between the fulcrum and end B until the ruler is balanced. The
distance of this mass from the fulcrum is d2 and is also measured in meters
(see diagram 3 on the previous page). Record the values of d1 and d2 in the
data table.
6. Calculate the moments about the fulcrum using the formula given on
pages 1 and 2, and enter the values in the data table.
7. Repeat steps 1 to 6 using different masses and distances from the fulcrum.
DATA
m1
(in grams)
d1
(in meters)
Moment of m1
(m1 × g × d1)
TABLE
m2
(in grams)
d2
(in meters)
Moment of m2
(m2 × g × d2)
Analysis
1. In diagram 3 on the previous page, which mass was tending to turn the ruler
in a clockwise direction?
2. In diagram 3 on the previous page, which mass was tending to turn the ruler
in a counterclockwise direction?
3. In diagram 3 on the previous page, what is the relation between the clockwise
and counterclockwise moments?
4. If two equal masses are used, what can you say about their distance from the
fulcrum if the ruler is to balance?
5. Should the mass of the ruler be considered in the calculations?
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Special Safety Note To Experimenters
Each experiment includes any special safety precautions that are relevant to that
particular project. These do not include all of the basic safety precautions that are
necessary whenever you are working on a scientific experiment. For this reason, it is
absolutely necessary that you read, copy, and remain mindful of the General Safety
Precautions that follow this note. Experimental science can be dangerous, and good
laboratory procedure always includes carefully following basic safety rules. Things
can happen very quickly while you are performing an experiment. Things can spill,
break, even catch fire. There will be no time after the fact to protect yourself. Be
prepared for unexpected dangers by following basic safety guidelines the entire time
you are performing the experiment, whether or not something seems dangerous to
you at a given moment.
We have been quite sparing in prescribing safety precautions for the individual
experiments. We made this choice for one reason: We want you to take very seriously
every safety precaution that is printed in this book. If you see it written here, you can
be sure that it is here because it is absolutely critical to your safety.
One further note: The volume assumes that you will read the safety precautions
that follow, as well as those in the box within each experiment you are preparing to
perform, and that you will remember them. Except in rare instances, these
precautions will not be repeated in the procedure itself. It is up to you to use your
good judgment and pay attention when performing potentially dangerous parts of the
procedure. Just because the book does not say BE CAREFUL WITH HOT LIQUIDS
or DON’T CUT YOURSELF WITH THE KNIFE does not mean that you should be
careless when simmering water or stripping an electrical wire. It does mean that when
you see a special note to be careful, it is extremely important that you pay attention
to it. If you ever have a question about whether a procedure or material is dangerous,
wait to perform it until you find out for sure that it is safe.
GENERAL SAFETY PRECAUTIONS
Accidents caused by carelessness, haste, insufficient knowledge, or taking
unnecessary risks, can be avoided by practicing safety procedures and being alert
while conducting experiments. Be sure to check the individual experiments in this
book for additional safety regulations and adult supervision requirements. If you will
be working in a lab, do not work alone.
PREPARING:
—Clear all surfaces before beginning experiments
—Read the instructions before you start
—Know the hazards of the experiments and anticipate dangers
PROTECTING YOURSELF:
—Follow the directions step-by-step; only do one experiment at a time
—Locate exits, fire blanket and extinguisher, gas and electricity shut-offs, eyewash, and first-aid kit
—Make sure there is adequate ventilation
—Act sensibly at all times
—Wear an apron and safety glasses
—Do not wear open shoes, loose clothing, or loose hair
—Keep floor and workspace neat, clean, and dry
—Clean up spills immediately, being careful to follow the recommended procedure for dealing with
the split substance
—Never eat, drink, or smoke in the laboratory or workspace
—Do not eat or drink any substances tested unless expressly permitted to do so by a knowledgeable
adult
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USING EQUIPMENT WITH CARE:
—Set up apparatus far from the edge of the desk
—Use knives and other sharp or pointed instruments with caution
—Pull plugs, not cords, when removing electrical plugs
—Don’t use your mouth to pipette liquids; use a suction bulb
—Check glassware is clean and dry before use
—Check glassware for scratches, cracks, and sharp edges
—Report broken glassware immediately so that it can be cleaned up by a responsible person
—Do not use reflected sunlight to illuminate your microscope
—Do not touch metal conductors
—Use only low voltage and current materials such as lantern batteries
—Be careful when using stepstools, chairs, and ladders
USING CHEMICALS:
—Never taste or inhale chemicals
—Label all bottles and apparatus containing chemicals
—Read labels carefully
—Avoid chemical contact with skin and eyes (wear safety glasses, lab apron, and gloves)
—Do not touch chemical solutions
—Wash hands before and after using solutions
—Wipe up spills thoroughly
HEATING SUBSTANCES:
—Wear safety glasses, apron, and gloves when boiling water
—Keep your face away from test tubes and beakers
—Use test tubes, beakers, and other glassware made of Pyrex™ or borosilicate glass
—Use alcohol-filled thermometers (do not used mercury-filled thermometers).
—Never leave apparatus unattended
—Use safety tongs and heat-resistant mittens
—If your laboratory does not have heat-proof workbenches, put your Bunsen burner on a heat-proof
mat before lighting it
—Take care when lighting your Bunsen burner; use a Bunsen burner lighter in preference to wooden
matches
—Turn off hot plates, Bunsen burners, and gas when you are done
—Keep flammable substances away from heat
—Keep sheets of paper and other flammable objects away from your Bunsen burner
—Have a fire extinguisher on hand
FINISHING UP:
—Clean your work area and glassware (follow any instructions given by a supervising adult)
—Be careful not to return chemicals or contaminated reagents to the wrong containers
—Don’t dispose of materials in the sink unless instructed to do so
—Wash your hands
—Clean up all residues and put in proper containers for disposal
—Dispose of all chemicals according to all local, state, and federal laws
BE SAFETY CONSCIOUS AT ALL TIMES
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Settings And Warning Signs
Settings and hazard warning signs are used throughout the experiments to indicate where they should
take place and where particular care should be taken with the materials involved.
SCHOOL LAB
HOME
TOXIC
SPLASH
WARNING
IRRITANT
NAKED FLAMES
HOT LIQUIDS
CORROSIVE
CUT / STAB HAZARD
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10.01 • OUR FINDINGS
PHYSICS EXPERIMENTS ON FILETM
Forces
1.01 Finding The Point Where An Object’s Mass Acts
Part A: Determining the center of gravity of a flat shape
1. The point where the lines meet is the center of gravity of the shape.
2. The shape should balance on the end of a finger if it is placed at the center of
gravity of the shape.
Part B: Equilibrium
1. As the object is a regular shape, the center of gravity will be a point at the
object’s center.
2. The weight of an object acts straight down in a line from its center of gravity.
When an object is tilted, it remains stable only while this line remains within
its base (see the diagram below).
D is the least stable object, as it has a narrow base.
B is the second object to fall because its center of gravity is higher than the
others. Tilting the board causes its center of gravity to move beyond its base,
causing it to topple before A, which has a lower center of gravity.
C is the most stable object because it has the widest base.
weight acting down from
center of gravity
Direction of action of the weight of an object
1.02 Balancing Forces
1. Mass 1 tends to turn the ruler in a counterclockwise direction.
2. Mass 2 tends to turn the ruler clockwise.
3. The clockwise forces equal the counterclockwise forces when the ruler is in
equilibrium. This is the principle of moments.
4. If two equal masses are used, they should each be at the same distance from
the fulcrum (on opposite sides) if the ruler is in equilibrium.
5. Because the ruler is supported on the fulcrum at its center of gravity, you do
not need to consider its mass. This is because the force exerted by the mass
acts directly down through the fulcrum and therefore has no turning effect.
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