Fulcrums
Finding the point of support
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OBJECTIVES
Students will balance weights about a
fulcrum
Students will calculate the moment
about a fulcrum
Students will learn about fulcrums
and moment.
MATERIALS
toilet paper roll
6” of masking tape
ruler (symmetric about 6” mark)
6 pennies
CORE LEARNING GOALS
1.1.3 The student will apply addition,
subtraction, multiplication, and/or division
of algebraic expressions to mathematical
and real-world problems.
1.2.5 The student will apply formulas
and/or use matrices (arrays of numbers) to
solve real-world problems.
2.2.1 The student will identify and/or
verify congruent and similar figures and/or
apply equality or proportionality of their
corresponding parts
CALCULATOR SKILLS
 Simple calculations using order of
operations.
EQUATIONS
M=Fxd
F = weight = mass x accel. = mass x
gravity
ACTIVITIES
1. Hands-On Activities
2. Discussion
3. Think, Pair, Share
ADDITIONAL RESOURCES
http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=41
Fulcrums
Finding the point of support
TEACHER GUIDE
Lesson/Background:
- Forces can be generated in many ways. Some forces are caused by external
elements such as wind, rain, snow, and earthquakes. Force is exerted on a body by the
element. For example, the weight of snow causes a force to act upon a roof.
- A moment is a force times a lever arm or distance. Here the lever arm is the
distance from the pivot point of the object to the location of the force. The pivot point
can also be called the fulcrum.
- The moment of force is a force applied to a body may produce rotation about
some axis. You can easily see this if you push against an open door. Try pushing a door
at the handle, at the center, and right at the hinge. The further out from the hinge you
push, the less force you need to move the door. The effectiveness of a force in setting a
body in rotation is known as the moment of force. It is measured by the product of the
force times the length of the lever arm (here, the distance outward from the hinge.)
M=Fxd
Where:
M = moment of force
F = force
d = distance from fulcrum
- In order for a body to remain stationary, the moments must be equal and
opposite.
- The fulcrum is the support or point of support on which a lever turns in raising
or moving something. On a door that is open and free to swing, the fulcrum is the hinge.
Hands On:
Experiment #1:
1. Secure the toilet paper roll to your desk with the piece of masking tape.
2. Balance the ruler horizontally on the roll. It will probably balance when the 6 inch
mark is centered on the roll. The ruler is your lever and the toilet paper roll acts as the
fulcrum.
3. Balance one penny on each side of the roll so the ruler remains horizontal. Record
how far each penny is fro the fulcrum.
Teacher Tip:
Each group will probably place their penny at different distances. However, the pennies
should be equidistant from the fulcrum to make it balance.
4. Balance two pennies on the right side of the fulcrum and one penny on the left. Mae
sure the ruler remains horizontal. Record how far the pennies are from the fulcrum.
Teacher Tip:
The stack of 1 penny should be twice as far from the fulcrum as the stack of 2 pennies.
Teacher Tip:
This experiment is demonstrated in the movie: fulcrum.mpg
Discussion:
The Moment of Force is calculated by multiplying the force by the distance from the axis
of rotation.
M=FxD
For now, moments in the clockwise direction will be positive and moments in the
counterclockwise direction will be negative. The ruler will remain horizontal when the
sum of the moments is ZERO.
The pennies are exerting a force on the ruler at a distance from the fulcrum. The amount
of force the pennies exert is equivalent to their weight. We measure force in Newtons or
pounds force.
F = weight = mass x acceleration = mass x gravity
1. Calculate the moment created by 2 pennies placed 8 cm to the right of the fulcrum if:
mpenny = 2.50 grams and gravity = 9.8 m/s2
Answer:
F = weight = mass x acceleration = mass x gravity = 2(2.5g) x (9.8 m/s2) = 49N
M = F x d = 49N x 0.008m = 0.392N . m
2. Think of 3 different configurations of pennies that can be placed on the left side of the
ruler that will make it balance. In other words, the pennies on the left side must create an
equal and opposite moment to cancel out the moment created by the pennies on the right
side. Test your 3 configurations mathematically and experimentally.
There are many solutions to this problem. For each solution, the weight of pennies times
the distance from the center must be the same for each side.
THINK, PAIR, SHARE:
Can you think of how you would use a lever like a see-saw to move something that is
very heavy?
Place a board under the heavy object. Place a fulcrum under the board and close to the
object. Exert a force (i.e. push) on the other end of the board far away from the fulcrum.
The idea is to create a moment as large as the one created by the heavy object by using a
smaller force and a larger distance.
Fulcrums
Finding the point of support
Student Worksheet
Experiment #1
1. Secure the toilet paper roll to your desk with the piece of masking tape.
2. Balance the ruler horizontally on the roll. It will probably balance when the 6 inch
mark is centered on the roll. The ruler is your lever and the toilet paper roll acts as the
fulcrum.
3. Balance one penny on each side of the roll so the ruler remains horizontal. Record
how far each penny is fro the fulcrum.
4. Balance two pennies on the right side of the fulcrum and one penny on the left. Mae
sure the ruler remains horizontal. Record how far the pennies are from the fulcrum.
Discussion Questions
1. Calculate the moment created by 2 pennies placed 8 cm to the right of the fulcrum if:
mpenny = 2.50 grams and gravity = 9.8 m/s2
2. Think of 3 different configurations of pennies that can be placed on the left side of the
ruler that will make it balance. In other words, the pennies on the left side must create an
equal and opposite moment to cancel out the moment created by the pennies on the right
side. Test your 3 configurations mathematically and experimentally.
THINK, PAIR, SHARE:
Can you think of how you would use a lever like a see-saw to move something that is
very heavy?