centre de
développement
pédagogique
Pour la formation générale
en science et technologie
Nail claw (claw hammer)
Pencil sharpener
LEVERS
- Theory Lever to lift a rock
Working Documenl
Bicep curl
SECTION
JUNE 2004
A
CONCEPT OF “LEVER”
This practical lab is intended to help participants:
• understand the concept of “lever”
• acquire the vocabulary associated with this concept
• recognize levers in everyday objects
Following this lab, participants should be able to use levers in concrete
applications (i.e. in the design of technical objects).
This companion document comprises three sections:
• Theoretical aspects
• Experiments with simple materials (“classic” levers)
• Experiments with materials used in everyday objects
Record your observations and results throughout the process.
Have fun!
2
Centre de développement pédagogique
pour la formation générale en science et technologie
Theory
To Read . . . and Reread
3
Centre de développement pédagogique
pour la formation générale en science et technologie
What is a force?
If an object moves, a force is being applied to it (it is being pushed or pulled).
An object cannot move, activate, accelerate, slow down, change direction, stop or distort without a force
being applied.
What produces force?
Energy is what produces force. It makes it possible to perform a task. A person can lift a dumbbell using
muscle energy. This energy makes it possible to apply a force to the dumbbell.
Only for those who want to know more
The concept of force is one of the foundations of mechanics and is closely tied to the concept of motion
and the principle of inertia. A force may be defined as:
the only effect likely to alter the motion of a body
Thus, a body in motion tends to continue in a straight line unless acted upon by an external force (principle
of inertia). The following equation is the mathematical version of this definition:
F = ma
where F is the vectorial sum of all forces applied to a body of mass m (mass considered constant in this
case) and a is its acceleration (i.e. the variation in its speed). If F = 0, the body undergoes n° acceleration (a
= 0), its speed is constant and the principle of inertia comes into play.
4
Centre de développement pédagogique
pour la formation générale en science et technologie
A force is a mechanical action that can:
- cause an object to move
- modify the speed and trajectory of an object
- distort an object
The symbol for mechanical action is an arrow (F ), referred to as FORCE.
Force is entirely determined by four properties:
- point of application
- orientation
- direction
- intensity (amount of force)
A force’s intensity is measured in newtons (N) using a dynamometer.
Types of force:
o Tension (force that stretches)
o Compression (force that crushes)
o Torsion (force that twists)
o Shear (force that cuts)
o Flexion (force that bends)
These are the most common forces applied to and by technical objects.
Other types of forces also exist, such as friction, buoyancy (Archimedean force), pressure,
centripetal force and inertia.
Teacher’s note :
For students, effort and force are usually applied by muscles, which results in fatigue.
Understanding that an inert object can apply a force on another object is a difficult concept.
We therefore suggest that you use the physics term “force,” rather than “effort” or “action,” which
are more likely to conjure up intervention by a living organism.
The word “effect” refers to the concept of the moment of force.
Moment is equal to the product of the distance of the lever arm from the fulcrum and the intensity
of the force. This concept will be discussed in more detail later in the document.
Moment arm
Fulcrum
Force application point
Force
5
Centre de développement pédagogique
pour la formation générale en science et technologie
Levers
Generally speaking, a lever is a rigid body that can turn about a fulcrum and that is subject to at least two
forces known as “effort” and “load.”
Levers are used in a wide range of machines.
We will now define and illustrate three types of levers:
1) Those where the fulcrum is placed between the effort and the load (seesaw)
2) Those where the load is placed between the fulcrum and the effort (nutcracker)
3) Those where the effort is placed between the fulcrum and the load (sugar tongs)
1
1 First-class levers
Effort
Load
The fulcrum is placed between the
effort and the load (e.g. seesaw).
Fulcrum (rotation axis)
2
2 Second-class levers
Load
Effort
The load is placed between the
fulcrum and the effort
(e.g.nutcracker).
Fulcrum (rotation axis)
3
Load
3 Third-class levers
Effort
The effort is placed between the
fulcrum and the load (e.g.
tweezers).
Fulcrum (rotation axis)
6
Centre de développement pédagogique
pour la formation générale en science et technologie
The lever arm of a force applied to a solid is the distance from the fulcrum to the line of action of this
force F. Equilibrium is reached when the algebraic sum of the moments of forces in relation to the fulcrum
is zero. This means that two forces must be applied in opposite directions at equal intensities in relation to
the lever arm.
Weight of a child F 2
Weight of an adult F 1
Lever arm r1
Lever arm
r2
Archimedes’* law of levers maintains that unequal forces applied perpendicularly to the ends of a rod that
pivots are balanced if:
F 1x r 1=F 2xr 2
where r 1 and r 2 are the distances between the fulcrum and the force application points. Both the forces
and their distances from the fulcrum must be taken into account.
The moment of force is the measurement of the torque produced about a specific axis. It is the magnitude
of a force multiplied by its distance. The product of the force generated through the lever arm is
expressed in newton-metres.
Moment arm
Fulcrum
Force application point
Force
*Archimedes (287-212 BC) was the first person to establish the laws of equilibrium. He claimed that if he were given a long
enough lever arm he could lift the Earth.
7
Centre de développement pédagogique
pour la formation générale en science et technologie
Note: The mechanic’s torque wrench measures torque. This torque is commonly known as “torque.”
Torque wrenches used in North America are often calibrated in foot-pounds rather than newton-metres.
Moment arm
Fulcrum
Force application point
Force
In technical diagrams, the following symbols
are used to represent applied force:
F
because the ‡ symbol is
used to indicate linear motion..
Mechanical Advantage or Disadvantage
When designing a lever, designers must work with an energy source that can perform the work the
machine requires. They must often use levers to make the work of a user or component easier. A
machine is said to have a mechanical advantage when the effort force required is less than the load
force. It is expressed by a number indicating the ratio between the effort force and load force. If the
applied force is four times less than the value of the load force, the mechanical advantage is said to be 4.
Force and Movement
When forces are applied to a lever with a mechanical advantage, the lever’s movement at the effort
force application point is greater than that of the load force. As such, what is gained in force is lost in
distance covered.
Effort force
application point
Ai
Distance D
Load to lift
Fulcrum
Load force
Distance d
Af
Lifting lever
Ai: Initial position of force application point
Af: Final position of force application point
8
Load force
application
point
Centre de développement pédagogique
pour la formation générale en science et technologie
centre de
développement
pédagogique
Pour la formation générale
en science et technologie
Nail claw (claw hammer)
Pencil sharpener
LEVERS
- Lab Lever to lift a rock
Working Documenl
Bicep curl
SECTION
JUNE 2004
B
CONCEPT OF “LEVER”
This practical lab is intended to help participants:
• understand the concept of “lever”
• acquire the vocabulary associated with this concept
• recognize levers in everyday objects
Following this lab, participants should be able to use levers in concrete
applications (i.e. in the design of technical objects).
This companion document comprises three sections:
• Theoretical aspects
• Experiments with simple materials (“classic” levers)
• Experiments with materials used in everyday objects
Record your observations and results throughout the process.
Have fun!
2
Centre de développement pédagogique
pour la formation générale en science et technologie
An Experiment
For You to Try
EXPERIMENTING WITH THE MATERIALS
Now that you have learned the theoretical aspects of levers, it’s time to conduct an experiment using
the following materials :
- Material A includes marked weights and a plastic plate that is screwed to a vertical mount
- Material B includes dynamometers (devices used to measure force) and a plastic plate bolted
to a perforated panel
Arrange the components to create the different types of levers.
Write a report on your observations and check the math.
How do you plan to present your results?
The holes are
1 cm apart.
A
B
A few pictures
Do you understand what happens when there
are two forces (effort and load)? Now try using
two load forces and one effort force.
What happens?
FIRST-CLASS LEVER
EXPERIMENT REPORT
Diagram of your assembly, indicating forces, lever arms and fulcrum
1 cm d’entraxe
Mathematical explanation
Explanation of your results (mechanical advantage, distance covered)
SECOND-CLASS LEVER
EXPERIMENT REPORT
Diagram of your assembly, indicating forces, lever arms and fulcrum
1 cm d’entraxe
Mathematical explanation
Explanation of your results (mechanical advantage, distance covered)
THIRD-CLASS LEVER
EXPERIMENT REPORT
Diagram of your assembly, indicating forces, lever arms and fulcrum
1 cm d’entraxe
Mathematical explanation
Explanation of your results (mechanical advantage, distance covered)
Back to Reality
Levers can be found in:
• Wheelbarrows
• Oars and paddles
• Car doors
• Shovels and garden forks
• Hand pumps
• Hand trucks
• Nail pullers and nail claws
• Seesaws
• The human skeleton (e.g. arms, legs, neck)
• Screwdrivers
• Salad tongs
• Hole punches
• Crescent wrenches
• Staplers
• and more
Now you need to be able to recognize them!
We took pictures of certain familiar objects (salad tongs, combination pliers, a hammer,
a wheelbarrow and a crescent wrench) then mounted them on a polystyrene board and
punched a number of holes at various locations.
These holes correspond either to a location where effort or load could be applied or
where the fulcrum could be placed. You can reproduce a number of different operating
scenarios for each object.
COMBINATION PLIERS
Assembly diagram and explanation
WHEELBARROW
Assembly diagram and explanation
SALAD TONGS
Assembly diagram and explanation
CRESCENT WRENCH
Assembly diagram and explanation
CLAW HAMMER
Assembly diagram and explanation
centre de
développement
pédagogique
Pour la formation générale
en science et technologie
Nail claw (claw hammer)
Pencil sharpener
LEVERS
- Applications and Answers Lever to lift a rock
Working Documenl
Bicep curl
SECTION
JUNE 2004
C
CONCEPT OF “LEVER”
This practical lab is intended to help participants:
• understand the concept of “lever”
• acquire the vocabulary associated with this concept
• recognize levers in everyday objects
Following this lab, participants should be able to use levers in concrete
applications (i.e. in the design of technical objects).
This companion document comprises three sections :
• Theoretical aspects
• Experiments with simple materials (“classic” levers)
• Experiments with materials used in everyday objects
Record your observations and results throughout the process.
Have fun !
2
Centre de développement pédagogique
pour la formation générale en science et technologie
LEGEND
Effort
Load
Rotation point
Third-class lever
TCL
Second-class lever
SCL
First-class lever
FCLi
Mechanical advantage:
positive
nil
negative
+MA
0MA
–MA
3
OTHER APPLICATIONS
All the objects in the following pictures make use of a type of lever. Use coloured
pencils to indicate the type of lever, the forces in effect—effort (FE) and load
(Fr)—and the fulcrums of each lever directly on the pictures.
example
Fm
Fr
Scissors
Scale
Stapler
4
Centre de développement pédagogique
pour la formation générale en science et technologie
Compass
Can opener
Scissors
Paper clamp
Broom clip
Tweezers
5
Centre de développement pédagogique
pour la formation générale en science et technologie
Caulking gun
Camera tripod
6
Centre de développement pédagogique
pour la formation générale en science et technologie
Snap fastener
Screw-and-nut
fastener
Plastic injection
machine
Centre de développement pédagogique
7
pour la formation générale en science et technologie
Screwdriver
Hole punch
Spring clamp
Nutcracker
Nutcracker
8
Centre de développement pédagogique
pour la formation générale en science et technologie
Cherry picker
9
Centre de développement pédagogique
pour la formation générale en science et technologie
10
Centre de développement pédagogique
pour la formation générale en science et technologie
ANSWERS
11
Centre de développement pédagogique
pour la formation générale en science et technologie
LEGEND
Effort
Load
Rotation point
Third-class lever
TCL
Second-class lever
SCL
First-class lever
FCL
Mechanical advantage:
positive
nil
negative
+MA
0MA
–MA
12
Centre de développement pédagogique
pour la formation générale en science et technologie
OTHER APPLICATIONS
All the objects in the following pictures make use of a type of lever. Use coloured
pencils to indicate the type of lever, the forces in effect—effort (FE) and load (Fr)—and
the fulcrums of each lever directly on the pictures.
examples :
FCL
+AM
Scissors
FLC
+AM
FCL
0AM
Scale
SCL
+AM
SCL
0AM
Stapler
13
Centre de développement pédagogique
pour la formation générale en science et technologie
compas
TLC
+AM
FLC
+AM
Can opener
Scissors
FLC
+AM
Paper clamp
Broom clip
being opened
TLC
-AM
SCL
+AM
Spring
Tweezers
14
Centre de développement pédagogique
pour la formation générale en science et technologie
Caulking gun
SCL
+AM
FLC
+AM
Camera tripod
FLC
+AM
FLC
+AM
15
Centre de développement pédagogique
pour la formation générale en science et technologie
Snap fastener
SCL
+AM
SCL
+AM
Screw-and-nut
fastener system
Plastic injection machine
SCL
+AM
16
Centre de développement pédagogique
pour la formation générale en science et technologie
Screwdriver
Hole punch
Spring clamp
FCL
+AM
SCL
+AM
Nutcracker
SCL
+AM
SCL
+AM
Nutcracker
17
Centre de développement pédagogique
pour la formation générale en science et technologie
SCL
-AM
SCL
-AM
Cherry picker
18
Centre de développement pédagogique
pour la formation générale en science et technologie
TCL
-AM
The effort is being
spleet in two
FCL
-AM
The effort is being
spleet in two
The load is being
spleet in two
19
Centre de développement pédagogique
pour la formation générale en science et technologie