The student will learn about the main purposes and the basic
components of all machines.
SIMPLE MACHINES
SPH4C
Findlay
What do you think of when you hear
the word “machine”?
Simple Machines

Machines created thousands of years ago and even
the machines used today are still based on basic
machines. Tools such as arrows (wedges) and ramps
(inclined plane) are examples of simple machines.
Simple Machines

A Machine is a device that helps perform tasks. It is
designed to achieve at least 1 of the 5 main
functions.
The Purposes of Machines

Change energy from one form into another.
 Example:
hydroelectric – converts the energy of falling
water into electrical
The Purposes of Machines

Transfer forces from one object to another.

Car transmission – transfers the force from the motor to the
wheels
The Purposes of Machines

To reduce the amount of force that is required for
a job.
The Purposes of Machines

To modify the speed of something.
The Purposes of Machines

To change the direction of motion.
 Flag
pole – pull down on the rope to raise the flag by
a pulley system.
The Purposes of Machines


It is usually a trade-off between force and speed
For Example…
A block and tackle makes it easier to lift a heavy
object but it rises more slowly
The Purposes of Machines

A ramp makes it easier to lift something but you
have to move it farther to get it to the same height.
The Components of Machines


Complex Machines are known as compound
machines
Compound machines are made of…
Simple Machines: Lever Family

A lever is a rigid bar that can rotate freely around
a support called a fulcrum.
Simple Machines: Lever Family

Levers are divided into three classes, depending on
the position of the load, effort force, and the
fulcrum.
Simple Machines: Lever Family
Simple Machines: Lever Family


An effort force, FE, is a force applied to one part of a
lever to move a load at another part; the load exerts a
load force, FL.
The perpendicular distance from the fulcrum to the
effort force represents the effort arm, symbol dE, and
the perpendicular distance from the fulcrum to the load
force represents the load arm, symbol dL.
dL
Simple Machines: Lever Family

The Wheel and Axel
Apply force to the
wheel (makes it easier)
Apply force to the axel
(makes it go faster)
Simple Machines: Lever Family

The Pulley
This one changes
the direction of
the force
Simple Machines: Lever Family

Gears
These also change the
direction of motion
Simple Machines: Inclined Plane Family

Basic Inclined Plane - A ramp that increases the
load that can be raised by an effort force.
Simple Machines: Inclined Plane Family

Screw – an inclined plane wrapped around a
central shaft..
Seven Archimedes screws pump
wastewater in a treatment plant
in Memphis, Tennessee, USA.
Each of these screws is 96 inches
(2.44 meters) in diameter and
can lift 19,900 gallons per
minute
Simple Machines: Inclined Plane Family

Wedge – Two inclined planes back to back that
increases the applied or effort force.
What is the Simple Machine?
Lever
fulcrum
What is the Simple Machine?
Inclined Plane
What is the Simple Machine?
Screw
What is the Simple Machine?
Pulley
What is the Simple Machine?
Lever - handles
Wedgeblades
What is the Simple Machine?
Lever (handles)
Wedge (blades)
Gears
The student will be able to solve
problems involving torque, force,
load-arm length, and effort-arm
length as they relate to levers.
TORQUE
SPH4C
Findlay
Feeling Torque


When a force or set of forces causes a rigid body
to rotate, we say a torque has been applied.
Torque – the turning effect caused by a force on a
rigid object around a axis or fulcrum, symbol T; it is
measured in Newton-meters, or Nm; it can be
called a “moment force”.
Torque on Doors


Every time you open a door, you are producing a torque on
the door.
A small force applied far from the hinges can produce the
same amount of torque as a large force applied closer to the
hinges.
Distance
Distance
Torque

In order to create the largest amount of torque
possible when pushing on the door, the force
generated must be at a 90 degree angle to the
door.
Magnitude of Torque
The amount of torque produced depends on
two factors.
1. The magnitude of the force (F) applied to
the rigid object.

2.
The distance (d) between the force and the
axis or fulcrum.
Amount of Torque




Using the symbol T for the magnitude of torque, the
following statements hold true:
T increases as F increases ( T  F)
T increases as d increases ( T  d)
Torque = force x distance or T = Fd (where F is
perpendicular to the ridge object)
Example Problem

Calculate the torque of a wrench experiencing a
force of 84 N, a distance of 0.35 m away from the
bolt.
𝑇 = 𝐹𝑑
𝐹 = 84 N
𝑇 = 84 N 0.35 m
𝑑 = 0.35 m
𝑇 = 29 Nm
𝑇=?
∴ the magnitude of the torque on the wrench
is 29 Nm.
Torque on Levers


Two torques can be calculated for a lever: the effort torque
(TE) and the load torque (TL).
The associated distances are the effort distance, or effort arm
(dE), and the load distance, or load arm (dL).
dE
TE
dL
TL
Torque on Levers

Effort torque = effort force x effort arm
TE = FEdE
Or


Load Torque = load force x load arm
TL = FLdL
In each case, the force is perpendicular to the lever,
which allows us to deal with magnitudes only, thus
avoiding vector signs.
Example Problem

A camper is using a large plank as a first class lever
to move a rock. The effort force has a magnitude of
4.5 x 102 N, and the distance from the fulcrum to
the effort force is 2.2 m. What is the magnitude of
the effort torque produced? (ignore the mass of the
plank)
𝐹𝐸 = 4.5 × 102 N 𝑇𝐸 = 𝐹𝐸 𝑑𝐸
2
𝑇
=
4.5
×
10
N 2.2 m
𝑑𝐸 = 2.2 m
2
𝑇
=
9.9
×
10
Nm
𝑇𝐸 = ?
∴ the magnitude of the effort torque produced
is 9.9 × 102 Nm.
Static Equilibrium of Levers
The word static means at rest. A rigid object
that is in static equilibrium is at rest in two
ways.
1. It is not moving in any direction
2. It is not rotating

Law of the Lever

When a lever is in static equilibrium, the
magnitude of the effort torque equals the
magnitude of the load torque.
Law of the Lever


This law can be written in the equation form
Effort torque = load torque
Effort force x effort arm = load force x load arm
FEdE = FLdL
For this equation, only the magnitudes of the
quantities are considered. This eliminates the need
for positive or negative signs.


Example Problem

A camper wants to mount a trailer on blocks for the
winter. One corner of the trailer is lifted by
applying an effort force using a 3.00 m steel bar.
The trailer is applying a load force of
1.8 x 103 N, a distance of 0.45 m away from the
fulcrum. Determine the magnitude of the effort
force required (ignore the mass of the bar)
Example Problem
𝐹𝐿 = 1.8 × 103 N
𝑑𝐿 = 0.45 m
𝑑𝐸
= 3.00 m − 0.45 m
𝑑𝐸 = 2.55 m
𝐹𝐸 = ?
𝐹𝐸 𝑑𝐸 = 𝐹𝐿 𝑑𝐿
𝐹𝐿 𝑑𝐿
𝐹𝐸 =
𝑑𝐸
1.8 × 103 N 0.45 m
𝐹𝐸 =
2.55 m
𝐹𝐸 = 3.2 × 102 N
∴ the force needed to lift the
trailer is 3.2 × 102 N.
Law of the Lever




For any rigid object, the law of the lever can be stated
in more general terms based on which way it is turned.
The clockwise torque is balanced by the counter clockwise
torque.
TCW = TCCW
Where TCW = magnitude of the clockwise torque on an
object around the fulcrum.
Where TCCW = magnitude of the counter clockwise
torque on an object around the fulcrum.