Transcript Mechanical Systems - University of KwaZulu

Mechanical Systems
UNIT 3:Mechanical Systems
LEVERS

What is the prime purpose of Mech.
Systs.?
 Basically 2 things:
 To transmit motion.
 To transmit power.
Where can they be found?
 Almost everywhere:
 Land;
 Sea;
 Air transport;
 Power generation;
 Manufacturing plants;
 Domestic products etc.
Focus for school curriculum?
 The focus should be on the following:
 The uses and operation of mechanical power
transmission
 Types of motion
 Efficiency
The 6 Simple Machines
Inclined Plane
Gears
Pulley
Lever
Wedge
Wheel and Axle
What is a machine?

A device used to make doing work easier.
 It consists of a power source and a power
transmission system, which provides controlled
application of the power
 Machines employ power to achieve desired forces
and movement (motion).
Functions of machines
 Transfer energy from one placeto another;
 Multiply forces – MA ≥ 1;
 Multiply speed – speed ratio, where MA ≤ 1;
 Change the direction of force – single pulley used to
pull up a weight, where Force input = Force output.
Types of motion
 There are four basic types of motion in mechanical
systems:
 Rotary motion is turning round in a circle, such as a wheel
turning.
 Linear motion is moving in a straight line, such as on a paper
trimmer.
 Reciprocating motion is moving backwards and forwards in a
straight line, as in cutting with a saw.
 Oscillating motion is swinging from side to side, like a pendulum
in a clock.
Rotary motion
 Motion in a circle is called rotary motion.
 The number of complete revolutions made per minute (rpm), is
called rotary velocity.
Oscillating motion
 Oscillating motion is motion backwards and forwards in a
circular arc. e.g. playground swings and clock pendulums.
Linear motion
 Linear motion is motion in a straight line.
 An example of linear motion is the cutting arm of a paper
guillotine (photo below) as it travels from one side of the
machine to the other.
Reciprocating motion

Reciprocating motion is linear motion backwards and forwards
in a straight in a straight line.
 Sewing machines make use of this type of motion
What is a LEVER?
 A lever is the simplest kind of mechanism.
 It is a rigid bar which pivots at a point called a
fulcrum.
 It changes an Input motion and force into a
desired Output motion and force.
 Refer to examples in the course pack on pg.94
What are the parts of a LEVER?
 The class of a lever
depends on the relative
position of the load, effort
and fulcrum:



The load is the object
you are trying to move.
The effort is the force
applied to move the
load.
The fulcrum (or pivot) is
the point where the load
is pivoted . (Point of
turning)
Types of Levers
 There are three different types of lever.
 Class 1 levers
 Class 2 levers
 Class 3 levers
Class 1 levers
 A class 1 lever has the load and the effort on
opposite sides of the fulcrum, like a seesaw.
 Examples of a class-one lever are a pair of
pliers and a crowbar. Illustrate these in line
drawings.
Class 2 levers
 A class 2 lever has the load and the effort
on the same side of the fulcrum, with the
load nearer the fulcrum.
 Examples of a class-two lever are a pair of
nutcrackers or a wheelbarrow.
Class 2 levers
 In the diagram, the wheel
or fulcrum on the
wheelbarrow is helping to
share the weight of the
load.
 This means that it takes
less effort to move a load
in a wheelbarrow than to
carry it
Class 3 levers
 In a class 3 lever the input force (effort) is greater than the
force produced at the load. There is a greater distance
moved by the load than the distance moved by the effort.
Class 3 levers

A class 3 lever does not have the mechanical
advantage of class-one levers and class-two levers,
so examples are less common.

The effort and the load are both on the same side of
the fulcrum, but the effort is closer to the fulcrum than
the load, so more force is put in the effort than is
applied to the load.

These levers are good for grabbing something small
or picking up something that could be squashed or
broken if too much pressure is applied.
MECHANICAL ADVANTAGE
 Class 1 and class 2 levers both provide
mechanical advantage.
 The number of times a machine multiplies your
effort
 This means that they allow you to move a large
output load with a small effort.
 Load and effort are forces and are measured
in Newtons (N).
 Mechanical advantage is calculated as follows:

Mechanical advantage = load ÷ effort
MECHANICAL ADVANTAGE
Calculate the Mechanical Advantage?
 What will be the mechanical
advantage if the load = 500N
and the effort = 100N.
 What does this tell us about
the machine?
Velocity ratio
 The mechanical advantage gained with class-one levers
and class-two levers makes it seem like you are getting
something for nothing:
 moving a large load with a small effort – where’s the
catch?
 The catch is that to make the effort smaller, you have to
move a greater distance.
 In the first diagram the trade-off is that you need to push
the lever down further to move the load up a smaller
distance.
 This trade-off is calculated by the velocity ratio:
 Velocity ratio = distance moved by effort ÷
distance moved by load
VELOCITY RATIO
Velocity Ratio Exercise
A pole is used to lift a car that fell off a jack. The fulcrum is 0.85m
from the car. Two women apply a force of 1300N at a distance of
3.00m from the pivot.
Work out:
•What class lever is used in the example above? (1)
•What is the output force required to lift the car? (5)
The handles of the wheelbarrow are 2.00m long from the front
wheel. A 95kg load is placed 25cm behind the wheel.
Work out:
•What class lever is used in the example above? (1)
•What is the input force required to support the
wheelbarrow? (5)
MOMENTS
 A lever is balanced when the moments on both
sides are equal. The moment (or turning force) can
be calculated by multiplying the force (or load) by
the distance from the fulcrum (or pivot).
Calculations with MOMENTS

This beam balances because 5N × 2m
(on the left) = 10N × 1m (on the
right). If you multiply N by m you get
Nm so each moment is equal to
10Nm. The same principle applies if
you have more than one force on
one side of the beam.

This beam balances because 5N × 2m
(on the left) = (4N × 1m) + (3N × 2m)
(on the right). The individual
moments on the right are calculated
first then added together.
Classwork Activity
 Refer to pg.99 of your course pack and complete
the calculations at:
 14 a & b
 15 a & b
 16.
 Consolidate these before the end of the session.
DESIGNING AND MAKING
MODELS: LEVERS




Construct a model of a 2nd class lever
system using available materials.
Provide a 3-D sketch of each stage of your
construction.
How will you use the model you’ve created
in your teaching?
What would you hope to achieve with the
learners?

LEVERS IN ACTION PRACTICAL

HYPOTHESIS

a supposition or proposed explanation made on
the basis of limited evidence as a starting point for
further investigation.

an educated guess about how things work. Most of
the time a hypothesis is written like this: "If _____[I
do this] _____, then _____[this]_____ will ...
 a tentative statement about the relationship
between two or more variables.
VARIABLES
 An independent variable is the variable that is
changed in a scientific experiment.
 Independent variables are the variables that the
experimenter changes to test their dependent
variable (position of the fulcrum and the load).
 A dependent variable is the variable being tested in
a scientific experiment (how much force must be
exerted?).
MV and RV

A manipulated variable (also called the independent variable) is
the thing in an experiment that is PURPOSELY changed to gather
data, etc.

The responding variable (aka the dependent variable) is the
variable that, well, responds to the manipulated variable. The RV
(responding variable) changes because the MV (manipulated
variable).

If you wanted to graph this, the MV (or independent variable)
goes on the x-axis and the RV (or the dependent variable) goes
on the y-axis.
IV and DV on the graph
 the independent variable is the one on the x axis (the
horizontal line).
 it's the one you can control.
 the dependent variable is the one whose results
*depend* on the independent variable. This goes on the
y axis (the one going up and down)
 for example, if you were making a bar graph of people's
favorite colors, you'd put the colors (independent) on
the x axis. then you'd survey everyone and put your
newfound results (dependent) on the y axis.
Inclined Planes
 An inclined plane is a flat surface that is higher on
one end
 Inclined planes make the work of moving things
easier
The Inclined Plane
 Inclined planes are used to raise heavy
objects that are heavy to lift vertically.
 By rolling an object up an incline or a ramp,
you require less strength than required to
pick the object up the same height, but you
do have to travel a greater distance.
 This ability to move an object to another
height works the same as with a lever.
The Inclined Plane
The Inclined Plane
Answer the following questions:
 What is the effort required? (input force)
 What is the Velocity ratio / speed ratio (IMA)?
IMA – Ideal Mechanical Advantage
 What is the Mechanical Advantage (AMA)?
AMA – Actual Mechanical Advantage
The Inclined Plane
ANSWER
 What is the effort force required?
AMA and IMA
The Inclined Plane
 If you lifted a barrel that weighed 200 Newtons up 6
meters in height, the work against gravity would be:
200N x 6m = 1200 Nm.
 If you rolled that barrel up a ramp 12 meters long,
you would only have to push with a force of 100 N.
 That is because 200N x 6m = 100N x 12m.
Problem
A worker is pushing a box weighing 1650N up a
ramp 4.50m long onto a platform 1.50m above the
ground.
 Sketch the problem.
 What is the force required to lift the load?
 What is the AMA/MA?
 What is the IMA/VR?
Problem

Questions
1. What is the height of the inclined plane?
2. What is the length of the inclined plane?
3. How much effort force would be needed to push the dump truck up the
mountain?
4. What is the mechanical advantage of the inclined plane?
The Inclined Plane
 An object placed on a tilted surface will often slide
down the surface.
 The rate at which the object slides down the surface
is dependent upon how tilted the surface is; the
greater the tilt of the surface, the faster the rate at
which the object will slide down it.
The Screw and the inclined plane
The Inclined Plane and other
mechanisms
 The wedge is also an adaption of the
inclined plane.
 It is simply Two inclined planes joined
back to back.
The Screw
 A screw is an inclined plane wrapped around a
cylinder.
 A central core with a thread or groove wrapped
around it to form a helix.
 While turning, a screw converts a rotary motion
into a forward or backward motion.
Terminology to be explored
 Pitch
 this is the distance that a jack screw rises or the
distance the wood screw advances a piece of
wood in one revolution;
 i.e. the pitch of a screw is actually the distance
between 2 successive threads.
 Thread
 simply a ramp that is wrapped around a cylinder
like a bolt.
Pitch
The
thread
The screw jack, when
a load is inserted in the
holes a load is lifted.
The law of simple machines as applied
to the screw:
Work done on the screw by the input force
turning it is equal to the work done by the
screw on the load force
W in = W out
Input
Output
In screws the law of simple
machines is applied as follows:
 Win= Wout
 Fi x Si (Circumference)= Fo x So (pitch)
 Fi x 2(πr) = Fo x pitch not correct
 𝐹𝑖 2𝜋𝑟 = 𝐹𝑜 (𝑝𝑖𝑡𝑐ℎ)
Note: 2(πr) is how we work out the circumference of a
circle.
2(πr)= 2x 3.14 x radius not correct!
Task 1 a)
A jack screw has a pitch of 3.2mm and a handle radius of 24cm.
Ideally, what load can be lifted, if a force of 120N is exerted?
Use this formula: Fi x 2(πr) = Fo x pitch
Need to
convert to
cm
120 N x (2x 3.14 x 24cm)= Fo x 3.2mm
120 N x 150.72cm = Fo x 0,32cm
Fo= 18086.4 N.cm
0,32cm
Fo = 56520 N
The jack screw can lift the load of 56520N with the input force of 120N.
Task 1 b)
The jack screw has a pitch of 3.2mm and a handle radius of 24cm. We now
know that ideally, a load of 56520 N can be lifted, if a force of 120N is
exerted?
What is the mechanical advantage?
Use this formula:
MA= Fout
Fin
MA= 56520 N
120N
MA= 471
The jack screw gives you an MA of 471.
Task 2:
 A truck of mass 2100kg is raised using a
jackscrew having a pitch of 7.1mm and a
handle radius of 50cm.
 What input force is needed?
 If its efficiency is 15%, what is the actual
mechanical advantage?
References
•
http://learn.uci.edu/media/OC08/11004/OC0811004_L6Class2L
evers.jpg
http://www.professorbeaker.com/lever_fact.ht
ml
• http://depssa.ignou.ac.in/wiki/images/0/06/Eg
2.jpg
• http://sfscience.files.wordpress.com/2010/04/
elephant-lever.png%3Fw%3D588