LESSON 1.15 - MACHINES
Overview
This lesson deals with simple machines such as levers,
pulleys and inclined planes. On completion of the lesson,
you should be able to calculate the mechanical advantage
of a lever, a system of pulleys or a system employing an
inclined plane.
ACTIVITIES
- Construct a simple
lever with a movable fulcrum using a wooden rod
or
yardstick. Use the lever to lift a metal object (1-kg
weight) and show how
moving the fulcrum away from the weight makes it
more difficult to lift.
- Use a pulley and a
piece of string to show that it is easier to lift
an object
with the pulley if one of the ends of string is
anchored and the pulley moves.
Machines
Machines are devices that
are used to overcome forces. A machine converts an effort
at one point in the machine to a force at another point
in the machine. This overcomes the load on the machine.
Mechanical advantage
The work produced by a
machine can never be more that the work done on the
machine. If the output force produced by a machine is
larger than the input force, the input force must move
through a greater distance than the output force. In a
perfect machine, the product of force and distance at the
input and output points of the machine must be the same.
In practice, some energy is always lost due to friction
and the efficiency or ratio of useful output work to work
input is less than 1.
An inclined plane
An inclined plane is a
surface that is at an angle to the horizontal. It is
easier to raise an object by moving up an inclined plane
than to lift it directly. The mechanical advantage of an
inclined plane is the distance moved along the plane
divided by the change in height of the object being moved.
Example 1.15.1 Lever
What is the mechanical
advantage of the lever shown below?
Solution
The distance from the
fulcrum to the load is 0.2 m.
The distance from the
point at which the effort is applied is 0.5 m
The mechanical advantage =
0.5 m / 0.2 m
Mechanical advantage = 2.5
Example
1.15.2 Inclined Plane
a) Calculate the
mechanical advantage of the inclined plane shown below:
- If the load weighs
200 N, what force is needed to move the load up
the plane?
(Assume that no energy is lost due to friction.)
Solution
The mechanical advantage =
250 / 50 = 5
The force needed to move
the load = 200 N ÷ 5 = 40 N
Review
Questions
- Can we say that
machines are devices that are used to multiply
forces or change the direction of forces?
- If someone lifts a
rock weighing 75 N using a lever and the downward
force needed to do this at the other end of the
lever is 10 N, What is the mechanical advantage
of the lever?
- How far should the
downward force need to move for the rock to be
lifted 200 cm?
- Sketch three common
types of levers showing the fulcrum, load and
applied force in each case.
- Sketch a system in
which a single pulley is used to change the
direction of the applied force without any
mechanical advantage
- Sketch a system in
which a single pulley can be used to lift an
object with a mechanical advantage of 2
- Sketch a system
consisting of 2 pulleys that can be used to lift
an object with a mechanical advantage of 2
- Why is there a
difference between the theoretical mechanical
advantage and the actual mechanical advantage of
a machine?
- How does this relate
to the efficiency of the machine?
- What is the
theoretical mechanical advantage of the system of
pulleys shown below?
 - A large rock with a
mass of 200 kg is placed on Teflon ® lined skids
and raised to a height of 3 meters by pulling it
up a Teflon ® coated inclined plane 6 meters
long. What is the theoretical mechanical
advantage of the inclined plane?
- A screw-type jack
lifts an automobile by 20 cm when the screw is
rotated 150 times. If the diameter of the screw
is 2 cm, what is the theoretical mechanical
advantage of the jack?
ACTIVITIES
- Construct a simple
lever with a movable fulcrum using a wooden rod
or
yardstick. Use the lever to lift a metal object (1-kg
weight) and show how
moving the fulcrum away from the weight makes it
more difficult to lift.
- Use a pulley and a
piece of string to show that it is easier to lift
an object
with the pulley if one of the ends of string is
anchored and the pulley moves.
.
.
HANDS-ON
HOMEWORK
Select one or more of the recommended
activities for Lesson 1.16, collect the items needed and test the
procedure before demonstrating the activity during the
next theory lesson.
Lesson 1.16 Rotation
- Drive shafts transfer
torque.
- Yes.
- B.
- The wheel with the
diameter of 1.0 meters. Rotational inertia
depends on the mass and the average distance of
the mass from the center of rotation.
- The one with their
arms extended. This increases the average
distance of the person’s mass from the
center (or axis) of rotation.
- 3 N x 0.2 m = 0.6
N-m.
For the ruler to be balanced, the counter-clockwise
moment should also be = 0.6 N-m.
If the distance is 0.35m, the force must be = 0.6N-m
/ 0.35m = 1.71 N.
- The weight of 5 kg is
5 x 9.81 = 49.05 N. The clockwise moment = 49.05
x 0.2 = 9.81 N-m.
The force on the left-hand side should be 9.81
/ 0.35 = 28.03 N.
This is equivalent to the weight of 28.03 / 9.81
= 2.86 kg.
- The circumference of
the circular path is 2p x
1.5 = 9.43 m. At 0.7 revolutions per second, the
tangential speed is 0.7 x 9.43 = 6.6 m/s.
The angular momentum = mvr = 20 x 6.6 x 1.5 = 198
kg-m2 /s.
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