Ideal
Mechanical Advantage

Expectation
#28: The student will calculate the
Ideal Mechanical Advantage of a lever, an inclined plane, and a block and tackle
system.

Expectation
#29: The student will manipulate the following type of simple
machines in order to understand the directional nature of forces and the
multiplication of forces: inclined
plane, level, simple pulley, block and tackle, and wheel and axle.

Expectation#30:
The student will understand that no machine operates with perfect
efficiency (Work_{out} is less than Work_{in }) and identify
friction as one reason for a decrease in efficiency.

1.
Have you
used a machine today? You probably
know that a bicycle is a machine.
Pencil sharpeners and can openers are also machines.
A **machine** is a device that makes work easier.

2.
Some
machines are powered by engines or electric motor; others are people-powered.
A simple machine is a device that does work with only one movement.
There are six types of simple machines.
Can you name some in the kitchen, in sports, in construction?

3.
Suppose
you wanted to pry a lid off a wooden crate with a crowbar.
You would slip the end of the crowbar blade under the edge of the crate
lid and push down on the handle.
You would do work on the crowbar, and the crowbar would do work on the
lid. Two forces are involved when a
machine is used to do work. The
force applied to the machine is called the effort force (F_{e}).
The force applied by the machine to overcome resistance is called the
resistance force(F_{r}). In
the crate lid example, you apply the effort force to the crowbar handle.
The resistance force is the force the crowbar applies to the lid.

4.
There are
also two kinds pf work to be considered when a machine is used-the work done on
the machine and the work done by the machine. The work done on the machine is called work input(W_{in});
the work done by the machine is called work output(W_{out}).

5.
Recall
that work is the product of force and distance: W = F x d.

6.
Work
input is the product of the effort force and the distance that force is exerted:
W_{in} =F_{e} x
d_{e}

7.
Work
output is the product of the resistance force and the distance that force
moves: W_{out} =F_{r
} x d_{r}.

8.
Remember
that energy is always conserved. So,
you can never get more work out of a machine than you put into it.
In other words, W _{out }can never be greater than W_{in}.
In fact, whenever a machine is used, some energy is changed to heat due
to friction. So, W_{out} is
always smaller than W_{in}.

9.
Although
a perfect machine has never been built, it helps to imagine a frictionless
machine in which no energy is converted to heat. Such an ideal machine is one in which work input equals work
output. For an ideal machine,

W_{in} =
W_{out}

F_{e} x
d_{e} =F_{r } x
d_{r}

The
number of times a machine multiplies the effort force is the mechanical
advantage(MA) of the machine. To
calculate mechanical advantage, you divide the resistance force by the effort
force.

MA = __resistance force =__
__Fr
__

Effort force
F_{e }

Calculating
Mechanical Advantage

A
worker applies an effort force of 20N to pry open a window that has a resistance
force of 500N. What is the
mechanical advantage of the crowbar?

What
is known? Resistance force
= 500N

Effort force =
20N

What
is unknown? Mechanical advantage

MA
__= Fr
__

Fe

MA
= __500N__= 25

20N

Practice
Problem

Find
the mechanical advantage needed to lift a 2000N rock, using a jack with a
mechanical advantage of 10.

MA
=F_{r}/F_{e}

F_{e}=F_{r}/MA
= 2000N/10 =200N

MiniQuiz

1.
A simple machine does work with only one ________________________.

2.
The force applied to a machine is called the ________________________.

3.
The force applied by a machine is called the _______________________.

4.
The number of times a machine multiplies is the ____________________ of the
machine.

Section
Wrap-Up

1.
Explain
how simple machine can make work easier without violating the law of
conservation of energy.

2. A
carpenter uses a claw hammer to pull a nail from a board.
The nail has a resistance of 2500N.
The carpenter applies an effort force of 125N.
What is the mechanical advantage of the hammer?

3.
Think
Critically: Give an example of a simple machine you’ve used recently.
How did you apply effort force? How
did the machine apply resistance force?

Vocabulary
Terminology

1.
machine

2.
simple
machine

3.
effort
force

4.
resistance
force

5.
ideal
machine

6.
mechanical
advantage

7.
lever

8.
fulcrum

9.
effort
arm

10.
resistance
arm

11.
pulley

12.
wheel and
axle

13.
inclined
plane

14.
screw

15.
wedge

16.
bionics

17.
compound
machine

18.
efficiency

19.
power

Section
7.2 The Simple Machines

1.
A lever
is a bar that is free to pivot, or turn, about a fixed point.
The fixed point of a lever is called the fulcrum.
The part of the lever on which the effort force is applied is called the
effort arm. The part of the lever that exerts the resistance force is
called the resistance arm.

2.
The
following equation, which assumes no friction, can be used to find the ideal
mechanical advantage(IMA) of any lever.

IMA = __length
of effort arm__ =
__L _{e}__

length of resistance arm L_{r
}

_{
}

A worker uses an iron bar to raise a manhole cover weighing 65N.
the effort arm of the lever is 60cm long.
The resistance arm is 10cm long. What
is the ideal mechanical advantage of the bar?

L_{e} = 60cm

resistance arm L_{r
}= 10cm

????ideal mechanical advantage
IMA

IMA = L_{e}/L_{r}

60cm/10cm =
6.0

Complete the practice problems on page 187

Refer to page 199.
Create your own Rube Goldberg device