Foundations of Physical Science

Unit 2: Work and Energy

Chapter 4: Machines and Mechanical Systems

• 4.1 Force and Machines

• 4.2 The Lever

• 4.3 Designing Gear Machines

Learning Goals • Describe and explain a simple machine.

• Apply the concepts of input force and

output force to any machine.

• Determine the mechanical advantage of a machine.

• Construct and analyze a block and tackle machine.

• Describe the difference between science and engineering.

• Understand and apply the engineering cycle to the development of an invention or product.

• Describe the purpose and construction of a prototype.

• Design and analyze a lever.

• Calculate the mechanical advantage of a lever.

• Recognize the three classes of levers.

• Build machines with gears and deduce the rule for how pairs of gears turn.

• Design and build a gear machine that solves a specific problem.

Vocabulary

• engineering gear • engineering cycle • engineers • force • fulcrum • gear • input • input arm • input force • input gear

• lever • machine • mechanical advantage • mechanical systems • output • output arm • output force • output gear • prototype • simple machine

• The world without machines

• Technology of today

• So…what is a machine?

4.1 Forces in Machines

Machine

• A device: • with moving parts that work together to accomplish a task. • that multiplies forces or changes the direction of forces • that employs the conservation of energy

• A bicycle is a good example!

• Input: everything you do to

make the machine work, like pushing on the pedals

• Output: what the machine does

for you, like going fast

Simple Machines

• An unpowered mechanical device, such as a:

– Lever

– Wheel and axle

– Block and tackle

– Gear

– Ramp

Simple Machines: Input and Output

• Lever – Input force: what you apply – Output force: what the lever applies to what you

are trying to move

• Block and Tackle (Pulley) – Input force: what you apply to the rope – Output force: what gets applied to the load you

are trying to lift

• Most machines we use today are made up of combinations of different simple machines

Mechanical Advantage

• The ratio of output force to input force

• If the mechanical advantage is > 1, the output force is greater than the input force

• If the mechanical advantage is < 1, the output force is smaller than the input force

How a Block and Tackle Works

• The forces in ropes and strings – Ropes and strings carry tension forces along

their length…a pulling force (not a pushing force!)

• Every part of a rope has the same tension

– If friction is very small, the force in a rope is the same everywhere

• The forces in a block and tackle

– More rope, easier to pull (see diagram slide)

How a Block and Tackle Works

• Mechanical advantage – More ropes, more output force than input

force…easier to lift!

• Multiplying force with the block and tackle – Input force can be much less with more

ropes…

– If the mechanical advantage is 4, the input force for the machines is ¼ the output force

4.2 The Lever Archimedes

“GIVE ME A PLACE

TO STAND AND I WILL MOVE THE

EARTH”

• Greek scientist

• 3rd century BC

What is a Lever?

• Another simple machine

• Pliers, wheelbarrow, human biceps, forearm

• Your bones and muscles work as levers to perform everything from chewing to throwing a ball

What is a Lever? • A stiff structure that rotates around a

fixed point called the fulcrum

• We can arrange the fulcrum and the lengths of the input and output arms to make almost any mechanical advantage we need

How a Lever Works • Fulcrum in the middle: input and output forces are

the same

• Input arm is longer: output force is larger than the input force – Input arm is 10x longer than the output arm, the

output force will be 10x bigger than the input force

• Input arm is shorter: output force is smaller than the input force

– Input arm is 10x shorter than the output arm, the

output force will be 10x less than the input force

4.3 Designing Gear Machines

• Engineering/Technology: The application of science to solve problems

• Scientists: study the world to learn the basic principles behind how things work

• Engineers: use scientific knowledge to create or improve inventions that solve problems

Sample Engineering Problem

• Conceptual design

• Prototype

• Testing the prototype

• Changing the design and testing again

Gears and Rotating Machines

• Many machines require that rotating motion be transmitted from one place to another.

• Gears change force and speed.

• Gears are better than wheels because they have teeth and don’t slip as they turn together.

What is the Gear Ratio?

• Gears have input and output

• Input gear: the one you turn, or apply forces to

• Output gear: the one that is connected to the output of the machine

• Gear ratio: the ration of output turns to input turns

• Smaller gears turn faster; the gear ratio is the inverse of the ratio of teeth in two gears

Designing Machines

• Machines are designed to do specific things

• Simple machines can be combined to solve more complex problems – Two pairs of gears with a 2:1

ratio can be combined to make a machine with a ratio of 4:1

Designing Machines

• Design involves trade offs

• Even the best designs are always being improved

Rube Goldberg Machine

• (1883-1970) Pulitzer Prize winning cartoonist, sculptor and author