Work, Power, and Machines

Chapter 14

Chapter 14 Pretest

• According to Newton’s first law, if no net force acts on an object, the object continues in motion with constant ______.a) Velocity

b) Force

c) acceleration

Chapter 14 Pretest

• A horizontal force on an object can be broken down into these components: 5 N north and 5 N east. If no other forces act on the object, in what direction will the object move?– Northeast

• Newton’s second law states that the net force acting on an object equals the product of what two variables?– Mass and acceleration

Chapter 14 Pretest

• A machine produces an output force of 12.3 N when an input of 8.6 N is applied. What is the ratio of the machine’s output force to its input force?– 1.4

• A person exerts 22 N on a box. If a frictional force of 3 N opposes this force, what is the net force acting on the box?– 19 N

Chapter 14 Pretest

• A machine has an output force of 57.3 N when a force of 32.6 N is used to operate the machine. What is the percentage increase of the force?– 176%

Chapter 14 Pretest

• A small wheel has a radius of 32 cm, and a large wheel has a diameter of 128 cm. What is the ratio of the diameters of the large wheel to the small wheel?a) 4

b) 2

c) 0.25

d) 0.5

Work• Work is the product of force and distance. Work

is done when a force acts on an object in the direction the object moves. If a force acts on an object but the object does not move, no work is done.1. A man pushes a grocery cart at constant speed

from one end of an aisle to the other. Identify the force, the distance, and the work.• The man supplies the force by pushing on the cart. The

length of the aisle is the direction. The work done is the product of the force and the distance.

2. Describe two examples of work you do on a typical day.• Lifting a heavy school bag, pushing or pulling a door open

14.1- Work

• In science, work is the product of force and distance.– Work is done when a force acts on an object

in the direction the object moves.

• Work requires motion.– If there is no movement, no work is done.– For a force to do work on an object, some of

the force must act in the same direction as the object moves.

14.1 – Work

• Work depends on two things:– The direction of the force– The direction of the movement

• A force does not have to act entirely in the direction of the movement to do work. – Any part of a force that does not act in the

direction of motion does no work on an object.

14.1 – Calculating Work

• Work done is calculated by multiplying the constant force acting in the direction of motion by the distance the object moves.

• Work = Force X Distance

• SI unit for work is joule (J) – Force = newtons (N), distance = meters (m)

14.1 - Power

• Power is the rate of doing work.

• Power is required when you want work done fast.– Doing work at a faster rate requires more power.– To increase power

• you can increase the amount of work done in a given time

• or you can do a given amount of work in less time.

14.1 Calculating Power

• Power is calculated by dividing the amount of work done by the time needed to do the work.

• Power = Work / Time

• SI unit for power is watt (W) – Work = joules (J), time = seconds (s)

• Horsepower is another common unit for power.– 1 horsepower (hp) is equal to ~746 watts

Chapter 14.1 Assessment• What conditions must exist in order for a

force to do work on an object?– Some of the force must act in the same

direction as the object moves.

• What formula relates work and power?– Power = work/time

• How much work is done when a vertical force acts on an object moving horizontally?– No work is done.

Chapter 14.1 Assessment• A desk exerts an upward force to support a

computer resting on it. Does this force do work? – The supporting force does no work because the

object it acts on (the computer) does not move.

• Two cars have the same weight, but one of the cars has an engine that provides twice the power of the other. Which car can make it to the top of a mountain first?– The car with the more powerful engine will reach the

top first.

• Which car does more work to reach the pass?– Both cars do the same amount of work to reach the

top.

Chapter 14.1 Assessment

• You carry two heavy bags of groceries upstairs to your kitchen. Will you do more work on the bags if you carry them up one at a time?– Carrying one bag at a time uses only half the

force, but requires that the force be applied through twice the distance. The work done is the same in both cases.

14.2 - Machines

• A machine is a device that changes a force.

• Machines make work easier to do.– They do this by one of the following:

• change the size of a force needed, • the direction of a force, • or the distance over which a force acts.

14.2 – Machines Do Work

• Increasing Force– A small force exerted over a large distance

becomes a large force exerted over a short distance

– If a machine increases the distance over which you exert a force, then it decreases the amount of force you need to exert

• Example – jacking up a car

14.2 – Machines Do Work

• Increasing Distance– Some machines decrease the applied force,

but increase the distance over which the force is exerted

– A machine that decreases the distance through which you exert a force increases the amount of force required.

• Example: rowing with oars

14.2 – Machines Do Work

• Changing Direction– Some machines change the direction of the

applied force

• Example: rowing with oars

14.2 – Work Input• Because of friction, the work done by a

machine is always less than the work done on the machine.

• The force you exert on a machine is called the input force.

• The distance the input force acts through is known as the input distance.

• The work done by the input force acting through the input distance is called the work input.

14.2 – Work Output

• The force that is exerted by the machine is called the output force.

• The distance the output force is exerted through is the output distance.

• The work output of a machine is the output force multiplied by the output distance.

14.2 - Assessment

• How can using a machine make a task easier to perform?– Machines make work easier to do by altering

the size of the force needed, the direction of a force, or the distance over which a force acts.

• How does the work done on a machine compare to the work done by a machine?– Because of friction, the work done by a

machine is always less than the work done on the machine.

14.2 - Assessment• What changes can a machine make to a

force?– Size of force; direction of force; distance

through which a force acts

• A machine produces a larger force than you exert to operate a machine. How does the input distance of the machine compare to its output distance?– Because the output force is greater than the

input force, the input distance must be greater than the output distance.

14.2 - Assessment• You do 200 J of work pulling the oars of a

rowboat. What can you say about the amount of work the oars do to move the boat?– Less than 200 J of work are done to move the

boat because some of the input work is lost due to friction.

• How can you increase the work output of a machine?– Increase the work input to the machine, or

reduce any friction that limits work output.

14.2 - Assessment

• When you swing a baseball bat, how does the output distance the end of the bat moves compare with the distance you move your hands through? Why might this difference be useful?– The output distance is much greater than the

input distance. The high speed of the bat end helps the batted ball to also acquire a high speed (and travel far).

14.2 - Assessment

• An advertisement for a new type of wrench claims it reduces the force needed to tighten the bolt. If the advertisement is correct, what do you know to be true about the input distance?– If the input force is decreased, then the input

distance must be increased.

14.3 – Mechanical Advantage

• The mechanical advantage of a machine is the number of times that the machine increases an input force.

• The mechanical advantage determined by measuring the actual forces acting on a machine is the actual mechanical advantage.

• Actual Mechanical Advantage = Output Force (AMA) Input Force

14.3 – Ideal Mechanical Advantage

• The ideal mechanical advantage of a machine is the mechanical advantage in the absence of friction.– If any machine were frictionless, its AMA would be the

maximum possible value.

• Because friction is always present, the actual mechanical advantage of a machine is always less than the ideal mechanical advantage.– AMA is less than IMA– Engineers design machines that use low-

friction materials and lubricants.

14.3 – Calculating Mechanical Advantage• Ideal mechanical advantage is easier to measure than

actual mechanical advantage because it depends only on the locations of the forces and the distances over which they act.

• Ideal Mechanical Advantage = Input Distance

(IMA) Output Distance

• *Remember that the effects of friction are neglected when calculating ideal mechanical advantage!

14.3 – Calculating Efficiency• Because some of the work input to a machine is

always used to overcome friction, the work output of a machine is always less than the work input.

• The percentage of the work input that becomes work output is the efficiency of a machine.

• Because there is always some friction, the efficiency of any machine is always less than 100 percent.

• Efficiency = work output x 100%

work input

14.3 – Assessment• Why is the actual mechanical advantage

of a machine always less that its ideal mechanical advantage?– The presence of friction results in the actual

mechanical advantage of a machine always being less than its ideal mechanical advantage.

• Why can no machine be 100% efficient?– Because there is always some friction, the

efficiency of any machine is always less than 100%.

14.3 - Assessment• You test a machine and find that it exerts a force

of 5N for each 1N of force you exert operating the machine. What is the actual mechanical advantage of the machine?AMA = output force = 5N = 5

input force 1N

• How can two machines appear identical and yet not have the same actual mechanical advantage?–If the amount of friction acting on the machine differs, then the actual mechanical advantage of the machines will also differ.

14.3 - Assessment

• What information would you use to calculate the efficiency of a machine?– Efficiency is calculated from work input and

work output.

• When is the ideal mechanical advantage of a machine greater than 1?– The IMA of a machine is greater than 1

whenever the output force is greater than the input force.

14.3 - Assessment

• Suppose you are an inventor in 1900. You are constructing a bicycle of your own design. What could you do to ensure your bicycle efficiently changes work input into forward motion?– Main goal is to keep friction to a minimum.

14.3 - Assessment

• You have just designed a machine that uses 1000 J of work from a motor for every 800 J of useful work the machine supplies. What is the efficiency of your machine?Efficiency = (work output / work input) x100%

= (800J/1000J) x 100% = 80%

14.3 - Assessment

• If a machine has an efficiency of 40%, and you do 1000 J of work on the machine, what will be the work output of the machine?Efficiency = (work output / work input) x 100%

Work output = (efficiency x work input) / 100%

= (40% x 1000 J) / 100% = 400 J

14.4 – Simple Machines

• The six types of simple machines are:– Lever– Wheel and axle– Inclined plane– Wedge– Screw– Pulley

14.4 - Levers• A lever is a rigid bar that is free to move around a fixed

point, called a fulcrum.

• There are three classes of levers based on locations of input force, output force, and fulcrum.

• The input arm of a lever is the distance between the input force and the fulcrum.

• The output arm of a lever is the distance between the output force and the fulcrum.

• Ideal Mechanical Advantage = input arm / output arm

14.4 – First-Class Levers

• First-Class Levers – the fulcrum is always located between the input force and the output force.

• Ideal Mechanical Advantage - can be greater than, less than, or equal to 1

• Examples: seesaw, scissors, tongs

14.4 – Second-Class Levers

• Second-Class Levers – the output force is located between the input force and the fulcrum.

• Ideal Mechanical Advantage – always greater than 1

• Example: wheelbarrow

14.4 – Third Class Levers

• Third-Class Levers – the input force is located between the fulcrum and the output force.

• Ideal Mechanical Advantage – always less than1.

• Examples: baseball bats, hockey sticks, golf clubs, broom

14.4 – Wheel and Axle

• A wheel and axle is a simple machine that consists of two disks or cylinders, each one with a different radius.

• IMA = input force radius / output force radius– Can use diameter rather than radius in formula– IMA can be greater than or less than 1.

• Examples: car steering mechanism, turning a screw with a screwdriver

14.4 – Inclined Planes

• A inclined plane is a slanted surface along with a force moves an object to a different elevation.

• IMA = distance along the incline plane change in height

• Examples: switchback roads, ramp

14.4 – Wedges and Screws

• Wedges – a V-shaped object whose sides are two inclined planes sloped toward each other.

• IMA greater than 1.– A thin wedge of a given length has a greater IMA than a

thick wedge of the same length.

• Examples: knife blade, zipper, axe

• Screws – is an inclined plane wrapped around a cylinder.– Screws with threads that are closer together have a

greater IMA.

14.4 - Pulleys

• Fixed Pulleys – a wheel attached in a fixed location– IMA is always equal to 1– Examples: flagpole, window blinds

• Movable Pulley – is attached to the object being moved rather than to a fixed location– Examples: pull in sails, platforms for skyscraper

window washers

• Pulley System – combined fixed and movable pulleys

14.4 – Compound Machines

• A compound machine is a combination of two or more simple machines that operate together.

• Examples: scissors, car, washing machine, clock