Foundations of Physical Science Unit 2: Work and Energy
Chapter 5: Work, Energy, and Power 5.1 Work 5.2 Energy Conservation 5.3 Energy Transformations
Learning Goals Calculate the amount of work done by a simple machine. Use units of joules to measure the amount of work done. Analyze the effects of changing force or distance in a simple machine. Calculate the efficiency of a machine. Calculate power in machines. Discuss perpetual motion machines.
Vocabulary chemical energy electrical energy energy transformations heat efficiency horsepower joule energy kinetic energy law of conservation of energy nuclear energy potential energy watt power work radiant energy radiation solar power
5.1 Work The word work is used in many different ways Work: force multiplied by distance If you push a box with a force of one newton for a distance of one meter, you have done exactly one joule of work.
Work = Force x Distance W = F x d It takes energy to push something and make it move We do work when we lift a load against Earth s gravity The heavier the load or the higher we lift it, the more work we do
The Amount of Work Depends On: How much force is applied How far the force causes the object to move If the wall doesn't move, the prisoner does no work
Measurement of Work: the joule Force = newtons (N) Distance = meters (m) Work = newtons x meters = N x m Work = N x m = joule (J)
The joule One joule of work is done when a force of 1 newton is exerted over a distance of 1 meter For larger values: 1 kilojoule (kj) = 1,000 joules 1 megajoule (MJ) = 1,000,000 joules
Example How much work is needed to lift an object that weighs 500 N to a height of 4 m? W = F x d = 500 N x 4 m = 2000 J
Example How much work is needed to lift it twice as high? Twice the height requires twice the work. That is, W = F x d = 500 N x 8 m = 4000 J
Example How much work is needed to lift a 1000 N to a height of 8 m? Lifting twice the load twice as high requires four times the work That is, W = F x d = 1000 N X 8 m = 8000 J
Work Input = Work Output If heat from friction forces is small enough to neglect, the work input is equal to the work output Work output of a simple machine can never exceed the work input
Work Input = Work Output (Force x distance) input = (Force x distance) output Small force applied over large distance is the same as large force applied over a small distance.
Efficiency In a very efficient machine, all or most of the work input becomes work output In real machines the work output is always less than the work input (why? Friction, heat, etc.) Efficiency: the ratio of work output to work input Expressed as a percent
Efficiency Some machines do more work than others given the same energy input The machine that can do more work is said to be more efficient Efficiency = work done energy used
The Ideal Machine 100 % efficient
Power The rate at which work is done The rate at which energy is changed from one form to another It makes a difference how fast you do work
Power
Watt power = work done (joules)/time interval (seconds) joule/second = watt (W) James Watt: 18 th century developer of the steam engine
Watt One watt (W) of power is used when one joule of work is done in one second 1 kilowatt (kw) = 1,000 watts 1 megawatt (MW) = 1,000,000 watts
Example You do work when you do push-ups. If you do the same number of pushups in half the time, how does your power output compare? Your power output is twice as much
Example How many watts of power are needed when a force of 1 N moves a book 2 m in a time of 1 s? P = W/t = (F x d) / t (1 N x 2 m) / 1 s = 2 W
Example If both jobs are done in the same time, who expends more power? They both do the same amount of work in the same time, so both expend the same power
5.2 Energy Conservation Energy is the ability to do work Any object that has energy has the ability to create force Energy is measured in the same units as work. A joule is a unit of force that acts over a distance
Mechanical Energy Potential Energy Work is done on the bow The work done is stored in the bow and string as elastic potential energy (mgh)
Potential Energy (PE) The stored energy that a body possesses because of its position Gravitational potential energy = weight x height PE = mgh
Potential Energy (PE) The PE of the 10 N ball is the same (30 J) in all three cases. Depends on height, not the path to get there!
Kinetic Energy Mechanical Energy After release, the arrow is said to have kinetic energy (½ mv 2 ) Energy is measured in the same units (joules) as work
Kinetic Energy (KE) Energy of motion, described by the relationship:
Example A car travels at 30 km/h and has kinetic energy of 1 MJ. If it travels 2X as fast, 60 km/h, how much kinetic energy will it have? KE = ½ mv 2 2X as fast means 4X the kinetic energy, 4 MJ
Example If it travels 3X as fast, at 90 km/h, what will its kinetic energy be? KE = ½ mv 2 3X as fast means 9X the kinetic energy, 9 MJ
Conservation of Energy Energy can never be created or destroyed, just transformed from one form into another Total amount of energy never changes
Work-Energy Theorem Work equals a change in kinetic energy Work = KE We are referring to net work, based on net force No change in energy no work done
Work-Energy Theorem A weightlifter raises a barbell over his head Work is done on the barbell A weightlifter holds the barbell stationary above his head No work is done on the barbell
Work-Energy Theorem What if you push a box on the floor and it doesn t slide? You are not doing work on the box!
Work-Energy Theorem Theorem applies to speed as well The more KE something has, the more work required to stop it 2X as much KE means 2x work
Work-Energy Theorem As you apply brakes to a car, you do work on it This work is the friction force supplied by the brakes, multiplied by the distance over which the friction force acts Friction is the same whether the car moves slowly or quickly (Friction doesn t depend on speed)
Work-Energy Theorem What is the variable in friction? The distance of braking A car moving at 2x the speed as another car takes 4x (2 2 = 4) as much work to stop it Therefore, it takes 4x the distance to stop the faster car
How to Solve the Problems Work = KE F x d = ½ mv 2 d = (½ mv 2 ) F
Example When the brakes of a car are locked, the car skids to a stop. How much farther will the car skid if it s moving 3X as fast? 9X farther: ½ mv 2 The car has 9X as much energy when it travels 3X as fast
Example Can an object have energy? Yes An elevated object may possess PE relative to the ground, but none relative to a point at the same elevation. The KE of an object is relative to a frame of reference, usually taken to be the Earth s surface
Example Can an object have work? No, unlike energy, work is not something an object has Work is something an object does to some other object An object can do work only if it has energy
Work-Energy Theorem KE often appears hidden in different forms of energy Heat Sound Light Electricity
5.3 Energy Transformations Occur between different types of energy radiant energy electrical energy chemical energy nuclear energy
Energy Transformations Chemical potential energy stored in the food you eat is converted into simple sugars Where does spent energy go? Lost as heat Chemical changes in muscles Evaporation of sweat from you skin Into kinetic energy!!!
Energy Transformations Power Plants convert chemical energy into electrical energy. 1. chemical energy 2. heat energy 3. mechanical energy 4. electrical energy
Energy Relationship: Conservation of Energy Total Energy = KE + PE Total Energy = ½ mv 2 + mgh
Energy Transformation The work done in lifting the mass gives the mass gravitational PE PE becomes KE KE then does work to push stake into ground
Energy Transformation
Other Forms of Energy Energy is nature s money! Mechanical energy Radiant energy Light energy from the sun Also known as electromagnetic energy