Energy Chapter 9 Objectives Define and describe work

Energy Chapter 9

Objectives Define and describe work. u Define and describe power. u State the 2 forms of mechanical energy. u State 3 forms of potential energy. u Describe how work and kinetic energy are related. u State the work-energy theorem. u State the law of conservation of energy. u Describe how a machine uses energy. u Explain why no machine can have an efficiency of 100%. u Describe the role of energy in living organisms. u

9. 1 Work u Recall that a change in an object’s momentum is related to an impulse – a force and how long the force acts. u “How long” does not always mean time, however. It can also mean distance. u Force x distance = work ØWork is the product of the force on an object and the distance through which the object is moved.

9. 1 Work u For work to be done in Physics, a force acts on an object and the object moves in the direction of the force. ØWork is done on a load when you lift it against Earth’s gravity. ØNo work is done on the load to hold it once it has been lifted or to carry the load around the room.

9. 1 Work u u Work is done only in lifting the barbell. The physics of a weightlifter holding a stationary barbell is no different than the physics of a table supporting a barbell's weight. NO NET FORCE acts on the barbell (forces are balanced!!), no work is done, and no change in its energy occurs.

Is This Work? ? ? u. A student applies a force to a wall and becomes exhausted. u A book falls off a table and lands on the ground. u You do some push-ups. u A waiter carries a tray full of meals across the room.

9. 1 Work u The waiter does NO work because the object is NOT moving in the direction of the force. (The force is against gravity – its in an up & down direction. )

9. 1 Work u Mathematically, work = force x distance. ØW = Fd u The unit for work combines the unit force, N, with the unit for distance, m. u A N-m is also called a joule (J). Ø 1 k. J equals 1000 J.

W=Fxd Recall that when lifting an object against gravity, the force required equals the object’s weight. u Fgrav = Weight = mg u Therefore, W = mgd u So, if the mass is doubled, the required force and work are doubled. u If the distance is doubled, the work is doubled. u Force (F) and distance (d) are both directly proportional to work. u

9. 1 Work u There are 2 kinds of work. 1. Work done against another force • To pick up an object you do work against gravity. • To push an object, you do work against friction. 2. Work is done to change the speed of an object. • Work is done to speed up or slow down a car. u In either case, when work is done, a transfer of energy occurs between an object and its surroundings.

Practice A weight lifter lifts a barbell. How much work is done if he lifts a barbell that is twice as heavy the same distance? If he lifts a barbell that is twice as heavy and 2 x as far? u If you apply a 50 N force to a package, pushing it across the floor 3 m, how much work do you do? u A tugboat pulls a ship with a constant net horizontal force of 5000 N. How much work does the tugboat do on the ship if each moves a distance of 3. 00 km? u

9. 2 Power When you climb a staircase, you do the same amount of work whether you get to the top in 30 sec. or 2 minutes. u What is different in each case is how fast the work is done or the power. u

9. 2 Power is the rate at which work is done. u Power equals the amount of work done divided by the time interval during which the work is done: P = Fd = mgd t t u

9. 2 Power u Power = Work/Time. This means power is directly proportional to work and indirectly proportional to time. u Having twice the power, then, can mean several things. ØTwice the work can be done in the same amount of time. ØThe same work can be done in ½ the time.

9. 2 Power The unit of power is the joule per second or watt (W). u For historical reasons, the horsepower is occasionally used to describe the power delivered by a machine. u One horsepower is equivalent to approximately 750 Watts. u To lift a ¼ lb. cheeseburger a distance of 1 m in 1 s requires 1 watt of power!

Practice u u u Two physics students, Will and Ben, are in the weightlifting room. Will lifts the 100 -pound barbell over his head 10 times in one minute; Ben lifts the 100 -pound barbell over his head 10 times in 10 seconds. Which student does the most work? Which student delivers the most power? If little Nellie Newton lifts her 40 -kg body a distance of 0. 25 meters in 2 seconds, then what is the power delivered by little Nellie's biceps? Joe elevates his 80 -kg body up the 2. 0 meter stairwell in 1. 8 seconds. What is his power?

9. 3 Mechanical Energy u When work is done on an object, the object acquires the ability to do work on something else. ØFor example, when you do work to lift a hammer, the hammer now has the ability to do work on a nail. u The property of an object that enables it to do work is energy. ØEnergy is measured in joules.

9. 3 Mechanical Energy u Mechanical energy is the energy due to the position or movement of an object. u The 2 forms of mechanical energy are kinetic energy and potential energy.

9. 4 Potential Energy that is stored and held in readiness is called potential energy (PE). u Stored energy has the potential to do WORK. u 3 kinds of PE are: elastic PE, chemical PE, and gravitational PE. u

Elastic Potential Energy A compressed or stretched spring has the potential to do work. u Other examples include a stretched rubber band or a stretched string on a bow and arrow. u

Chemical Energy Fuels (like oil or food) have chemical potential energy. u This energy is available to do work when a chemical reaction breaks the bonds between the atoms in a fuel and thereby releases the energy stored in them. u

Gravitational Potential Energy Work is required to elevate objects against gravity. The lifted objects then have PEgrav. u The work required (above) will be the same in each case because the work is equal to the force (weight of the object) times the distance it is moved against gravity (3 m in each case). u

Gravitational Potential Energy u The amount of gravitational PE possessed by an elevated object is equal to the work done in lifting it. PEgrav = Fd Since F = weight & weight = mg, PEgrav = mgh (where h = height or distance lifted)

Gravitational Potential Energy u u u The height is the distance above a chosen reference level. Often this reference level is the ground or floor. A book on a table will have no height relative to the table and no PE. It does, however, have a positive PE relative to the floor.

Uses of PEgrav u u Hydroelectric power makes use of the gravitational potential energy of water. Falling water drives a turbine, which is connected to a generator. The generator converts the energy from the falling water into electrical energy.

Practice u Knowing that the potential energy at the top of the tall pillar is 30 J, what is the potential energy at the other positions shown on the hill and the stairs.

Practice u If a force of 15 N is used to lift a load to height 3 m from the ground, what is the PE of the load? u A 10 kg mass is suspended 5 m from the ground. ØHow much work was done to the mass? ØIf it is lifted in 2 sec. , how much power is expended? ØWhat is the PEgrav of the mass?

9. 5 Kinetic Energy u u u If an object is moving, it is capable of doing work. It has energy of motion or kinetic energy (KE). The amount of kinetic energy which an object has depends upon two variables: Ø the mass (m) of the object Ø the speed (v) of the object. KE = 2 ½mv

9. 5 Kinetic Energy u The kinetic energy of a moving object is equal to the work required to bring it to its speed from rest or to the work it can do while it is being brought to rest. KE = W 1/2 mv 2 = Fd

1/2 mv 2 = Fd What this means: – If the speed of a vehicle is doubled, its KE is quadrupled. – So, 4 x as much work must be done to stop the vehicle. – If the braking force used to stop the vehicle is the same, the distance required for stopping will be 4 x as great. u What if the speed is tripled?

Types of Kinetic Energy Thermal energy u Sound u Light u Electricity u

Kinetic Energy Kinetic energy often appears “hidden” in one of its different forms, such as heat, sound, light, and electricity. • Random molecular motion is sensed as heat. • Sound consists of molecules vibrating in rhythmic patterns. • Light energy originates in the motion of electrons within atoms. • Electrons in motion make electric currents.

Practice Determine the kinetic energy of a 1000 -kg roller coaster car that is moving with a speed of 20. 0 m/s. u If the roller coaster car in the above problem were moving with twice the speed, then what would be its new kinetic energy? u Alison, a platform diver for the Ringling Brother's Circus, has a kinetic energy of 15, 000 J just prior to hitting a bucket of water. If Alison’s mass is 50 kg, then what is her speed? u

9. 6 Work-Energy Theorem u The work-energy theorem describes the relationship between work and energy: whenever work is done, energy changes. u Work = ΔKE

9. 6 Work-Energy Theorem u Work equals change in KE. Ø If you push on a box and it does not slide, then no work is done on the box. Ø If there is no friction, the box will slide. The force and distance of your push will be the KE of the box. (If there is some friction, the net force is what is considered. ) Ø If the box has a constant speed, your push is just enough to overcome friction. Since the net force is 0, work is 0 and there is no change in KE of the box.

9. 6 Work-Energy Theorem u u The more KE an object has, the more work must be done to stop it. This infrared shot of a tire shows that some of the KE of a vehicle was transferred into thermal energy of the tire when the vehicle was stopped.

9. 6 Work-Energy Theorem u u Recall our skidding example from a previous slide. The maximum braking force that brakes supply is independent of speed – it is nearly always the same. Therefore, a car moving at twice the speed has 4 x as much KE. It will take 4 x as much distance to stop. Distances may be even greater if a driver’s reaction time is taken into account.

9. 7 Conservation of Energy Nearly every process in nature can be analyzed in terms of transformations of energy from one form to another. u In this toy car, for example, work is done to wind it up. The car then has elastic potential energy. When released, it is converted into kinetic energy and heat. u Energy changes from one form to another, without a net loss or gain. u

9. 7 Conservation of Energy u The law of conservation of energy states that energy cannot be created or destroyed. It can be transformed from one form into another, but the total amount of energy never changes.

9. 7 Conservation of Energy In a swinging pendulum system, there is one quantity that does not change: the total energy of the system. Due to friction, energy will eventually be transformed into heat.

9. 7 Conservation of Energy changes from one form to another but the total amount of energy remains the same. In this example, the total amount of energy can also be called the total mechanical energy.

Practice 1. As the object moves from point A to point D across the surface, the sum of its gravitational potential and kinetic energies ____. a. decreases only b. decreases and then increases c. increases and then decreases d. remains the same 2. The object will have a minimum gravitational potential energy at point ____. a. A b. B c. C d. D e. E 3. The object's kinetic energy at point C is less than its kinetic energy at point ____. a. A only b. A, D, and E c. B only d. D and E

Practice 0 m/s

9. 8 Machines u u u A machine is a device that is used to multiply or change the direction of forces. Based on the law of conservation of energy, a machine cannot put out more energy than is put into it. What a machine can do is transfer energy from one place to another or transform it from one form to another.

Levers A lever is a simple machine made up of a bar that turns about a fixed point. u The fixed point is called the fulcrum. u A lever changes the direction of a force – when the lever is pushed down, the load is lifted up. u

Levers If we neglect friction: work input = work output u Since work = Fd, (Fd)input = (Fd)output u On one end of this lever, a small input force is exerted over a large distance. u This produces, on the other end of the lever, a large force exerted through a short distance. u This machine has multiplied the force (but not the work)! u Note: in this lever, the fulcrum is relatively close to the load.

Mechanical Advantage Consider an ideal example: the girl pushes with a force of 50 N and lifts a load of 5000 N. u The ratio of Foutput to Finput for a machine is called the mechanical advantage. u Foutput =5000 N = 100 Finput 50 N u

Mechanical Advantage MA = Foutput = 100 Finput u Notice that doutput is 1/100 th of dinput. u This means, mechanical advantage can also be calculated using the distances: u MA = dinput doutput

Types (or Classes) of Levers A type 1 lever has the fulcrum between the input and output forces. u Examples include: u

Types of Levers In a type 2 lever, the output force (the load) is between the fulcrum and the input force (the effort). u In this lever, the forces have the same direction. u Examples include: staplers, bottle openers, nut crackers, and u

Types of Levers In a type 3 lever, the fulcrum is at one end and the output force (the load) is at the other. The input force (the effort) is between them. u In this lever, the forces have the same direction. u Examples include: your biceps and u

Pulleys u u A pulley is a kind of lever that can be used to change the direction of a force. This single pulley is like a type 1 lever – the fulcrum (pulley axis) is between the input and output forces. Someone pulls down on the rope and the load is lifted up. The MA of this type of pulley is 1: Finput = Foutput ( & dinput = doutput)

Pulleys u u This single pulley acts as a type 2 lever - the load is between the input force and the fulcrum (ropepulley contact point). Pulling up on the rope lifts the load up. The MA of this pulley is 2: a 2 N load can be lifted with a 1 N force; the rope will be pulled 2 m for every 1 m the load is lifted. An easy way to determine MA is to count the number of ropes that support the load: 2!

Pulleys The MA for pulley systems is the same as the number of strands that support the load. u In this diagram, there are 5 strands of rope but only 4 support the load. The MA, then, is 4. u Calculated: MA = Foutput = 100 = 4 Finput 25 u

Practice u If a pulley can lift a 500 N load with a force of 100 N, what is its MA? u A lever is pushed downward a distance of 1 m. As a result, a load is lifted up 1/8 m. What is the MA of this lever? u John’s biceps contract 1 cm to lift a 10 N load a distance of 10 cm. What is the MA of his biceps?

9. 9 Efficiency u In our IDEAL examples, Winput = Woutput IDEAL machines have 100% efficiency. u REAL machines are not 100% efficient. In REAL machines, some input energy is used to overcome frictional forces and is converted into thermal energy.

9. 9 Efficiency The efficiency of a machine is the ratio of useful energy output to total energy input. It is often expressed as a percentage. u E = useful Woutput x 100 total Winput u If you do 50 J of work on a lever and get out 42 J of work, the efficiency of the lever is: 42 J x 100 = 0. 84 or 84%. 50 J u Ø 8 J of your work is “lost” to heat. Ø The lower the efficiency, the greater the amount of energy that is wasted.

Practice Problems 1. 2. Using a lever, a person applies 60 N of force and moves the lever by 1 m. This moves the 200 N rock at the other end by 0. 2 m. What is this machine’s efficiency? A person in a wheelchair exerts a force of 25 N to go up a ramp that is 10 m long. The weight of the person and wheelchair is 60 N and the height of the ramp is 3 m. What is the efficiency of this machine?

Inclined Plane This machine is generally used to elevate heavy loads. Less force is required (Finput) to slide a load up an incline than is required to lift it vertically (Foutput). u Recall that MA = dinput doutput u MA = 6 m/3 m = 2 u This is an IDEAL (or theoretical) MA , the IMA. u

Inclined Planes However, inclined planes do not have efficiency’s of 100%. Some of the work done to go up a ramp, for example, is “lost” to the ramp through friction. Actual MA is much less than theoretical MA (IMA). u AMA = Foutput Finput u

Inclined Planes u u u Efficiency can also be expressed as a ratio of actual MA to ideal MA. E = actual MA x 100 ideal MA Practice: 1. If an inclined plane has a theoretical MA of 2 but an actual MA of 1. 8, what is its efficiency? 2. A pulley has an IMA of 6 and an AMA of 5. What is its efficiency?

Complex Machines u Inclined plane u An auto jack is a combination of 2 simple machines – a lever and an inclined plane wrapped around a cylinder. Turning the handle raises the load a distance of 1 pitch (the distance between ridges). The theoretical MA of a jack is very high; however, the efficiency is only about 20%. Actual MA approximates 100.

Complex Machines u Automobile engines are also complex machines. u In the engine, the chemical energy of a fuel is released when the fuel is burned. Much of the energy (65%) released is transformed into thermal energy; the remainder is transformed into the mechanical energy used to run the engine.

9. 10 Energy for Life Cells are machines and need a supply of energy. They use the energy stored in hydrocarbons (like glucose). The energy is released during respiration (a reaction of the fuel with oxygen). u There is more energy stored in the molecules of food than is stored in the products of food metabolism. This energy difference is used to sustain life. u Metabolism is like the burning of fuel in an engine. The difference is the rate of energy release. Reaction rates in metabolism are very slow. u

9. 11 Sources of Energy The SUN is the source of nearly all our energy on Earth. u Plants use sunlight during photosynthesis to produce hydrocarbon compounds. These compounds become our wood, fossil fuels and our food. u

Solar Power SOLAR POWER takes sunlight and converts it directly into electricity by using photovoltaic cells. u Indirectly, the sun powers the water cycle; here falling water can turn generator turbines and generate electricity. u

Solar Power u Wind power is another indirect form of solar power. Wind, caused by the unequal heating of the Earth’s surface, can be used to turn generator turbines in special windmills.

Fuel Cells u Much is being done today to use hydrogen as a fuel. When it is burned, water vapor is the only product. u Hydrogen is NOT a source of energy, however, because it must be “made” from water and carbon compounds. This requires energy.

Fuel Cells Electricity is used to split water molecules into hydrogen and oxygen in a process called electrolysis. Fuel cells makes the electrolysis process run in reverse. Water is produced and electric current is generated.

Nuclear and Geothermal Energy u u u Nuclear fuels, like uranium and plutonium, are the most concentrated forms of usable energy. Radioactivity from such fuels keeps the Earth’s interior hot. Geothermal energy is held in underground reservoirs of hot water. They can be tapped to provide steam for running generator turbines.