Chapter 7: Energy

Chapter 7: Energy

Today Ch. 7 on Energy Note, all lectures and pre-lectures posted up as always at Looking ahead: Sep 27: Review (Chs 2,3,4,5,6,7,8) Sep 30: Midterm Chapter 7 -- Energy Energy is a central concept in all of science. We will discuss how energy appears in different forms, but cannot be created or destroyed. Some forms are more useful than others in the sense of doing work. Before getting into this, check out:

Hold pendulum bob at tip of nose and release. It will never hit nose on swinging back! Energy of position potential energy energy of motion kinetic energy As time goes on, pendulum motion decays: its energy heat Lets start with closely related concept: Work Work = force x distance W = Fd ( c.f. Impulse, last class, which was force x time. A different measure of the effectiveness of the force)

Note this may differ from everyday notion of what work is! Here, we speak of work done on an object. Eg. Weight-lifting If I lift a weight up above my head, I do work: I exert a force, moving the weight a distance = height. Lifting it twice as high, I do twice as much work. But if I am just holding the weight up above my head, I do zero work on the weight, as it is not moved (d=0). (I get tired due to work done on my muscles contracting and expanding, but no work is done on the weight) Clicker Question This poor guy is pushing really hard on the wall but it wont budge. What can you say is true? A) He exerts a large force on the wall but does zero work on it. B) He exerts zero force on the wall and does zero work on it.

C) He exerts a large force on the wall and does a large amount of work on it. D) None of the above is true Answer: A He exerts a large force on the wall but it does not move as there is an equally large frictional force from the ground in the opposite direction. As the wall does not move there is no work done (W=F.d) on the wall. Power Asks how fast is the work done i.e. Power = Work done time interval Eg. A tank of fuel can do a certain fixed amount of work, but the power

produced when we burn it can be any amount, depending on how fast it is burned. It can run one small machine for longer time than a larger machine. Units: Work = Fd, so units are Newton x meter = Joule, J 1 J = 1 N.m Common for biological activity and food, is 1000 J = 1 kJ Power = Work/t, so units are Joule per second = Watt, W 1 kW = 1000 W and 1 MW = 1 000 000 W Eg. About 1 W of power is needed in vertically lifting a quarter-pound one meter in one second. See soon for how we got this Mechanical Energy When work is done on an object, energy is transferred to that object. This energy is what enables that object to then do work itself. Mechanical energy = potential energy + kinetic energy Energy due to relative

position of interacting bodies Energy due to motion Potential Energy (PE) A stored energy due to the configuration of the system (i.e. position of objects). System then has potential to do work. - A stretched or compressed spring, or rubber band if attach an object on the end, it can move that object, so can do work on it. Egs. - Chemical energy in fuels, food etc, due to positions of the constituent atoms. When these atoms are rearranged (chemical process), energy becomes available.

Potential Energy continued An important example: gravitational potential energy Work is required to raise objects against Earths gravity this work is stored as gravitational PE. Eg. In some hydroelectric power plants, water is raised from a lower reservoir up to a higher one so to a state of higher grav. PE. When electric energy is in demand, it is then released from high, PE transforms to motional (kinetic) energy and then electrical energy. Eg. Pendulum: when pull to one side, you are raising it against gravity, exerting a force and doing work on it, giving it grav. PE: How much gravitational PE is stored when object is raised a height h? Must equal the amount of work done in lifting it.: W = F.d , where F = mg, and d = h i.e. gravitational PE = mgh

Eg. How much gravitational potential energy does a quarter-pound hamburger vertically raised 1 m have? Recall 1lb ~ 4.4 N and pound measures weight = mg grav. PE = mgh = (4.4N)(1m) = 1.1 J (recall 1-lb is about 4.4 N) So this is the work done in vertically lifting it 1m, and hence the power needed to do this in 1s is Power = W/t = 1.1 J/1s = 1.1 W (c.f earlier statement) Clicker Question A 1000-kg car and a 2000-kg car are hoisted up the same distance. Raising the more massive car requires A) Less work B) Twice as much work

C) Four times as much work D) As much work E) More than four times as much work Answer: B. Work done = gain in potential energy = mgh. So twice the mass means twice the PE, means twice the work PE = mgh Important note! It doesnt matter how the raise was done: The potential energy of the ball is the same at the top, in all three cases, because the total work done, W = Fd = mgh is the same whether lifted, pushed, or hopped up. (This assumes no force needed to

move it horizontally so neglecting friction) Another important note! h is defined relative to some reference level. Often we take that reference to be the ground. But we dont need to and if we dont, the #s we get for PE are different. Thats ok PE doesnt have absolute meaning. Only changes in it have meaning. When PE changes, the energy gets transformed to a different form (esp. motional) the change has physically measurable consequences. Kinetic Energy (KE) Is the energy of motion: KE = mass x speed x speed i.e. KE = m v 2 KE depends on the reference frame in which it is measured (like the speed). e.g When you are sleeping, relative to your bed, you have zero KE. But relative to the sun, you have KE = (your mass) (107 000 km/h) 2

Work-Energy Theorem When an object speeds up, its gain in KE comes from the work done on it: Work = D KE Can be an increase (+) or decrease (-) in speed Net work Eg. Pushing a table from rest. Its gain in KE = Fnet x distance, where Fnet = your force friction. Only part of the work you do KE of table, the rest heat. Clicker Question Which has greater kinetic energy, an adult running at 3 mi/hr or a child of half the mass running at 6 mi/hr? A) the adult B) the child C) Both have the same kinetic energy. D) More information is needed about the distance traveled.

Answer: B KE = mv2, so for child, mass halved but v doubled means KE is doubled. Questions (1) A father pushes his child on a sled on level ice, a distance 5 m from rest, giving a final speed of 2 m/s. If the mass of the child and sled is 30 kg, how much work did he do? W = D KE = m v2 = (30 kg)(2)2 = 60 J (2) What is the average force he exerted on the child?

W = F.d = 60 J, and d = 5 m, so F = 60/5 = 12 N More Questions (3) Consider a 1000-kg car going at 90 km/h. When the driver slams on the brakes, the road does work on the car through a backwarddirected friction force. How much work must this friction force do in order to stop the car? W = D KE = 0 - m v2 = - (1000 kg) (90 km/h)2 (1000 m/3600 s)2 = -312500 J = -312.5 kJ So W = 312.5 kJ (the sign just means the work leads to a decrease in KE) Clicker Question Stopping Distance: How much more distance do you need to come to a complete stop

when you slam on the brakes while going at 90 km/h compared to 45 km/h ? (Note that the frictional force the road exerts does not depend on speed). A) Half the distance B) The same C) Twice the distance D) Four times the distance E) Need more information in the problem Answer: D W = F d = D KE, where F is the friction force. Since, for speeds twice as large, the KE is four times as large, this means the stopping distance is also four times as large. Conservation of Energy Law Kinetic and potential are two fundamental forms of energy; another is

radiation, like light. Other (less fundamental) forms of energy: chemical, nuclear, sound Note that work is a way of transferring energy from one form to another, but itself is not a form of energy. Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes. Energy is recycled between different forms. eg. Earlier pendulum example Eventually, pendulum stops, due to energy transformed to heat in air and string

Another example Eg. Dropping down from a pole. As he dives, PE becomes KE. Always total energy constant. If accounted for air resistance, then how would the numbers change? In presence of air, some energy gets transformed to heat (which is random motion of the air molecules). Total energy at any height would be PE + KE + heat, so at a given height, the KE would be less than in vacuum. PE would be the same for same height. What happens to the energy when he hits the ground? Just before he hits ground, he has large KE

(large speed). This gets transformed into heat energy of his hands and the ground on impact, sound, and energy associated with deformation . Clicker Question A marble is rolling down an incline, starting from rest at the top. At what point is its kinetic energy equal to its potential energy? A) At the top B) At the bottom C) Halfway down D) A quarter of the way down Answer: C From energy conservation: at the top, zero KE and PE = mgh where h is the height of the incline. As it rolls, the marble loses PE which turns into KE, and it speeds up. At half the height of the incline, hh/2 so the

PE is halved and, the other half of the PE has become KE. And another example: sun and then to earth.. In the core of the sun, thermonuclear fusion occurs: due to gravity and very high temperature, hydrogen nuclei fuse together making helium nuclei, releasing lots of radiant energy. i.e potential + kinetic radiant energy. A small part of this radiation reaches the earth stored as chemical energy in plants, coal etc. kinetic energy, electric energy, etc Recall hydroelectric power earlier : in fact suns radiant energy gravitational potential energy of water as it evaporates it from oceans etc, some may return to earth trapped in a dam at high elevation then be transformed to kinetic as it falls electric energy powering our homes Clicker Question Three baseballs are

thrown from the top of the cliffalong paths A, B, and C. I f their initial speeds are the same and air resistance is negligible, the ball that strikes the ground below with the greatest speed will follow path 1. A. 2. B. 3. C. 4. Either A or C. 5. All strike with the same speed. Answer: all strike with

same speed. Three baseballs are thrown from the top of the cliffalong paths A, B, and C. I f their initial speeds are the same and air resistance is negligible, the ball that strikes the ground below with the greatest speed will follow path 1. A. 2. B. 3. C. 4. Either A or C.

5. All strike with the same speed. The speed of impact for each ball is the same. With respect to the ground below, the initial kinetic + potential energy of each ball is the same. This amount of energy becomes the kinetic energy at impact. So for equal masses, equal kinetic energies means the same speed. Machines Something that multiplies forces, and/or changes their direction. Main principle: energy is conserved, Work input = work output (if we can neglect friction) Eg. Lever : put load close to fulcrum. Then small input force (down on the left) yields a large output force on the load (up on the right). Input force

moves over large distance, load is lifted up short distance (W = Fd same for output and input) fulcrum Eg. Pulley same principle as lever Here, it just reverses direction of input force (no multiplication) Here (block and tackle pulley system), man pulls with a force of 50 N, but can lift 500 N weight up: he moves the rope 10x the distance that the weight moves vertically

up. NB: Always, energy is conserved machines just trade force for distance, but so that the product Fd is the same input as output. Efficiency In reality, Work output < Work input, because some energy is dissipated as heat i.e. thermal energy, which is random molecular kinetic energy, not useful. Define Efficiency = useful energy output total energy input Eg. Pulley system much of the input energy goes into thermal energy from friction, with ropes and pulleys turning and rubbing about the axles.

Say you put in 100 J of work but the output is only 40 J. Then efficiency = 40%. Comparing kinetic energy and momentum Both are a measure of motion, and both are bigger when things go faster, and when things are heavier. Differences: momentum is a vector, with direction, whereas KE is a scalar, always greater or equal to 0. Also, momentum is always conserved in a collision, whereas KE is not Momentum scales with speed as v, however KE scales as v2 The change in momentum is determined by impulse imparted on the object, whereas change in KE is determined by the work done on it.

Example: Youre standing on a log while a friend tries to knock you off by throwing balls to you. Should you try to catch the ball, or let it bounce off you, in order to try not to fall off the log? (analyze in terms of change in momentum) If you catch the ball, ball changes its mom. from mv to 0. Whereas, if you let it bounce off you, ball reverses direction of momentum, so change in momentum is twice as large. So its better to try to catch it, as there is less change. That example has similar physics to one in your book metal vs rubber bullet on a wooden block (or a person ). The rubber bullet tends to bounce off, whereas the metal bullet penetrates. For rubber bullet, the change in

mom. and the impulse, is greater: if it bounces back elastically, the change is 2x that for the metal bullet. Because it does not penetrate, it does little damage very little (none if elastic) change in its KE. Whereas the metal bullet comes to rest and all its KE becomes heat so damage Sources of energy Except for nuclear, and geothermal power, source of our energy is ultimately the sun: eg. Gas, wood, coal, petroleum combustion all these come from plants, which used suns radiant energy in photosynthesis. Also, sun is responsible for energy in photovoltaic cells in solar-powered panels, and in generating electricity (see earlier, hydropower) Wind power, in a sense comes from sun too, since wind is due to

unequal warming of Earths surface. Harder for us to control. Nuclear power - uranium, plutonium, very powerful. Fears of radiation leakage have limited its growth. Note that the earths core is so hot because of naturally occurring nuclear radioactive decay! Geothermal energy from underground reservoirs of hot water, so often in volcanic lands. Two smooth tracks of equal length have bumpsA up, and B down, both of the same curvature. I f two balls start simultaneously with the same initial speed, the ball to complete the journey first is along 1. Track A.

2. Track B. Both at same 3. Track C. time Answer: Track B Recall question from Lec 2 Two smooth tracks of equal length have bumpsA up, and B down, both of the same curvature. I f two balls start simultaneously with the same initial speed, the ball to complete the journey first is along 1. Track A.

2. Track B. 3. Track C. Although both balls have the same speed on the level parts of the tracks, the speeds along the curved parts differ. The speed of the ball everywhere along curve B is greater or same than the initial speed, whereas everywhere along curve A it is less. So the ball on Track B finishes first. Does the gain in speed at Bs bottom equal the loss at As top? No! Speed isnt conserved: energy is. The loss in kinetic energy at the top of A will be equal to the gain in kinetic energy at the bottom of Bif there is enough energy to begin with. (Extra Question) Two smooth tracks of equal length have

bumpsA up, and B down, both of the same curvature. I f the initial speed = 2 m/ s, and the speed of the ball at the bottom of the curve on Track B is 3 m/ s, then the speed of the ball at the top of the curve on Track A is 1. 1 m/ s. 2. > 1 m/ s. 3. < 1m/ s. Answer: < 1m/s Two smooth tracks of equal length have bumpsA up, and B down, both of the same curvature. I f the initial speed = 2

m/ s, and the speed of the ball at the bottom of the curve on Track B is 3 m/ s, then the speed of the ball at the top of the curve on Track A is 1. 1 m/ s. 2. > 1 m/ s. 3. < 1m/ s. The change in the speed in either track comes from change in the kinetic energy that happens because potential energy changes (change in height) while total energy remains constant. For track B, at the bottom, gain in KE = mgh = m(32 -22) = m(5). This means for track A, loss in KE = m(5) at the top but this is greater than the initial KE m (2)2 = m(4). So the ball actually never makes it to the top of As curve!

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