Work, Power, Energy Work

Vocabulary Work (force x distance) Kinetic Energy ( ½ mass x velocity2) Potential Energy( mass x g x height) Review P = mv J = mΔv F = ma The Daytona 500 ( centimeters that is!!!)

World’s Fastest Roller Coaster How did the car get up high? What changes take place during fall? What changes take place during rise? Are these changes related?

Work Work – Exerting force in a way that makes a change in the world. Throwing a rock is work: you’re exerting a force, and the rock’s location changes (i.e. “the world has been changed”) Pushing on a brick wall is not work: you’re exerting a force, but “the world doesn’t change” (the wall’s position doesn’t change).

Work So exerting force alone isn’t enough. You have to both exert a force, and make a change. If you’re not exerting a force, you’re not doing work. Example: Throwing a ball. While you are “throwing the ball” (as opposed to just holding it) you are exerting a force on the ball. And the ball is moving. So you’re doing work. After the ball leaves your hand, you are no longer exerting force. The ball is still moving, but you’re no longer doing work.

Work Done By “Lifting” Something When we were pushing something along the ground, the work done didn’t depend on the mass. Lifting up something does do work that depends on mass. Because of gravity: Gravity always pulls down with a force equal to mg, where m is the mass, and g = 9.8 m/s2. So we must exert at least that much force to lift something. The more mass something has, the more work required to lift it.

W = Fd cos Work is a scalar The work done by force is defined as the product of that force times the parallel distance over which it acts. The unit of work is the newton-meter, called a joule (J) The kilowatt hour is the unit of work. If a force is doing work at a rate of 1 kilowatt (which is 1000J/s), then in 1 hour it will do 1kW.h of work. A kW.h = 3.6 x 106 J Work is a scalar

Force is NOT Work If the force is perpendicular to the direction the object moves, the work done is 0. If the object doesn’t move, the work done is 0.

Two Conditions for Work 1. Force must act through a distance 2. Distance must be in the direction of force Discuss work required for satellite orbit

Negative Work All of our examples have increased the potential energy or the kinetic energy Recall, Work = (Force in the direction of motion) x distance traveled in the direction of the force When force is opposite the direction of motion, negative work is done. Work decreases the energy

Working at an advantage Often we’re limited by the amount of force we can apply. Simple Machines such as ramps, levers, pulleys, etc allow us to do the same amount of work, but by applying a smaller force over a larger distance Work = Force x Distance = Force x Distance

Ramps Ramps allow the exertion of a smaller force over a longer distance to achieve the same change in gravitational potential energy (the same amount of work) M

Horizontal Force and the Resulting Horizontal Acceleration Only the horizontal component of the force does work in the horizontal How much work is done moving the wagon 3 meters?

Vertical Work??? I lift a book of mass 2 kg. from the floor to the desk, or 1.2 meters. W = ??? I lift the same book from the desk to 2.2 m above the desk. W = ??? What work is done to get the same book from the floor to total height of 3.3m ??

Work, Power, Energy Power

Power Rate of doing work: Power = Work per unit time (1 Joule per second = 1 Watt) 1000 Watts = 1 kilowatt 1 horsepower (hp) = 746 W Power is a scalar quantity

Power The rate of using energy If you do 100 joules of work in one second (using 100 joules of energy), the power is 100 watts Power keeps something moving:

Work, Power, Energy Work-Energy Theorem

Wnet = DKE Work – Energy Theorem The work done on an object by a net force equals the object’s change in kinetic energy. Wnet = DKE The amount of energy transferred to the object is equal to the work done. DE = W In changing speed from 0 to v, work is done. The kinetic energy increases by an amount equal to the work done.

The capacity to do work. Energy You must have energy to accomplish work – it is like the "currency" for performing work. To do 100 joules of work, you must expend 100 joules of energy.

Doing work exchanges energy Kinetic Energy = energy of motion A rolling bowling ball can “do work” A falling anvil can do work Potential Energy = Latent capacity for doing work Gravitational potential energy Nuclear potential energy Chemical potential energy Processes can convert energy from one form to another, but the total amount is always conserved. Why is the usable energy decreasing even though total energy is conserved??

Energy We call this “energy of motion” kinetic energy. An object’s kinetic energy is given by this equation: K = ½ mv2 Velocity of the moving object (m/s) Mass of the moving object (kg) Kinetic Energy (J)

Remember the Book? If we put work into the book to lift it, where did that work energy go??? Can we get it back??

Potential Energy (stored energy) Potential Energy – The amount of energy something has “available” that can be converted to other forms of energy. There are different “sources” of potential energy. Gravity – Gravity can exert force through a distance. Force – force due to gravity between the two objects. Distance – how far an object is allowed to fall.

Energy can be converted into other forms As something falls, gravitational potential energy is converted into kinetic energy A sliding frictional force converts kinetic energy into “thermal energy” Just rub your hands together! Where did that energy originate? If you “do work” on something, you change its energy by an amount equal to the work done.

Kinetic Energy + Potential Energy = Mechanical Energy Work, Power, Energy Kinetic Energy + Potential Energy = Mechanical Energy

Kinetic Energy The energy possessed by an object because it is in motion. Is a scalar quantity Units of kinetic energy: Joules An object with mass of 1 kg, moving at 1 m/s, has a kinetic energy of 0.5 Joule.

Kinetic Energy An object’s kinetic energy depends on: the object’s mass. Kinetic energy is directly proportional to mass. the object’s speed. Kinetic energy is directly proportional to the square of the object’s speed. Destructive energy is proportional to KE!

PE - Mechanical

PE = - WorkF Potential Energy Work is not always converted directly into kinetic energy. Instead it is “stored”, or “hidden”. Potential energy is stored energy or stored work. Potential energy is energy that an object (system) has due to its position or arrangement. PE = - WorkF

Gravitational Potential Energy is the energy possessed by an object because of a gravitational interaction. The gravitational potential energy of an object at height h equals the negative of the work that gravity does when the object is lifted from the PE = 0 position PEg = mgh (= W x h or F x h or F x dist.)

Elastic Potential Energy A spring or other elastic media can store potential energy Can define PE as the work required by a external force to move the object without acceleration between the two points As spring is stretched (or compressed) the force changes, so we must average.

Conservation of Energy Work, Power, Energy Conservation of Energy

Mechanical Energy Mechanical Energy = PE + KE Energy by itself is impossible to determine (you can’t measure energy of any object at any single state) but you can measure changes in energy.

Conservation of Energy The Law of Conservation of Energy states that within a closed, isolated system, energy can change form, but the total amount of energy is constant. Energy can neither be created nor destroyed. If no external forces act on a system, the total energy of the system will remain constant.

Conservation of Energy As you throw a ball up in the air, the moment it leaves your hand the ball has little potential energy but a lot of kinetic energy. As the ball moves upward, the kinetic energy is transferred to potential energy and the ball slows down. At the top of the path, the ball has stopped traveling upward and has transferred all the kinetic energy into potential energy. Because of the force due to gravity, the ball starts to move down, the potential energy converting to kinetic energy, increasing the velocity of the ball, until it is caught.

KE-PE on an Inclined Plane

KE-PE in a Pendulum