Energy Chapter 5
What is energy? • The property of an object that allows it to produce a change in itself or its environment. • In this class we will study • Work • Gravitational Potential Energy • Kinetic Energy • Spring Potential Energy
Work • Generic term for energy given to an object from an outside source or energy lost to the outside from an object. • W=Fdcosθ • θ is the angle between the force and the displacement. • Unless explicitly told otherwise, assume that the angle between force and displacement is 0. • When θ=90o, cosθ=0 so no work is done.
Work • Unit for energy is the Joule. • Other units: calories, kilowatt hours, • Negative work means that the object in question is losing energy i.e. friction. • Sometimes labeled Q when referring to heat specifically.
Practice Problems • A man lifts a 150kg barbell up 2.5m. How much work does he do? • A woman pushes a penguin up an incline of angle 32 degrees. If she pushes horizontally and does 5000J of work, the penguin moves 10m. How much force does she exert?
Power • The rate at which energy is transferred. • Unit is a Watt • 1W=1J/s, so 1J=1Ws and we can convert from Joules to kWhr. • English unit is horsepower.
Power Problem • You leave the 65W bulb in your room on for two weeks. How much energy does it use? • If the electric company charges 12.5 cents per kilowatt hour, how much does it cost your parents?
Mechanical Energy • Energy due to movement or position. • Kinetic energy-energy of motion • Potential energy-energy due to position or shape of an object. • Total energy-the sum of all potential and kinetic energies of an object or system.
Kinetic Energy • Depends on velocity and mass • Doubling velocity quadruples the energy • If a bird flying at 5m/s has a kinetic energy of 1.4J, what is the mass of the bird? • What is the difference in kinetic energy between a 2000kg car moving at 5mph,10mph, and 15mph.
Work Kinetic Energy Theorem • A car accelerates on a frictionless road at a rate of 3.6m/s2. If the car has a final velocity of 42m/s and accelerates over 192m, what was its initial velocity?
Gravitational Potential Energy • H is subjective • Only really measures changes in PE • Can be negative whereas KE cannot • What is the potential energy of a roller coaster car of mass 450kg that is 17m off of the ground? • A 45kg diver dives off of a board which is 7m above the bottom of the pool. If the pool is 2m deep, what is the change in potential energy of the diver from when she is on the board to when she hits the surface of the water?
Conservation of Energy • In a closed system, energy cannot be created or destroyed, only changed from one form to another. • Closed system • Calculate total energy before and after and set them equal to each other. • Energy added to a system is work on the initial side, energy lost by the system is work on the final side.
Practice • A rock is dropped off of a 100m high cliff. How fast is it going right before it hits the ground? • A rock is thrown off of a cliff at an angle of 37 degrees above the horizontal at a speed of 21m/s. If it is going 43m/s when it hits a 2.5m tall man in the head, how high is the cliff?
Friction • Takes energy from the system and wastes it in heat. • It exerts a force over a distance so:
Practice • A 6kg tuna salad sandwich starts from rest and slides down a 20 degree incline that is 4m high. If the final velocity of the box is 7m/s what is the work done by friction? What is the magnitude of the frictional force? • A 10kg wagon full of bananas, starting from rest, is pulled with horizontally with a 25N force across level ground. If the coefficient of friction between the wagon and the ground is 0.2, how quickly is the wagon moving after 25m?
Additional Problems • If the 2kg ball above starts with an initial velocity of 6.7m/s at 2m but only rolls up to a height of 3.1m, how much work is done by friction? • A driver has a truck full of chickens. The chickens and truck have a combined mass of 2200kg. As the truck driver coasts down a frictionless hill, 300kg of the chickens fly out of the truck. If the hill is 11m high and his initial velocity is 12m/s, how fast is he going at the bottom of the hill?
Springs • x=How much the spring is streched or compressed from its equilibrium position. Measured in meters. • k=Spring constant, a measure of how stiff the spring is. The stiffer the spring, the higher the k. • Measured in N/m
Practice Problems • A spring attached to a 2kg block is stretched horizontally 12cm from its equilibrium position. If the block is traveling at 0.89m/s when the spring gets back to its equilibrium position, what is the spring constant of the spring? • A bungee jumper jumps off of a bridge at a speed of 2m/s. The bungee cord has a spring constant of 32N/m and is 12m long when unstreched. If the jumper falls a distance of 45m before switching directions, what is her mass?