Energy Chapter 5

Mechanical Energy Energy due to movement or position. Energy due to movement or position. Kinetic Energy – energy of motion Kinetic Energy – energy of motion Potential Energy – energy due to position or shape of an object. 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. Total Energy – the sum of all potential and kinetic energies of an object or system.

Kinetic Energy Depends on velocity & mass Depends on velocity & mass Doubling velocity quadruples the energy Doubling velocity quadruples the energy

Examples 5. If a bird flying at 5m/s has a kinetic energy of 1.4J, what is the mass of the bird? 6. What is the difference in kinetic energy between a 2000kg car moving at 5mph,10mph, and 15mph.

Work Kinetic Energy Theorem 7. A car accelerates on a frictionless road at a rate of 3.6m/s 2. 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 H is subjective Only really measures changes in PE Only really measures changes in PE Can be negative whereas KE cannot Can be negative whereas KE cannot

Examples 8. What is the potential energy of a roller coaster car of mass 450kg that is 17m off of the ground? 9. 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. In a closed system, energy cannot be created or destroyed, only changed from one form to another. Closed system Closed system TE before = TE after TE before = TE after Energy added to a system is work on the initial side, energy lost by the system is work on the final side. Energy added to a system is work on the initial side, energy lost by the system is work on the final side.

Examples 10.How tall is the Steel Force roller coaster if the train is moving at 34 m/sec at the bottom of the first hill assuming that it starts from 0 m/sec at the top? 11.How tall is the second hill on Steel Force if the train is moving at 9 m/sec? 12.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. Takes energy from the system and wastes it in heat. It exerts a force over a distance so: It exerts a force over a distance so:

Example #13 A)How much work is done by the brakes of your 1500 kg car in order to slow the car from 10 m/sec to 5 m/sec? B)What is  if the car takes 10 m to slow down?

Example #14 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?

Example #15 A penguin slides down a 6 m long incline of 35 degrees. If the coefficient of friction is 0.3, how fast is the penguin going at the bottom?

Example #16 What is the coefficient of friction if a tuna salad sandwich slides to the bottom of the hill that is 8 m long and at 40 degrees. The sandwich is moving at 2 m/sec at the top of the incline and it is moving at 7.5 m/sec at the bottom.

Example #17 As 65 kg diver jumps from a cliff that is 15 m above the surface of the water. A)How fast is the diver moving just before hitting the water? B)What is the drag force if he stops within 3 m upon entering the water?

Additional Problems 18. 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? 19. 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

Springs x=How much the spring is streched or compressed from its equilibrium position. Measured in meters. 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. k=Spring constant, a measure of how stiff the spring is. The stiffer the spring, the higher the k. Measured in N/m Measured in N/m

Example #20 A spring (k = 100-N/m) gets compressed 40- cm because a 2-kg object collided with it. How fast was the object going?

Example #21 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 un-stretched. If the jumper falls a distance of 45m before switching directions, what is her mass?