Energy

1. Energy Chapter 8

2. Energy • We discuss energy frequently, but what is energy? • Energy is the ability to do work but energy • Types of energy: • Kinetic • Potential • Gravitational • Elastic

3. Work • The Equation: W = Fd • The units: • W = Work = Joules (J) • F = Force = Newtons (N) • d = Distance = meters (m) • Work is defined as: • applied energy • It takes work to move something • Can make energy

4. As the equations states a force must be applied over a distance in order for there to be work. • If it does not move, then no work has been done • Often times, forces occur at an angle, in this case we find the x component of the distance and use it in the equation: W = Fd(cosΘ)

5. How do you know WORK is being done? • There is a force or a distance • There is friction • The objects slows down or speeds up

6. Sample Problem #1 • You push a 1000 newton car 5 meters at 30° to the ground. How much work did you do? F = 1000 N W = Fd(cosΘ) d = 5 m W = (1000 N)(5m)(cos 30° ) W = ? W = 5000J (.866) Θ = 30° W = 4330 J

7. Potential Energy • The equation: Ep = mgh • The units: • Ep = potential energy = Joules (J) • m = mass = kilogram (kg) • g = acceleration due to gravity = meters/squared seconds (m/s2) • h = height distance = meters (m)

8. Potential Energy is defined as energy due to position. • It comes from the pull or gravity • How do you know there is potential energy? • An object is above the ground • An object is dropped or tossed up • An object goes up or down

9. Sample Problem #2 • How much potential energy does a 4 kg object have that is 5 meters off the ground? m = 4 kg Ep = mgh h = 5 m Ep = (4kg)(9.8 m/s2)(5m) g = 9.8 m/s2Ep = 196.2 J Ep = ?

10. Kinetic Energy • The equation: Ek=½ mv2 • The units: • Ek=kinetic energy = Joules (J) • m = mass = kilogram (kg) • v = velocity = meters/second (m/s)

11. Kinetic Energy is defined as the energy of motion. • An object has kinetic energy when it is moving. • An object gets kinetic energy from falling (Ep) or by being pushed (from Work). • An object loses Ek by going up (due to gravity), friction, or negative force.

12. How do you know there is Kinetic Energy? • An object is moving (velocity). • An object is thrown or is falling. • An objet changes speed.

13. Sample Problem #3 • How much kinetic energy does a 10 kg object traveling 3 m/s have? m = 10 kg Ek=½ mv2 v = 3 m/s Ek=½ (10 kg)(3 m/s)2 Ek= ? Ek= 45 J

14. Elastic Potential Energy • The equation: Eep=½ kx2 • The units: • Eep=elastic potential energy = Joules (J) • k = spring constant = Newtons/meters (N/m) • x = distance = meters (m)

15. Elastic Potential Energy is defined as: • The potential stored (compress) or released (stretched) in a spring or elastic object. • The spring constant or force constant will be given. • The distance in the equation is the distance that the spring is stretched or compressed from its resting position.

16. How do you know there is Elastic Potential Energy? • There is a spring involved (or elastic object). • An object is compressed. • An object is stretched.

17. Sample Problem #4 • A spring has a 4 N/m spring constant and a resting position of 0.5 m. If it is stretched to 2.5 m, find its elastic potential energy. k = 4 N/m Eep=½ kx2 xi = 2.5 m Eep=½ (4 N/m)(2m)2 xf = .5 m Eep= 8 J x = 2 m

18. Power • The equation: P = W/t • The units: • P = power = Watts (W) • W = work = Joules (J) • t = time = seconds (s)

19. Power is defined as how fast work is done • The more powerful something is, the faster work is done • A less powerful device an do the same amount of work, but it will take a longer time

20. Sample Problem #5 • You do 120 J of work in 2 seconds. Find your power. W = 120 J P = W/t t = 2 s P = 120J/2s P = ? P = 60 W

21. The Law of Conservation of Energy • “Energy is never created no destroyed, just transformed into other forms of energy.” • We can answer a lot of questions using this law, but it may be trick remember which part of energy to use. • Remember: • EK if the object is moving • EP if the object is off the ground • Eep if the object is elastic or attached to a spring • W if there is a force, horizontal distance, or friction.

22. Sample Problem #6 • A 2 kg ball going 6 m/s stops in 4 m. Find the force of the friction that stopped it. m = 2 kg EK = W v = 6 m/s ½ mv2 = Fd d = 4 m ½ (2kg)(6m/s)2 = F (4m) F = ? F = 9N * We used EK because the mass is moving.

23. Remember that the height of EP must be straight up! • If you are given an angle, you may need to use sin, cos, or tan to find the vertical height

24. Practice Problem #1 Potential Energy at the top d is the length of the ramp not the height! m d = 6m h = 3m m Equals kinetic energy at the bottom Θ = 30°

25. Potential energy at the top should be equal to kinetic energy at the bottom- IF THERE IS NO FRICTION. • If there is friction slowing the object down: the potential energy at the tope equals the work done by the friction plus the kinetic energy of the object • We will only be dealing with frictionless examples…for now. 

26. Dropped and Thrown Objects • If an object is dropped, its potential energy is transformed into kinetic energy. In the absence of friction these two amounts are equal: • Part way down the object has both potential and kinetic energy. • A the bottom the object has no potential energy and all kinetic energy.

27. Look at the picture at the bottom left and answer these questions. • Calculate the potential energy the object has at the top of the inclined plane. • Calculate the potential energy the object has at the bottom of the inclined plane. • Calculate the kinetic energy the object has at the top of the inclined plane. • Calculate the kinetic energy the object has at the bottom of the inclined plane.

28. Sample Problem #7 • A 4 kg ball is thrown into the air. It reaches a height of 1.8 m. How fast was it going when thrown into the air? h = 1.8 m EP = EK m = 4 kg mgh = ½ mv2 g = 9.81 m/s2gh = ½ v2 v = ? (9.81 m/s2)(1.8m) = ½ v2 36 m2/s2 = v2 v = 6 m/s

29. Sample Problem #8 • A 4 kg ball is dropped from 12m. How fast is it going halfway down? htop = 12 m Etop = Ehalfway Hbottom = 6 m Ep = Ep + EK m = 4kg mgh = mgh + ½ mv2 g = 9.81 m/s2gh = gh + ½ v2 v = ? (9.81 m/s2)(12 m) = (9.81 m/s2)(6 m) + ½ v2 120 m2/s2 = v2 v = 11 m/s

30. That’s All Folks