Energy

1. Energy Chapter 9

2. Objectives • Define and describe work. • Define and describe power. • State the 2 forms of mechanical energy. • State 3 forms of potential energy. • Describe how work and kinetic energy are related. • State the work-energy theorem. • State the law of conservation of energy. • Describe how a machine uses energy. • Explain why no machine can have an efficiency of 100%. • Describe the role of energy in living organisms.

3. 9.1 Work • Recall that a change in an object’s momentum is related to an impulse –a force and how long the force acts. • “How long” does not always mean time, however. It can also mean distance. • Force x distance = work • Work is the product of the force on an object and the distance through which the object is moved.

4. 9.1 Work • For work to be done in Physics, a force acts on an object and the object moves in the direction of the force. • Work is done on a load when you lift it against Earth’s gravity. • No work is done on the load to hold it once it has been lifted or to carry the load around the room.

5. 9.1 Work Work is done only in lifting the barbell. The physics of a weightlifter holding a stationary barbell is no different than the physics of a table supporting a barbell's weight. NO NET FORCE acts on the barbell (forces are balanced!!), no work is done, and no change in its energy occurs.

6. Is This Work??? • A student applies a force to a wall and becomes exhausted. • A book falls off a table and lands on the ground. • You do some push-ups. • A waiter carries a tray full of meals across the room.

7. 9.1 Work • The waiter does NO work because the object is NOT moving in the direction of the force. (The force is against gravity – its in an up & down direction.)

8. 9.1 Work • Mathematically, work = force x distance. • W = Fd • The unit for work combines the unit for force, N, with the unit for distance, m. • A N-m is also called a joule (J). • 1 kJ equals 1000 J.

9. W = F x d • Recall that when lifting an object against gravity, the force required equals the object’s weight. • Fgrav = Weight = mg • Therefore, W = mgd • So, if the mass is doubled, the required force and work are doubled. • If the distance is doubled, the work is doubled. • Force (F) and distance (d) are both directly proportional to work.

10. 9.1 Work • There are 2 kinds of work. • Work done against another force • To pick up an object you do work against gravity. • To push an object, you do work against friction. • Work is done to change the speed of an object. • Work is done to speed up or slow down a car. • In either case, when work is done, a transfer of energy occurs between an object and its surroundings.

11. Practice • A weight lifter lifts a barbell. How much work is done if he lifts a barbell that is twice as heavy the same distance? If he lifts a barbell that is twice as heavy and 2x as far? • If you apply a 50 N force to a package, pushing it across the floor 3 m, how much work do you do? • A tugboat pulls a ship with a constant net horizontal force of 5000 N. How much work does the tugboat do on the ship if each moves a distance of 3.00 km?

12. 9.2 Power • When you climb a staircase, you do the same amount of work whether you get to the top in 30 sec. or 2 minutes. • What is different in each case is how fast the work is done or the power.

13. 9.2 Power Power = Work Time • Power is the rate at which work is done. • Power equals the amount of work done divided by the time interval during which the work is done: P = Fd = mgd t t

14. 9.2 Power • Power = Work/Time. This means power is directly proportional to workand indirectly proportional to time. • Having twice the power, then, can mean several things. • Twice the work can be done in the same amount of time. • The same work can be done in ½ the time.

15. 9.2 Power • The unit of power is the joule per second or watt (W). • For historical reasons, the horsepower is occasionally used to describe the power delivered by a machine. • One horsepower is equivalent to approximately 750 Watts. To lift a ¼ lb. cheeseburger a distance of 1 m in 1 s requires 1 watt of power!

16. Practice • Two physics students, Will and Ben, are in the weightlifting room. Will lifts the 100-pound barbell over his head 10 times in one minute; Ben lifts the 100-pound barbell over his head 10 times in 10 seconds. Which student does the most work? Which student delivers the most power? • If little Nellie Newton lifts her 40-kg body a distance of 0.25 meters in 2 seconds, then what is the power delivered by little Nellie's biceps? • Joe elevates his 80-kg body up the 2.0 meter stairwell in 1.8 seconds. What is his power?

17. 9.3 Mechanical Energy • When work is done on an object, the object acquires the ability to do work on something else. • For example, when you do work to lift a hammer, the hammer now has the ability to do work on a nail. • The property of an object that enables it to do work is energy. • Energy is measured in joules.

18. 9.3 Mechanical Energy • Mechanical energy is the energy due to the position or movement of an object. • The 2 forms of mechanical energy are kinetic energy and potential energy.

19. 9.4 Potential Energy • Energy that is stored and held in readiness is called potential energy (PE). • Stored energy has the potential to do WORK. • 3 kinds of PE are: elastic PE, chemical PE, and gravitational PE.

20. Elastic Potential Energy • A compressed or stretched spring has the potential to do work. • Other examples include a stretched rubber band or a stretched string on a bow and arrow.

21. Chemical Energy • Fuels (like oil or food) have chemical potential energy. • This energy is available to do work when a chemical reaction breaks the bonds between the atoms in a fuel and thereby releases the energy stored in them.

22. Gravitational Potential Energy • Work is required to elevate objects against gravity. The lifted objects then have PEgrav. • The work required (above) will be the same in each case because the work is equal to the force (weight of the object) times the distance it is moved against gravity (3 m in each case).

23. Gravitational Potential Energy • The amount of gravitational PE possessed by an elevated object is equal to the work done in lifting it. PEgrav = Fd Since F = weight & weight = mg, PEgrav = mgh (where h = height or distance lifted)

24. Gravitational Potential Energy • The height is the distance above a chosen reference level. • Often this reference level is the ground or floor. • A book on a table will have no height relative to the table and no PE. It does, however, have a positive PE relative to the floor.

25. Uses of PEgrav • Hydroelectric power makes use of the gravitational potential energy of water. • Falling water drives a turbine, which is connected to a generator. The generator converts the energy from the falling water into electrical energy.

26. Practice • Knowing that the potential energy at the top of the tall pillar is 30 J, what is the potential energy at the other positions shown on the hill and the stairs.

27. Practice • If a force of 15 N is used to lift a load to height 3 m from the ground, what is the PE of the load? • A 10 kg mass is suspended 5 m from the ground. • How much work was done to the mass? • If it is lifted in 2 sec., how much power is expended? • What is the PEgrav of the mass?

28. 9.5 Kinetic Energy • If an object is moving, it is capable of doing work. • It has energy of motion or kinetic energy (KE). • The amount of kinetic energy which an object has depends upon two variables: • the mass (m) of the object • the speed (v) of the object. KE = ½mv2

29. 9.5 Kinetic Energy • The kinetic energy of a moving object is equal to the work required to bring it to its speed from rest or to the work it can do while it is being brought to rest. KE = W 1/2mv2 = Fd

30. 1/2mv2 = Fd What this means: • If the speed of a vehicle is doubled, its KE is quadrupled. • So, 4x as much work must be done to stop the vehicle. • If the braking force used to stop the vehicle is the same, the distance required for stopping will be 4x as great. • What if the speed is tripled?

31. Types of Kinetic Energy • Thermal energy • Sound • Light • Electricity

32. Kinetic Energy • Kinetic energy often appears “hidden” in one of its different forms, such as heat, sound, light, and electricity. • Random molecular motion is sensed as heat. • Sound consists of molecules vibrating in rhythmic patterns. • Light energy originates in the motion of electrons within atoms. • Electrons in motion make electric currents.

33. Practice • Determine the kinetic energy of a 1000-kg roller coaster car that is moving with a speed of 20.0 m/s. • If the roller coaster car in the above problem were moving with twice the speed, then what would be its new kinetic energy? • Alison, a platform diver for the Ringling Brother's Circus, has a kinetic energy of 15,000 J just prior to hitting a bucket of water. If Alison’s mass is 50 kg, then what is her speed?

34. 9.6 Work-Energy Theorem • The work-energy theorem describes the relationship between work and energy: whenever work is done, energy changes. • Work = ΔKE

35. 9.6 Work-Energy Theorem • Work equals change in KE. • If you push on a box and it does not slide, then no work is done on the box. • If there is no friction, the box will slide. The force and distance of your push will be the KE of the box. (If there is some friction, the net force is what is considered.) • If the box has a constant speed, your push is just enough to overcome friction. Since the net force is 0, work is 0 and there is no change in KE of the box.

36. 9.6 Work-Energy Theorem • The more KE an object has, the more work must be done to stop it. • This infrared shot of a tire shows that some of the KE of a vehicle was transferred into thermal energy of the tire when the vehicle was stopped.

37. 9.6 Work-Energy Theorem • Recall our skidding example from a previous slide. • The maximum braking force that brakes supply is independent of speed – it is nearly always the same. • Therefore, a car moving at twice the speed has 4x as much KE. It will take 4x as much distance to stop. • Distances may be even greater if a driver’s reaction time is taken into account.

38. 9.7 Conservation of Energy • Nearly every process in nature can be analyzed in terms of transformations of energy from one form to another. • In this toy car, for example, work is done to wind it up. The car then has elastic potential energy. When released, it is converted into kinetic energy and heat. • Energy changes from one form to another, without a net loss or gain.

39. 9.7 Conservation of Energy • The law of conservation of energy states that energy cannot be created or destroyed. It can be transformed from one form into another, but the total amount of energy never changes.

40. 9.7 Conservation of Energy In a swinging pendulum system, there is one quantity that does not change: the total energy of the system. Due to friction, energy will eventually be transformed into heat.

41. 9.7 Conservation of Energy Energy changes from one form to another but the total amount of energy remains the same. In this example, the total amount of energy can also be called the total mechanical energy.

42. Practice 1. As the object moves from point A to point D across the surface, the sum of its gravitational potential and kinetic energies ____. a. decreases only b. decreases and then increases c. increases and then decreases d. remains the same 2. The object will have a minimum gravitational potential energy at point ____. a. A b. B c. C d. D e. E 3. The object's kinetic energy at point C is less than its kinetic energy at point ____. a. A only b. A, D, and E c. B only d. D and E

43. Practice 0 m/s

44. 9.8 Machines • A machine is a device that is used to multiply or change the direction of forces. • Based on the law of conservation of energy, a machine cannot put out more energy than is put into it. • What a machine can do is transfer energy from one place to another or transform it from one form to another.

45. Levers • A lever is a simple machine made up of a bar that turns about a fixed point. • The fixed point is called the fulcrum. • A lever changes the direction of a force – when the lever is pushed down, the load is lifted up.

46. Levers • If we neglect friction: work input = work output • Since work = Fd, (Fd)input = (Fd)output • On one end of this lever, a small input force is exerted over a large distance. • This produces, on the other end of the lever, a large force exerted through a short distance. • This machine has multiplied the force (but not the work)! Note: in this lever, the fulcrum is relatively close to the load.

47. Mechanical Advantage • Consider an ideal example: the girl pushes with a force of 50 N and lifts a load of 5000 N. • The ratio of Foutput to Finput for a machine is called the mechanical advantage. • Foutput =5000 N = 100 Finput 50 N

48. Mechanical Advantage • MA = Foutput = 100 Finput • Notice that doutput is 1/100th of dinput. • This means, mechanical advantage can also be calculated using the distances: MA = dinput doutput

49. Types (or Classes) of Levers • A type 1 lever has the fulcrum between the input and output forces. • Examples include:

50. Types of Levers • In a type 2 lever, the output force (the load) is between the fulcrum and the input force (the effort). • In this lever, the forces have the same direction. • Examples include: staplers, bottle openers, nut crackers, and