1 Work and Energy

2 Work In science, commonly used terms may have slightly different definitions from normal usage. The quantity work, is a perfect example of this.

3 Work Definition Work = Force x Distance W = Fd Thus, work depends on force applied, and distance moved.

4 Example of Work? The weightlifter holding the bar in a stationary position does NO work since distance equals zero.

5 Units Since W = F d Work is measured in N m One N m is also called 1 Joule.

6 More Work? Q: If one person lifts a 100 kg mass a distance of 1m up in 3 seconds, and another person does the same task in only 1 second, who does more work? A: Neither. Work is not dependent of time. However, power is dependent on time.

7 Which does more work?

8 Which path will require more work?

9 Energy When you do work on an object and lift it upwards, you change the state of the object. Since the object is higher now, it could fall and do work for you. Thus, the work you did increased the energy of the object.

10 Energy is the ability to cause change and perform work. Work involves movement but energy does not require movement. The unit for energy is a JOULE or N-m (Newton-meter)

11 Forms of Energy: 1. Heat energy 2. Chemical energy 3. Electrical energy 4. Radiant energy 5. Nuclear energy

12 Potential Energy: stored energy. There are many ways that energy can be stored and then released. It’s a lot like saving money in the bank so that it can be used later.

13 Chemical Potential Energy The chemical bonds between atoms can store energy. This can be released when the bonds are broken in chemical reactions.

14 Gravitational Potential Energy When an object is lifted to a particular height, the stored energy due to its elevated position increases. A dam is a good example of this.

15 Gravitational potential energy, PE, will be the main type considered. PE grav = weight x height PE grav = mg h Remember that you only increase PE when you work against gravity. Moving an object horizontally doesn’t change its PE.

16 PE Example: A crane lifts a steel beam with a mass of 2500 kg to a height of 20 m. How much potential energy was given to the beam?

17 Potential Energy Example The crane is lifting against gravity, so we find the gravitational potential energy. h= 20 m; g= 9.8 m/s 2 ; m = 2500kg PE grav = m g h 2500kg * 9.8 m/s 2 * 20 m J

18 Reference Point, Base Level When measuring an “h” to calculate PE, its important to know where you are measuring from. Any point can be used as a base level because the energy amount you calculate will be relative. However, you must be consistent.

19 Elastic Potential Energy If you compress a spring, or stretch a rubber band, the work you do can be returned later when the spring or rubber band bounces back.

20 Elastic potential energy (PE elast )is stored as a result of deformation of an elastic object, such as the stretching of a spring. It is equal to the work done to stretch the spring, which depends upon the spring constant k!

21 The Force required to stretch the spring will be directly proportional to the amount of stretch. F = kx then the work done to stretch the spring a distance x is

22

23 Kinetic Energy Kinetic Energy, KE: energy of motion KE = 1/2 m v 2 m = mass v = velocity Any object in motion has kinetic energy.

24 Objects with a small mass can have high kinetic energy if their velocity is high. (Example: a cannonball) BOOM

25 Objects moving at slow speed can have great kinetic energy if their mass is great. (Example: a freighter)

26 KE Example: Ex: A 80 kg sprinter may average about 10 m/s during a 100m dash. What would his KE be? m=80 kg; v = 10m/s; d = 100 m KE = 1/2 mv 2 KE = 1/2 (80kg) (10m/s) 2 KE = 4000 kgm 2 /s 2 or 4000 J

27 Work Energy Theorem Work = ΔE Work is equivalent to the change in energy. Work and energy both have the same unit, Joule.

28 Ex: You could do work by pushing an object to slide it across the floor. This work you do goes into increasing the KE of the object.

29 Ex: You lift an object and do work. This work goes into increasing the PE of the object.

30 The archer does work to draw the bow back. This is temporarily stored as PE in the bow. When the arrow is released, it is changed to KE in the form of the flying arrow.

31 Conservation of Energy: Energy cannot be created or destroyed; it may be transformed from one form into another, but the total amount of energy never changes.

32 Often, it may seem like energy is lost, but it merely is transformed into another type of KE or PE. Just look closely and consider where energy may be transferred.

33 At the top, the diver has all PE As he falls, PE is changed to KE. Before he hits, all the PE has changed to KE. Notice that the total amount of energy remains constant.

34 Example: Question: If a 2 kg brick were to fall from a building 20m high, how fast would it be traveling just before it hits the ground? m= 2 kg; h = 20m; g = 9.8 m/s 2 2kg

35 Solution: PE top = KE bottom mgh = ½ mv 2 (2kg) (9.8m/s 2 ) (20m) = ½ (2kg) v 2 solve for “v” (notice “m” cancels out) (2kg) (9.8m/s 2 ) (20m) = ½ (2kg) v 2 (392 m 2 /s 2 ) = v 2 (392 m 2 /s 2 ) = v v= 19.8 m/s In a previous chapter, we could solve this a different way but would get the same answer.

36 Total Mechanical Energy = KE + PE PE = mgh KE = 1/2 mv 2 #1 - Tot E = all PE #2 - Tot E = mostly KE + some PE #3 - Tot E = mostly PE + some KE #4 - Tot E = all KE

37 Power Power = Work / time P = W / t = F x d / t Power is a measure of how quickly work is done.

38 Units: Since work has units of Joules, power must be in units of Joules per second. 1 J/s = 1 Watt, W James Watt invented the steam engine.

39 A watt is not exclusively used for electrical measurements, although that is common. Since 1 watt is relatively small, kilowatts 10 3 W or megawatts 10 6 W are often used.

40 Power Example: Ex: A 50 kg boy wants to escape the monster beneath his steps. He climbs the 5m high steps in 2.0 seconds. How much power did he generate during his run? 5m high m= 50kg h= 5m t= 2s g = 9.8m/s 2

41 P = W / t = Fd / t (notice the force needed is the boy’s weight) = (mg)d / t = (50kg) ( 9.8m/s 2 ) ( 5.0 m) / (2.0s) = 1225 J/s = 1225 Watts = kilowatts

42

43

44