Energy. Chapter 5. Human history becomes more and more a race between education and catastrophe. H. G. Wells

Transcription

1 Energy Chapter 5 Human history becomes more and more a race between education and catastrophe. H. G. Wells

2 Forms of Energy Mechanical Chemical Electromagnetic Nuclear Thermal Elastic Sound

3 Energy Weapons Mechanical Chemical Electromagnetic Nuclear Thermal Elastic Sound

4 Some Energy Considerations Energy is neither created or destroyed but only changes form (transforms) Essential to the study of physics, chemistry, biology, geology, astronomy In an isolated system total energy is conserved (remains constant)

5 Energy Wikipedia definition Energy is the ability of a physical system to do work on other physical systems. Work is defined as a force acting through a distance (a length of space) Energy is then the ability to exert pulls or pushes along a path of a certain length.

6 Work The work, W, done by a force on an object is defined as the product of the component of the force along the direction of displacement and the magnitude of the displacement

7 Work, cont. W (Fcos q) x F is the magnitude of the force Δ x is the magnitude of the object s displacement q is the angle between F and x

8 Units of Work SI Newton meter = Joule N m = J J = kg m 2 / s 2 US Customary foot pound ft lb no special name

9 More About Work The work done by a force is zero when the force is perpendicular to the displacement cos 90 = 0 If there are multiple forces acting on an object, the total work done is the algebraic sum of the amount of work done by each force

10 When Work is Zero Displacement is horizontal Force is vertical cos 90 = 0

11 More About Work, cont. Work can be positive or negative Positive if the force and the displacement are in the same direction Negative if the force and the displacement are in the opposite direction

12 Work Can Be Positive or Negative Work is positive when lifting the box Work would be negative if lowering the box The force would still be upward, but the displacement would be downward

13 Problem 5.1 A weight lifter lifts a 350-N set of weights from ground level to a position over his head, a vertical distance of 2.00 m. How much work does the weight lifter do, assuming he moves the weights at constant speed?

14 Problem 5.2 A shopper in a supermarket pushes a cart with a force of 35 N directed at an angle of 25 downward from the horizontal. Find the work done by the shopper as she moves down a 50-m length of aisle.

15 Mechanical Energy Mechanical energy is the energy that is possessed by an object due to its motion or due to its position. Mechanical energy can be either kinetic energy (energy of motion) or potential energy (stored energy of position) or a combination of both.

16 Potential and Kinetic Energy Potential Energy Energy in a stored state. Energy held in readiness with a potential for doing work. Kinetic Energy Energy associated with the motion of an object The ability to do work through motion.

17 Kinetic Energy Scalar quantity with the same units as work KE 1 mv 2 2

18 Work-Kinetic Energy Theorem When work is done by a net force on an object and the only change in the object is its speed, the work done is equal to the change in the object s kinetic energy W KE KE KE net f i Speed will increase if work is positive Speed will decrease if work is negative

19 Work and Kinetic Energy An object s kinetic energy can also be thought of as the amount of work the moving object could do in coming to rest The moving hammer has kinetic energy and can do work on the nail

20 Problem 5.8 A 7.00-kg bowling ball moves at 3.00 m/s. How fast must a 2.45-g Ping-Pong ball move so that the two balls have the same kinetic energy?

21 Problem 5.14 A 0.60-kg particle has a speed of 2.0 m/s at point A and a kinetic energy of 7.5 J at point B. What is (a) its kinetic energy at A? (b) its speed at point B? (c) the total work done on the particle as it moves from A to B?

22 Problem 5.13 A 2.0-g bullet leaves the barrel of a gun at a speed of 300 m/s. (a) Find its kinetic energy. (b) Find the average force exerted by the expanding gases on the bullet as it moves the length of the 50-cmlong barrel.

23 Gravitational Potential Energy Gravitational Potential Energy is the energy associated with an object in space near the Earth s surface Objects interact with the earth through the gravitational force PE mgh

24 Work and Gravitational Potential Energy PE = mgy Wgrav ity PE Units of Potential Energy are the same as those of Work and Kinetic Energy i PE f

25 Reference Levels for Gravitational Potential Energy A location where the gravitational potential energy is zero must be chosen for each problem The choice is arbitrary since the change in the potential energy is the important quantity Choose a convenient location for the zero reference height often the Earth s surface may be some other point suggested by the problem Once the position is chosen, it must remain fixed for the entire problem

26 Types of Forces There are two general kinds of forces Conservative Work and energy associated with the force can be recovered Nonconservative The forces are generally dissipative and work done against it cannot easily be recovered

27 Conservative Forces A force is conservative if the work it does on an object moving between two points is independent of the path the objects take between the points The work depends only upon the initial and final positions of the object Any conservative force can have a potential energy function associated with it

28 More About Conservative Forces Examples of conservative forces include: Gravity Spring force Electromagnetic forces Potential energy is another way of looking at the work done by conservative forces

29 More About Conservative Forces The work done by the gravitational force on an object depends only on its change in height because the gravitational force is conservative. h E=mgh E=0

30 More About Conservative Forces example: potential energy of 10-N ball is the same in all 3 cases because work done in elevating it is the same

31 Nonconservative Forces A force is nonconservative if the work it does on an object depends on the path taken by the object between its final and starting points. Examples of nonconservative forces kinetic friction, air drag, propulsive forces

32 Friction as a Nonconservative Force The friction force is transformed from the kinetic energy of the object into a type of energy associated with temperature The objects are warmer than they were before the movement Internal Energy is the term used for the energy associated with an object s temperature

33 Conservation of Mechanical Energy Conservation in general To say a physical quantity is conserved is to say that the numerical value of the quantity remains constant throughout any physical process In Conservation of Energy, the total mechanical energy remains constant In any isolated system of objects interacting only through conservative forces, the total mechanical energy of the system remains constant.

34 E i KE i Conservation of Mechanical Energy, cont. Total mechanical energy is the sum of the kinetic and potential energies in the system Ef or E E E 0 PE i KE f PE f Mechanical f i Other types of potential energy functions can be added to modify this equation

35 Conservation of Mechanical Energy How high will she go if she leaves the trampoline at 10 m/s?

36 Potential Energy Stored in a Spring Involves the spring constant, k Hooke s Law gives the force F = - k x F is the restoring force F is in the opposite direction of x k depends on how the spring was formed, the material it is made from, thickness of the wire, etc.

37 Potential Energy in a Spring Elastic Potential Energy related to the work required to compress a spring from its equilibrium position to some final, arbitrary, position x PE 2 s 1 kx 2

38 Spring Example Spring is slowly stretched from 0 to xmax F applied W = ½kx² = - F = kx restoring

39 Spring Example, cont. The work is also equal to the area under the curve In this case, the curve is a triangle A = ½ B h gives W = ½ k x 2

40 Conservation of Energy Including a Spring The PE of the spring is added to both sides of the conservation of energy equation KE ( PE PE ) (KE PE PE ) g s i g s f The same problem-solving strategies apply

41 Nonconservative Forces with Energy Considerations When nonconservative forces are present, the total mechanical energy of the system is not constant The work done by all nonconservative forces acting on parts of a system equals the change in the mechanical energy of the system W nc Energy

42 Problem 5.36 A 25.0-kg child on a 2.00-m-long swing is released from rest when the ropes of the swing make an angle of 30.0 with the vertical. (a) Neglecting friction, find the child s speed at the lowest position. (b) If the actual speed of the child at the lowest position is 2.00 m/s, what is the mechanical energy lost due to friction?

43 Problem 5.54 A toy gun uses a spring to project a 5.3-g soft rubber sphere horizontally. The spring constant is 8.0 N/m, the barrel of the gun is 15 cm long, and a constant frictional force of N exists between barrel and projectile. With what speed does the projectile leave the barrel if the spring was compressed 5.0 cm for this launch?

44 Conservation of Total Energy Law of 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. E Total E f E i 0

45 Conservation of total Energy

46 Transferring Energy By Work By applying a force Produces a displacement of the system

47 Transferring Energy Heat The process of transferring heat by collisions between molecules For example, the spoon becomes hot because some of the KE of the molecules in the coffee is transferred to the molecules of the spoon as internal energy

48 Transferring Energy Mechanical Waves A disturbance propagates through a medium Examples include sound, water, seismic

49 Transferring Energy Electrical transmission Transfer by means of electrical current This is how energy enters any electrical device

50 Transferring Energy Electromagnetic radiation Any form of electromagnetic waves Light, microwaves, radio waves

51 Transferring Energy Rube Goldberg Simple task that is over engineered World record is 300 steps to inflate and pop a balloon

52 Power Often also interested in the rate at which the energy transfer takes place Power is defined as this rate of energy transfer W t SI units are Watts (W) J W s s 2 Fv kg m 2

53 Power, cont. US Customary units are generally hp Need a conversion factor ft lb 1hp 550 s 746 W Can define units of work or energy in terms of units of power: kilowatt hours (kwh) are often used in electric bills This is a unit of energy, not power

54 Problem 5.43 The electric motor of a model train accelerates the train from rest to m/s in 21.0 ms. The total mass of the train is 875 g. Find the average power delivered to the train during its acceleration.

55 Power, cont. Energy, Work and Power ure=related

56 Center of Mass The point in the body at which all the mass may be considered to be concentrated When using mechanical energy, the change in potential energy is related to the change in height of the center of mass

57 Work Done by Varying Forces The work done by a variable force acting on an object that undergoes a displacement is equal to the area under the graph of F versus x

58 Back up Slides

59 Potential Energy Potential energy is associated with the position of the object within some system Potential energy is a property of the system, not the object A system is a collection of objects interacting via forces or processes that are internal to the system

60 Work-Energy Theorem, Extended The work-energy theorem can be extended to include potential energy: W ( KE KE ) ( PE PE ) nc f i f i If other conservative forces are present, potential energy functions can be developed for them and their change in that potential energy added to the right side of the equation

61 Work and Dissipative Forces Work can be done by friction The energy lost to friction by an object goes into heating both the object and its environment Some energy may be converted into sound For now, the phrase Work done by friction will denote the effect of the friction processes on mechanical energy alone

62 Work and Potential Energy For every conservative force a potential energy function can be found Evaluating the difference of the function at any two points in an object s path gives the negative of the work done by the force between those two points

63 Problem Solving with Conservation of Energy Define the system Select the location of zero gravitational potential energy Do not change this location while solving the problem Identify two points the object of interest moves between One point should be where information is given The other point should be where you want to find out something

64 Problem Solving, cont Verify that only conservative forces are present Apply the conservation of energy equation to the system Immediately substitute zero values, then do the algebra before substituting the other values Solve for the unknown(s)

65 Work-Energy With Nonconservative Forces If nonconservative forces are present, then the full Work-Energy Theorem must be used instead of the equation for Conservation of Energy Often techniques from previous chapters will need to be employed

66 Friction Depends on the Path The blue path is shorter than the red path The work required is less on the blue path than on the red path Friction depends on the path and so is a nonconservative force

67 Work-Energy Theorem Including a Spring W nc = (KE f KE i ) + (PE gf PE gi ) + (PE sf PE si ) PE g is the gravitational potential energy PE s is the elastic potential energy associated with a spring PE will now be used to denote the total potential energy of the system

68 Nonconservative Forces and Energy In equation form: ( ) W KE KE PE PE or nc f i i f W ( KE PE ) ( KE PE ) nc f f i i The energy can either cross a boundary or the energy is transformed into a form of non-mechanical energy such as thermal energy

69 Notes About Conservation of Energy We can neither create nor destroy energy Another way of saying energy is conserved If the total energy of the system does not remain constant, the energy must have crossed the boundary by some mechanism Applies to areas other than physics