9/20/19

1

Unit 4: Momentum and

EnergyBrent Royuk

Phys-109Concordia University

2

Momentum

• Definition: momentum = mass x velocityp = mv

• Units: 1 kg m/s• The Conservation Law

– In the absence of any external force, the momentum of a system of objects remains constant.

3

Momentum

• What is a one-word synonym for momentum?

9/20/19

2

4

Conservation of Momentum• The Classic Example: Two skaters

5

Conservation of Momentum• Recoil: Jumping out of a boat, guns, etc.

6

Conservation of Momentum• Football players

9/20/19

3

7

Conservation of Momentum• Coupling boxcars

9

ConcepTest• A car rolls down the street with a certain

amount of momentum. If the car were twice as massive and moving twice as fast, its momentum would be _____ as much.

1. one fourth2. half3. twice4. four times

17

Conservation of Momentum• “Professor Goddard does not know the relation between

action and reaction and the need to have something better than a vacuum against which to react. He seems to lack the basic knowledge ladled out daily in high schools.” 1921 New York Times editorial about Robert Goddard's revolutionary rocket work. "Correction: It is now definitely established that a rocket can function in a vacuum. The Times regrets the error." NY times, July 1969.

9/20/19

4

19

ConcepTest• Suppose the entire population of the world gathers in one spot

and, at the sounding of a prearranged signal, everyone jumps up. While all the people are in the air, does Earth gain momentum in the opposite direction?

1. No; the inertial mass of Earth is so large that the planet’s change in motion is imperceptible.

2. Yes; because of its much larger inertial mass, however, the change in momentum of Earth is much less than that of all the jumping people.

3. Yes; Earth recoils, like a rifle firing a bullet, with a change in momentum equal to and opposite that of the people.

4. It depends.

22

Impulse• To change momentum, a force

must be applied for some time.• Impulse = force x time = Δ p

23

Impulse• Impulse = force x time = Δ p• Therefore: F t = m v• Push a 50.0 kg box with a force of

200.0 N for 3.0 s. How fast is it going?

• A 0.10 kg golf ball gets teed off at 40.0 m/s in 1.0 ms. How hard was it hit?

9/20/19

5

24

The Impulse Bargain

25

The Impulse Bargain• Bend legs when landing.• Let glove recoil when catching a baseball.• Airbags

26

ConcepTest• Consider two carts, of masses m and 2m, at rest on an

air track. If you push first one cart for 3 s and then the other for the same length of time, exerting equal force on each, the momentum of the light cart is _____ the momentum of the heavy cart.

1. four times 2. twice 3. equal to4. one-half5. one-quarter

9/20/19

6

29

ConcepTest• A person attempts to knock down a large wooden

bowling pin by throwing a ball at it. The person has two balls of equal size and mass, one made of rubber and the other of putty. The rubber ball bounces back, while the ball of putty sticks to the pin. Which ball is most likely to topple the bowling pin?

1. the rubber ball2. the putty ball3. makes no difference 4. need more information

30

ConcepTest• Suppose you are on a cart, initially at rest on a track

with very little friction. You throw balls at a partition that is rigidly mounted on the cart. If the balls bounce straight back as shown in the figure, is the cart put in motion?

1. Yes, it moves to the right.2. Yes, it moves to the left.3. No, it remains in place.

31

Energy Introduction• What do you know?• Definition• Forms

– Potential– Kinetic

• The Unifying Idea• Top-Down vs.

Bottom-Up• Note: No Machines or Efficiency

9/20/19

7

32

Work• Definition

– The product of force and the distance moved due to that force

W = F d• Units

– 1 N m = 1 kg m2/s2 = 1 joule (J)

33

Work• Note: No motion = no work

– Holding up a wall– Carrying a book– Satellites

• What if you push a car at constant speed?• Example: Lift a 1.0-kg weight a height of 2.0 m.

How much work have you done?

34

Power• Definition:

– MKS Unit– Another common power unit: 1 hp = 746 WEnergy = P t

• kWh’s

–Finding Energy Costs• Just take kW times hours to get kWh’s• You can figure each kWh costs about $0.10, to

get a quick estimate.• Examples

– How much does it cost to leave a 100-W light bulb on for a month

9/20/19

8

35

Power• Energy = Power x Time

36

Electric Bills

37

Defining Energy– The Work-Energy Definition Connection: Energy is the capacity…

• Work is a process, and energy is a property of a system– Aristotle coined the word “energy” from the Greek for “at work.”– The Nearly Well-Know Dave Watson Definition

• “Energy is a property or characteristic (or trait or aspect?) of matter that makes things happen, or, in the case of stored or potential energy, has the ‘potential’ to make things happen.”

9/20/19

9

38

Feynman on Energy– “It is important to realize that in physics today, we have no knowledge of what energy

is.” –Richard Feynman

– “There is a fact, or if you wish, a law, governing natural phenomena that are known to date. There is no known exception to this law—it is exact so far we know. The law is called conservation of energy [it states that there is a certain quantity, which we call energy that does not change in manifold changes which nature undergoes]. That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity, which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number, and when we finish watching nature go through her tricks and calculate the number again, it is the same.” –Richard Feynman, Lectures on Physics, Vol. 1

39

Forms of Energy

• Two types of energy: Kinetic and Potential– Kinetic Energy: Energy of ______– Potential Energy: Energy of _____

• Kinetic Energy Equation:– Units?

• Note v2 dependence.• What’s the other important type of

kinetic energy?

40

ConcepTest• When a car brakes to a halt, the stopping distance

depends on how fast the car is moving. Suppose that a 2000 Dodge Caravan travels at some speed and then brakes to a halt. If the minivan were to travel twice as fast, how much farther would it take to stop? Assume that the brakes apply a constant force to decelerate the car.

1. twice as far2. three times as far3. four times as far4. it depends on the original speed

9/20/19

10

41

Potential Energy• Potential energy is energy of ___________• Any system that wants to move: something springy:

springs, rubber bands, bent metal, item on a shelf, etc.

• For gravity: PE = weight x height = mgh

42

Potential Forms• Elastic Energy

– Anything that stretches and snaps back: springs, waistbands, etc.

• Electromagnetic Energy– Magnets, socks stick together, electricity that turns on lights

• Radiant Energy– Any type of ER: radio waves, microwaves, light, x-rays, etc.

• Chemical Energy– Comes from molecular arrangements- the energy you get when you burn things.

• Nuclear Energy– This form only shows up when nuclei rearrange themselves, and this doesn’t

happen on a large scale very often in everyday life.

43

The Law of Energy• AKA The Law of Conservation of Energy.• Nature’s Bookkeeping System• Energy can change forms, but is never

created or destroyed.• Examples

– Drop a Rock– Roller Coasters

• Path Independence

9/20/19

11

44

Energy Transformations

45

ConcepTest• Two marbles, one twice as heavy as the other,

are dropped to the ground from the roof of a building. Just before hitting the ground, the heavier marble has

1. as much kinetic energy as the lighter one.2. twice as much kinetic energy as the lighter

one.3. half as much kinetic energy as the lighter one.4. four times as much kinetic energy as the

lighter one.5. impossible to determine

46

Pendulum Energy

9/20/19

12

47

Pendulum Energy

52

Graphical Analysis

54

ConcepTestA girl throws a stone from a bridge. Consider the following ways she might throw the stone. The speed of the stone as it leaves her hand is the same in each case. Assume air friction is negligible.•Case A: Thrown straight up.•Case B: Thrown straight down.•Case C: Thrown out at an angle of 45 degrees above horizontal•Case D: Thrown straight out horizontallyIn which case will the speed of the stone be greatest when it hits the water below?a. Ab. Bc. Cd. De. The speed will be the same in all cases

9/20/19

13

55

ConcepTestA stone is launched upward into the air. In addition to the force of gravity, the stone is subject to a frictional force due to air resistance. The time the stone takes to reach the top of its flight path is

1.larger than2.equal to3.smaller than

the time it takes to return from the top to its original position.

56

Alternative Energy?

Two types of Medical Energy Therapy1.Veritable (Measurable)

– Magnet, Light, Sound, etc.2.Putative (Bioenergy, Qi, Prana; Has not been measured)

– Acupuncture, Qui Gong, Therapeutic Touch, Power Balance, etc.

57

Perpetual Motion

9/20/19

14

58

Perpetual Motion

59

Perpetual Motion

60

Perpetual Motion

9/20/19

15

61

Perpetual Motion

62

Perpetual Motion

63

Perpetual Motion