1. Unit 5 Momentum, Work and Energy

2. Critical Questions When have you heard the word momentum used? Which do you think has more momentum? Two identical Honda Accords, one going 20mph, the other going 40mph. Two vehicles going 30mph, one is a VW Bug, the other an 18-wheeler.

3. Momentum Momentum is the study of inertia in motion. Recall Inertia: The tendency of an object to remain in motion or stay at rest due to its mass. So, momentum only deals with objects that are in motion.

4. Momentum Momentum is the mass of an object multiplied by its velocity. p = mv Where: p = momentum (kg m/s) m = mass (kg) v = velocity (m/s)

5. Momentum Change in Momentum generally refers to a change in velocity, mass is constant. Δp = mΔv Or Δp = m(vf – vi)

6. Momentum Examples Find the momentum of a 1500kg car traveling at 30m/s. A 1200kg car has a momentum of 18,000kg m/s. What is its velocity? A 1000kg car slows from 45m/s to 30m/s. Find its change in momentum.

7. Critical Question Could an 18-wheeler and a 4-wheeler ever have the same momentum?

8. Impulse If an object changes velocity, what is it doing? Accelerating! What causes acceleration of an object? Force! The greater the force on an object, the more acceleration it obtains, the more velocity changes and, therefore, the more change in momentum it has!

9. Impulse Time is also a factor – a force applied over a long time is different than a force applied over a short time A “short” force only causes a small change in velocity. A “long” force can cause a great change in velocity. Think about the Skateboard Lab!

10. Warm Ups (4/18/08 – PROM DAY) 1. Find the momentum of a 1200kg car traveling at 37 m/s. 2. Find the momentum of a 2.6kg dove flying at 3.2 m/s. 3. Find the change in momentum if the same dove speeds up to 4.7m/s.

12. Impulse Cases Decreasing Momentum over a Long Time For a constant mass and constant change in velocity, if you increase time over which a force is applied, the force decreases! CQ: Why would you rather fall on grass than concrete? CQ: How does an air bag reduce your force of impact in a wreck?

13. Impulse Cases Decreasing Momentum over a Short Time For a constant mass and constant change in velocity, if you decrease time over which a force is applied, the force increases! Karate chops through materials

14. Impulse Impulse is force multiplied by time. Since more force causes more change in momentum, impulse is the change in momentum. J = Ft Where: J = Impulse (Ns) F = Force (N) t = time (s)

15. Impulse-Momentum Equation Impulse = Change in Momentum! Ft = m(vf – vi)

16. Impulse-Momentum Examples A 1200kg car traveling at 30m/s is brought to rest in 1.2s. What force is required to stop the car? A 1000kg car is traveling at 15m/s and is brought to rest in 0.8s. What force is required to stop the car? A –35,000N force is required to stop a 1300kg car traveling at 10m/s. How long does it take the car to come to a stop?

17. Warm Ups (4/21/08) 4. A 1000kg crash test car is sent toward a cement wall with a velocity of 14m/s. The impact brings the car to a stop in 8.0 x 10-2 seconds. What force is needed to stop the car? 5. You have a mass of 60kg and are driving at 25m/s in your car. You suddenly slam on your brakes to avoid hitting a dog crossing the road. If your seatbelt brings you to rest in 0.40 seconds, what force did the seat belt exert on you?

18. Bouncing When an object bounces, it has the greatest change in velocity. For example, if an object comes down with a velocity of –10m/s and bounces up with a velocity of +10m/s, the change in velocity is: vf – vi = 10 – (-10) = 20m/s

19. Conservation of Momentum CQ: How did Newton’s Third Law relate to a rifle being fired? Recall: Newton’s 3rd Law says, “For every action there is an equal and opposite reaction.” Those actions and reactions were forces, recall how force relates to momentum.

20. Conservation of Momentum For a rifle firing, the rifle and the bullet are at rest (equilibrium, so net force = 0N) before the bullet is fired. Strangely enough the net force after the bullet is fired is also 0! If the net force is 0N, the impulse is 0Ns, so there is no change in momentum! The momentum of a system cannot be changed without an outside force– called conservation.

21. Conservation of Momentum The Law of Conservation of Momentum says that the momentum of a system cannot be changed unless an outside force acts on it. (We will assume no outside forces ever act). Momentum before = Momentum after (mv)b = (mv)a (b = before, a = after)

22. Collisions Two Types Elastic Bouncing occurs Objects at no point stick together Inelastic Objects stick together either prior to separating or after a collision

23. Elastic Collisions Type 1 Type 2 Type 3

24. Elastic Collisions Equation (mv)1b + (mv)2b = (mv)1a + (mv)2a Where: (mv)1b = mass and velocity of Object 1, Before (mv)2b = mass and velocity of Object 2, Before (mv)1a = mass and velocity of Object 1, After (mv)2a = mass and velocity of Object 2, After

25. Inelastic Collisions Type 1 Type 2

26. Inelastic Collisions Equations Type 1: Sticks together after the collision (mv)1b + (mv)2b = (m1 + m2)va Type 2: Stuck together before they separate (m1 + m2)vb = (mv)1a + (mv)2a

27. Warm Ups (4/22/08) 6. You have a mass of 55kg and are traveling at 21m/s when you slam on your brakes and come to a stop. If your seatbelt stops you with a force of -6800N, how long were you in contact with the seatbelt?

28. Collision Examples A 1000kg car traveling at 20m/s rear-ends a 1200kg car sitting still at a red light. If the 1200kg car bounces forward at 5m/s, how fast is the 1000kg car going after the wreck?

29. Collision Examples Skinny Minny, who has a mass of 25kg, is traveling in a 100kg bumper car at 5m/s. Twins Chubby and Tubby, who have a mass of 200kg, are in the same size bumper car (100 kg) and are aiming for Skinny Minny with a velocity of 8m/s. If the twins have a velocity of 6m/s after the collision, how fast is Skinny Minny going now?

30. Collision Examples A 3kg rifle fires a 5g bullet with a velocity of 80m/s. With what velocity does the gun kick back?

31. Warm Ups (4/23/08) Find the momentum of a 16kg toddler running at 2m/s. Find the change in momentum of a 2kg ball slowing from 6m/s to 1m/s. A force of -1500N applied over 0.2 seconds is needed to stop an object that was originally traveling at 25m/s. What is the object’s mass?

32. Warm Ups 7. You have a mass of 60kg and are standing still on a skateboard holding an 8kg bowling ball. You throw the ball forward with a velocity of 3m/s. How fast are you going when you move backwards? 8. An 8.2kg remote control car is traveling at 4m/s when it hits a 10kg coffee table. If the car bounces forward at 2.9m/s, how fast is the table going after it is bumped?

33. Warm Ups (4/24/08) 11. In Dirty Dancing, Baby and Johnny are practicing their lift in the pond. 85kg Johnny remains still while 60kg Baby runs towards him with a velocity of 2m/s. After Baby leaps into Johnny’s arms, the two fall into the water together. What is their velocity?

34. Conservation of Momentum Activity Get a car, gun, stopwatch and meter stick Make sure there is velcro on the gun and car Get the gun close to the car and shoot the car so that the velcros stick. Time from the moment you shoot until the car comes to a stop Measure the distance the car travels. Do this 3 times – average the times and distances

35. Conservation of Momentum Activity You now have time, distance and a final velocity (no?). Calculate the (average) initial velocity of the car and dart stuck together. Get the masses of the dart and car (in KG!) Now, using the conservation of momentum, find out how fast the dart was going before it hit the car!

36. Warm Ups (4/25/08) A 1700 kg Toyota 4-Runner traveling at 16 m/s is rear-ended by a 1050 kg Acura traveling at 20 m/s. Find the velocity of the two cars if after the collision they lock bumpers. A 60-kg boy and a 40-kg girl are standing still on skates, facing each other. If the boy pushes the girl in the opposite direction giving her a speed of 4 m/s, what happens to the boy?

37. Work Work Recall Impulse – force times time (how long). Work is force times distance (another how long). W = Fd Where W = Work (Nm or J) F = Force (N) d = distance (m)

38. Work Work must have both components: An applied force on an object A distance over which an object moves

39. Work CQ: You lift a box and do 100J of work. How much work do you do if the box is twice as heavy? If it is the same weight, but you lift it twice as high? CQ: If you lean on a wall, are you doing work?

40. Work Examples You lift a 185N box 1.5m upward. How much work is done? Katie does 3.2J of work to raise the blinds in her bedroom 60cm. How much force does she use? A force of 825N is needed to push a car 35m across a parking lot. a) How much work is done? b) If it is raining and the ground is getting muddy, it takes twice as much force to push the car the same distance. What happens to the work now?

41. Power CQ: You lift a 100N box 2m above the ground. Your boyfriend lifts a 200N box 1m above the ground. Who does more work? Who is more powerful?

42. Power Work doesn’t distinguish between doing something quickly or slowly. Power takes time into account

43. Power Power is work divided by time P = W/t Where: P = Power (J/s or Watts) W = Work (J) t = time (s)

44. Power Think of a new sports car that can go 0 to 60(mph) in 4s vs. an old car that goes 0-60 in 10s. Which is more powerful? Something that is very powerful does work in a short amount of time. Something that isn’t powerful does work in a long amount of time.

45. Power You use 1000J of work to push a cart for 5s. How much power do you use? You lift a 200N barbell 1.5m over your head in 1.2s. How much power did you use?

46. English vs. Metric Units of Power Metric System The Watt (W) is the unit for measurement of power. 1 kW = 1000 W (how electricity is measured) English System Horsepower is the unit of measure for power Based off of the power 1 horse can sustain over a long period of time. 1hp = 0.75 kW

47. Energy Energy gives objects the ability to do work. Work Done = Energy Given Types of Energy: Heat, Electromagnetic, Nuclear, Mechanical, etc. We will work only with mechanical energy. Two forms of mechanical energy: potential energy and kinetic energy

48. Potential Energy PE is energy stored in an object and held in readiness. Energy can be stored in an object based on its position. Examples: Bow and arrow, Brick on top of a ladder Work required to raise an object above the ground gives the object Gravitational Potential Energy.

49. Potential Energy Example Recall W = Fd PE = mgh Where PE = Potential Energy (J) m = mass (kg) g = acceleration due to gravity (m/s2) h = height above ground (m)

50. Potential Energy Examples Ashley holds a 5kg weight above her head, 2.1m above the ground. What is the PE of the weight? A flea gains 1.0x10-7J of PE jumping to a height of 0.03m from a dog’s back. What is the mass of the flea?

51. Kinetic Energy An object in motion has the ability to do work – that’s kinetic energy! Kinetic Energy is based on an object’s speed. KE = ½ (mv2) Where KE = Kinetic Energy (J) m = mass (kg) v = velocity (m/s) Velocity is squared! If you double the velocity, the kinetic energy actually quadruples!

52. Kinetic Energy Examples A 20kg greyhound runs at 16m/s. What is its kinetic energy? A 1200kg car is traveling at 25m/s. What is its kinetic energy?

53. Conservation of Energy Consider a dropped object It isn’t moving before it is dropped (KE = 0J), but it is above the ground (PE). It reaches the ground (PE = 0J), but has picked up speed (KE). Total Energy is a combination of PE and KE.

54. Conservation of Energy Law of Conservation of Energy: Energy cannot be lost or gained. It is simply transformed into another form. Energy before = Energy after PEb + KEb = PEa + KEa Falling Example

55. Conservation of Energy A roller coaster is traveling at 2m/s at the top of a 34m hill. How fast is it going at the bottom of that hill (at ground level)? Mrs. Peak’s cat, Sylvester, has a mass of 9kg and is sleeping on top of the refrigerator when he rolls over and falls off. If Sylvester is traveling at 4.4m/s as he lands on his feet on the floor, how tall is the refrigerator?