1. Motion II Momentum and Energy

2. Momentum Obviously there is a big difference between a truck moving 100 mi/hr and a baseball moving 100 mi/hr. Obviously there is a big difference between a truck moving 100 mi/hr and a baseball moving 100 mi/hr. We want a way to quantify this. We want a way to quantify this. Newton called it Quantity of Motion. We call it Momentum. Newton called it Quantity of Motion. We call it Momentum.

3. Definition: Momentum = (mass)x(velocity) p = mv Momentum is a vector. Momentum is a vector. Combination of mass and velocity Combination of mass and velocity Large momentum for massive objects moving slowly or small objects moving quickly Large momentum for massive objects moving slowly or small objects moving quickly

4. Newton’s 2 nd Law Note: Sometimes we write  t instead of just t. They both represent the time interval for whatever change occurs in the numerator. Note: Sometimes we write  t instead of just t. They both represent the time interval for whatever change occurs in the numerator.

5. Newton’s 2 nd Law Since p = mv, we have  p =  (mv) Since p = mv, we have  p =  (mv) If m is constant (not true for rockets and ballons),  p = m  v and  v/  t = a If m is constant (not true for rockets and ballons),  p = m  v and  v/  t = a

6. Rearrange Newton’s 2 nd Law This is the impulse This is the impulse Impulse is the total change in momentum Impulse is the total change in momentum

7. Example Baseball Baseball  p= p f – p i  p= p f – p i = mv f – (-mv i ) = m(v f + v i ) F =  p/  t F =  p/  t Where  t is the time the bat is in contact with the ball

8. Realistic numbers Realistic numbers M = 0.15 kg M = 0.15 kg V i = -40 m/s V i = -40 m/s V f = 50 m/s V f = 50 m/s  t = 0.0007 s  t = 0.0007 s F = 19286 N F = 19286 N a = 128571 m/s 2 a = 128571 m/s 2 slow motion photography slow motion photography slow motion photography slow motion photography

9. Ion Propulsion Engine: very weak force (0.1 N, about the weight of a paper clip) but for very long times (months) Ion Propulsion Engine: very weak force (0.1 N, about the weight of a paper clip) but for very long times (months) Large momentum change Large momentum change Very efficient Very efficient

10. Crumple zones on cars increase the time for a car to stop. This greatly reduces the average force during accident. Crumple zones on cars increase the time for a car to stop. This greatly reduces the average force during accident. Air bags do the same thing Air bags do the same thing

11. A 70 kg person traveling at +15 m/s stops. What is the impulse? 1. -500 kgm/s 2. -1000 kgm/s 3. -1500 kgm/s 4. -2000 kgm/s

12. Example 70 kg person traveling at 15 m/s stops. 70 kg person traveling at 15 m/s stops.  p = p f – p i = 0 kgm/s – 1050 kg·m/s = - 1050 kg·m/s  p = p f – p i = 0 kgm/s – 1050 kg·m/s = - 1050 kg·m/s

13. Example 70 kg person traveling at 15 m/s stops. 70 kg person traveling at 15 m/s stops.  p = p f – p i = 0 kgm/s – 1050 kg·m/s = - 1050 kg·m/s  p = p f – p i = 0 kgm/s – 1050 kg·m/s = - 1050 kg·m/s If the person is stopped by the windshield  t = 0.01 s If the person is stopped by the windshield  t = 0.01 s What is the force? What is the force?

14. Example 70 kg person traveling at 15 m/s stops. 70 kg person traveling at 15 m/s stops.  p = p f – p i = 0 kgm/s – 1050 kg·m/s = - 1050 kg·m/s  p = p f – p i = 0 kgm/s – 1050 kg·m/s = - 1050 kg·m/s If the person is stopped by the windshield  t = 0.01 s If the person is stopped by the windshield  t = 0.01 s F = -1050 kgm/s/0.01 s = -105000 N F = -1050 kgm/s/0.01 s = -105000 N

15. Example 70 kg person traveling at 15 m/s stops. 70 kg person traveling at 15 m/s stops.  p = p f – p i = 0 kgm/s – 1050 kg·m/s = - 1050 kg·m/s  p = p f – p i = 0 kgm/s – 1050 kg·m/s = - 1050 kg·m/s If the person is stopped by an airbag  t = 0.40 s If the person is stopped by an airbag  t = 0.40 s What is the force? What is the force?

16. Example 70 kg person traveling at 15 m/s stops. 70 kg person traveling at 15 m/s stops.  p = p f – p i = 0 kgm/s – 1050 kg·m/s = - 1050 kg·m/s  p = p f – p i = 0 kgm/s – 1050 kg·m/s = - 1050 kg·m/s If the person is stopped by an airbag  t = 0.40 s If the person is stopped by an airbag  t = 0.40 s F = -1050 kgm/s/0.40 s = -2625 N F = -1050 kgm/s/0.40 s = -2625 N

17. A woman has survived after falling from the 23rd floor of a hotel in the Argentine capital, Buenos Aires. Her fall was broken by a taxi, whose driver got out moments before the impact crushed the roof and shattered the windscreen. Eyewitness said the woman had climbed over a safety barrier and leapt from a restaurant at the top of the Hotel Crowne Plaza Panamericano. She was taken to intensive care for treatment for multiple injuries. The woman, who has not been named, is reported to be an Argentine in her 30s. The taxi driver, named by local media as Miguel, said he got out of his vehicle just before the impact after noticing a policeman looking up. "I got out of the car a second before. If I had not got out, I would have been killed," he told Radio 10. "I was only 10 metres from the impact. It made a terrible noise," he added.

18. Estimate m = 50kg Estimate m = 50kg H= 23 x 3.5m = 80.5m H= 23 x 3.5m = 80.5m

19. Estimate Acceleration BUT Thus

20. Case 1: stops in deformation distance of body ~ 0.30 m (3 cm). Case 1: stops in deformation distance of body ~ 0.30 m (3 cm). Case 2: stops in height of roof, ~ 0.50 m (50 cm). Case 2: stops in height of roof, ~ 0.50 m (50 cm).

21. Conservation of Momentum Newton’s 3 rd Law requires F 1 = -F 2 Newton’s 3 rd Law requires F 1 = -F 2  p 1 /  t = -  p 2 /  t  p 1 /  t = -  p 2 /  t Or Or  p 1 /  t +  p 2 /  t = 0  p 1 /  t +  p 2 /  t = 0 Or Or  p 1 +  p 2 = 0  p 1 +  p 2 = 0 NO NET CHANGE IN MOMENTUM NO NET CHANGE IN MOMENTUM

22. Example: Cannon 1000 kg cannon 1000 kg cannon 5 kg cannon ball 5 kg cannon ball Before it fires P c + P b = 0 P c + P b = 0 Must also be true after it fires. If V b = 400 m/s M c V c + M b V b = 0 M c V c + M b V b = 0 V c = -M b V b /M c V c = -M b V b /M c = -(5kg)(400m/s)/(1000kg) = -(5kg)(400m/s)/(1000kg) = -2m/s = -2m/s

23. Conservation of Momentum Head on collision Head on collision Head on collision Head on collision Football Football Football Train crash Train crash Train crash Train crash Wagon rocket Wagon rocket Wagon rocket Wagon rocket Cannon Fail Cannon Fail Cannon Fail Cannon Fail

24. ENERGY & WORK In the cannon example, both the cannon and the cannon ball have the same momentum (equal but opposite). In the cannon example, both the cannon and the cannon ball have the same momentum (equal but opposite). Question: Why does a cannon ball do so much more damage than the cannon? Question: Why does a cannon ball do so much more damage than the cannon?

25. ENERGY & WORK In the cannon example, both the cannon and the cannon ball have the same momentum (equal but opposite). In the cannon example, both the cannon and the cannon ball have the same momentum (equal but opposite). Question: Why does a cannon ball do so much more damage than the cannon? Question: Why does a cannon ball do so much more damage than the cannon? Answer: ENERGY Answer: ENERGY

26. ENERGY & WORK E ssentially, energy is the ability to make something move. E ssentially, energy is the ability to make something move. What transfers or puts energy into objects? What transfers or puts energy into objects? A push A push

27. WORK We will begin by considering the “Physics” definition of work. We will begin by considering the “Physics” definition of work. Work = (Force) x (displacement traveled in direction of force) Work = (Force) x (displacement traveled in direction of force) W=F  d W=F  d 1) if object does not move, NO WORK is done. 1) if object does not move, NO WORK is done. 2) if direction of motion is perpendicular to force, NO WORK is done 2) if direction of motion is perpendicular to force, NO WORK is done

28. Example Push a block for 5 m using a 10 N force. Push a block for 5 m using a 10 N force. Work = (10 N) x (5 m) Work = (10 N) x (5 m) = 50 Nm = 50 Nm = 50 kgm 2 /s 2 = 50 kgm 2 /s 2 = 50 J (Joules) = 50 J (Joules)

29. I have not done any work if I push against a wall all day long but is does not move. 1. True 2. False

30. Doing WORK on a body changes its ENERGY Doing WORK on a body changes its ENERGY ENERGY is the capacity to do work. ENERGY is the capacity to do work. The release of energy does work, and doing work on something increases its energy The release of energy does work, and doing work on something increases its energy E = W = F  d Two basics type of energy: Kinetic and Potential. Two basics type of energy: Kinetic and Potential.

31. Kinetic energy: Energy of motion Kinetic energy: Energy of motion Potential energy: Energy of situation Potential energy: Energy of situation Position Position Chemical structure Chemical structure Electrical charge Electrical charge

32. Kinetic Energy: Energy of Motion Derivation: Push a ball of mass m with a constant force. Derivation: Push a ball of mass m with a constant force. KE = W = F  d = (ma)d But d = ½ at 2 KE = (ma)(½ at 2 ) = ½ m(at) 2 But v = at KE = ½ mv 2

33. A 6000 kg truck travels at 10 m/s. What is its kinetic energy? 1. 3000 J 2. 30000 J 3. 300000 J 4. 3000000 J

34. If the speed of the truck doubles, what happens to the energy? 1. Increases by ½x 2. Increases by 2x 3. Increases by 4x

35. Potential Energy Lift an object through a height, h. Lift an object through a height, h. PE = W = F  d= (mg)h PE = mgh Note: We need to decide where to set h=0.

36. Units of energy and work W = Fd W = Fd KE = mv 2 /2 KE = mv 2 /2 PE = mgh PE = mgh

37. Other types of energy Electrical Electrical Chemical Chemical Thermal Thermal Nuclear Nuclear

38. Conservation of Energy We may convert energy from one type to another, but we can never destroy it. We may convert energy from one type to another, but we can never destroy it. We will look at some examples using only PE and KE. We will look at some examples using only PE and KE. KE + PE = const. OR KE i + PE i = KE f + PE f

39. Drop a rock of 100m cliff Call bottom of cliff h = 0 Call bottom of cliff h = 0 Initial KE = 0; Initial PE = mgh Initial KE = 0; Initial PE = mgh Final PE = 0 Final PE = 0 Use conservation of energy to find final velocity Use conservation of energy to find final velocity mgh = ½mv 2 v 2 = 2gh

40. For our 100 m high cliff For our 100 m high cliff Note that this is the same as we got from using kinematics with constant acceleration Note that this is the same as we got from using kinematics with constant acceleration

41. A 5 kg ball is dropped from the top of the Sears tower in downtown Chicago. Assume that the building is 300 m high and that the ball starts from rest at the top. 1. 5880 m/s 2. 2940 m/s 3. 76.7 m/s 4. 54.2 m/s

42. A 5 kg ball is dropped from rest from the top (300 m high) of the Sears Tower. From conservation of energy, what is its speed at the bottom? 1. 5880 m/s 2. 2940 m/s 3. 76.7 m/s 4. 54.2 m/s

43. Pendulum At bottom, all energy is kinetic. At bottom, all energy is kinetic. At top, all energy is potential. At top, all energy is potential. In between, there is a mix of both potential and kinetic energy. In between, there is a mix of both potential and kinetic energy. Bowling Ball Video Bowling Ball Video Bowling Ball Video Bowling Ball Video

44. Energy Content of a Big Mac 540 Cal = 540000 cal 540 Cal = 540000 cal 1 Cal = 4186 Joules 1 Cal = 4186 Joules

45. How high can we lift a 1kg object with the energy content of 1 Big Mac? PE = mgh PE = mgh h = PE/(mg) h = PE/(mg) PE = 2,260,440 J PE = 2,260,440 J m = 1 kg m = 1 kg g = 9.8 m/s 2 g = 9.8 m/s 2

46. 2 Big Macs have enough energy content to lift a 1 kg object up to the orbital height of the International Space Station. 2 Big Macs have enough energy content to lift a 1 kg object up to the orbital height of the International Space Station. 150 Big Macs could lift a person to the same height. 150 Big Macs could lift a person to the same height. It would take about 4,000,000 Big Macs to get the space shuttle to the ISS height. It would take about 4,000,000 Big Macs to get the space shuttle to the ISS height. Note: McDonald’s sells approximately 550,000,000 Big Macs per year. Note: McDonald’s sells approximately 550,000,000 Big Macs per year.

47. Revisit: Cannon Momentum 1000kg cannon 1000kg cannon 5kg cannon ball 5kg cannon ball Before it fires P c + P b = 0 P c + P b = 0 Must also be true after it fires. Assume V b = 400 m/s M c V c + M b V b =0 M c V c + M b V b =0 V c = -M b V b /M c V c = -M b V b /M c = -(5kg)(400m/s)/(1000kg) = -(5kg)(400m/s)/(1000kg) = -2m/s = -2m/s

48. Cannon: Energy KE b = ½ mv 2 = 0.5 (5kg)(400m/s) 2 = 400,000 kgm 2 /s 2 = 400,000 kgm 2 /s 2 = 400,000 J KE c = ½ mv 2 = 0.5 (1000kg)(2m/s) 2 = 2,000 kgm 2 /s 2 = 2,000 kgm 2 /s 2 = 2,000 J Note: Cannon Ball has 200 times more ENERGY

49. When I drop a rock, it start off with PE which gets converted in to KE as it falls. At the end, it is not moving, so it has neither PE or KE. What happened to the energy? 1. Energy is not conserved in this case. 2. The energy is converted into Thermal energy 3. The energy is transferred to whatever it is dropped on.

50. Important Equations