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# Momentum &amp; Energy

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### Momentum &amp; Energy

1. 1. MOMENTUM & ENERGY 1. Define momentum as mass times velocity . 2. Recognise that momentum is a vector quantity, and that its direction must always be stated or shown. 3. Describe experiments that show that momentum is conserved during collisions 4. Distinguish between external and internal forces in a collision 5. Introduce Force - time graphs in the context of a collision and use this to relate the change in momentum to the force impulse 6. Explain the difference between elastic and inelastic collisions. 7. Define work and calculate the work done in a variety of situations. 8. Define energy and give examples of different forms of energy. 9. Describe the various forms of mechanical energy (Gravitational and elastic potential, Kinetic) and show how each can be calculated. 10. Carry out an investigation that relates force to spring extension 11. Use the relationship between force and extension to derive the expression for elastic potential energy 12. Recognise situations where mechanical energy is conserved and us this principle to solve problems. 13. Define Power and be able to calculate the power output in a variety of contexts. Reading p121 to 130 and p147 to 156 Monday, 7 June 2010
2. 2. BUILDING A DEFINITION Example 1 Why would this ship be difficult to slow down? ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Example 2 What makes the Ferrari difficult to slow down ___________________________________________ ___________________________________________ ___________________________________________ Monday, 7 June 2010
3. 3. BUILDING A DEFINITION Example 1 Why would this ship be difficult to slow down? ___________________________________ ___________________________________ ___________________________________ ___________________________________ ___________________________________ Example 2 What makes the Ferrari difficult to slow down ___________________________________________ ___________________________________________ ___________________________________________ The harder an object is too stop, the greater momentum it has. Monday, 7 June 2010
4. 4. MOMENTUM IS A QUANTITY OF MOTION Clikview: “Collisions” > Conservation of momentum It is the product of an object’s mass and velocity. Momentum = Mass x velocity p = the object’s momentum (kgms-1) p = mv m = the object’s mass (kg) ~ ~ v = the object’s velocity (ms-1) Note Momentum is a vector quantity since it depends on velocity which is a vector quantity. Change in Momentum The change in momentum of an object equals the final momentum minus the initial momentum. p = pf - pi ~ ~ ~ Monday, 7 June 2010
5. 5. EXAMPLES 1. Calculate the momentum of a car that has a mass of 1200 kg and is travelling at 30 ms-1 __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ 2. Calculate the mass of a cricket ball that is bowled at 36 ms-1 and has a momentum of 7.2 kgms-1 __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ 3. Calculate the velocity of a person that has a mass of 140 kg and has a momentum of 1400 kgms-1 __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ Complete Q.1 - “Momentum & Impulse” Monday, 7 June 2010
6. 6. INTERNAL & EXTERNAL FORCES Example Consider a collision between two billiard balls A and B. v=0 F F A B A B A B BEFORE DURING AFTER In this situation there are no external forces. The forces necessary for the separation are internal. A exerts a force on B and B exerts a force on A as shown in the diagram (below). These forces are equal and opposite and are called an action - reaction couple. Examples of external forces: 1. friction 2. a push on one of the objects as it collides with the other object. Monday, 7 June 2010
7. 7. THE LAW OF CONSERVATION OF MOMENTUM In physics, “conservation” means remains constant or unchanged In all collisions and explosions, provided there is no external force then the total momentum remains the same. We say that momentum is conserved. There are two types of collisions: 1. Bouncy collisions 2. Sticky collisions Total momentum before = Total momentum after Note that momentum is a vector and therefore direction needs to be shown. In a problem where objects travel in a straight line, use + and - to indicate direction. Monday, 7 June 2010
8. 8. a “bouncy” collision v=0 Before A B v=0 After A B a “sticky” collision v=0 Before A B v After A B Explain why momentum is conserved in these collisions: Monday, 7 June 2010
9. 9. Examples For the “bouncy” collisions below, calculate v. 1 2 ms-1 0.5 ms-1 v=? A B A B 0.1 kg 0.1 kg 0.1 kg 0.1 kg BEFORE AFTER 2 v=? 0.50 ms-1 A B A B 0.40 kg 0.40 kg 0.1 kg 0.1 kg Monday, 7 June 2010
10. 10. 3 For the “sticky” collision below, calculate v. v=0 Before 5 kg 2 ms-1 3 kg v After 5 kg 3 kg Monday, 7 June 2010
11. 11. 4 An explosion is an interaction where things fly apart from a central point. The only forces acting are internal (action and reaction) forces so total momentum is conserved. Before 5 kg 3 kg 2 ms-1 v After 5 kg 2 kg Calculate v Monday, 7 June 2010
12. 12. 5 All the momentum problems that you will need to solve this year will be limited to motion in a straight line. This means the object will either be travelling forwards or backwards. It is therefore important to reference your answer with directions if you are unsure what direction an object will travel after a collision. Use + - An example of an easy problem: Calculate v Complete Q.1 to 3 - “Collisions & Explosions” Monday, 7 June 2010
13. 13. CHANGE IN MOMENTUM & IMPULSE [Examples: 1.Airbags 2. Jumping from a burning building onto a matress] • Impulse is a term that means “The change in momentum of an object” • Impulse = the final momentum - the initial momentum of the object. p = the object’s Impulse p = pf - pi ~ ~ ~ pf = the object’s final momentum pi = the object’s initial momentum Note: • Momentum is a vector and therefore direction needs to be shown. In a problem where objects travel in a straight line, use + and - to indicate direction. • Change in momentum is also a vector quantity and will therefore be positive or negative • An object experiences a change in momentum or impulse when it experiences a force over a period of time: Where F = the force acting on the object ∆p = F∆t ~ ~ and t = the time for which that force acts Monday, 7 June 2010
14. 14. Change in momentum & force EXAMPLES 1. An apple of mass 250 g falls of a branch and lands on the ground. It is travelling at 3 ms-1 just before it hits the ground and stops. Calculate its change in momentum. 2. A 0.2 kg tennis ball collides with a solid wall as shown: After Before 20 ms-1 20 ms-1 Determine the change in momentum of the ball. ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ Describe the force responsible for this change in momentum. ___________________________________________________________________ If the collision time is 0.1 s, calculate the size of this force. ___________________________________________________________________ ___________________________________________________________________ Complete Q.2 - “Momentum & Impulse - Exercises” Monday, 7 June 2010
15. 15. THE FORCE - TIME GRAPH An object receives an impulse when we change its momentum by applying a force to the object over a period of time. ∆p = F∆t ....... a rearrangement of F = ∆p ~ ~ ~ ∆t Impulse Force applied Consider... Taking a fall and hitting your head on the pavement wearing a helmet compared to having the equivalent fall without the helmet. F Without helmet With helmet => LESS force over a LONGER period of time. SAME AREA under the graph. Impulse = Area under the Force - time graph t Complete Q.3, 4, 7 & 8 - “Impulse & Momentum - Exercises” Monday, 7 June 2010
16. 16. ELASTIC & INELASTIC COLLISIONS Momentum is always conserved in a collision (provided there are no external forces) Kinetic energy is not always conserved: • During elastic collisions, Kinetic energy is conserved. Ek before the collision = Ek after the collision • During inelastic collisions, Kinetic energy is not conserved. Some of the Ek is converted into other forms during the collision - commonly heat and sound Examples A trolley of mass 3 kg and speed 4 ms-1 collides head on with a stationery trolley of mass 1 kg. They stick together and move off with a speed of 3 ms-1. Momentum can be shown to be conserved in this collision. (a) Show that kinetic energy is not conserved in the collision. ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ (b) Where has the lost energy gone? ________________________________________________________________ ________________________________________________________________ Monday, 7 June 2010
17. 17. Example A ballistic pendulum is used to measure the speed of a bullet. It is a large soft mass which has been suspended from the ceiling. When a bullet with speed v1 embeds itself into the mass the mass swings and rises a distance h as shown: 1 2 3 v1 v2 M m h v= 0 M +m The masses and the height are measured and recorded as follows: M = 998 g m=2g h = 10 cm Calculate the speed of the bullet v1 (in ms-1) ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ ___________________________________________________________________ Monday, 7 June 2010
18. 18. WHEN IS WORK DONE? Work is done when energy is transferred to an object or when energy changes from one form to another. You do work when you: 1. move an object because you are giving the object kinetic energy 2. lift an object because you are giving the object gravitational potential energy. 3. slow an object down because kinetic energy is being changed to heat energy. Whenever an object moves in the direction of a force work has been done Examples - Has work been done ?? ▢ A woman lifts a poodle. ▢ The moon circles the earth. ▢ An ice skater drifts (without pushing) towards the centre of the ice-skating rink. Monday, 7 June 2010
19. 19. WORKING OUT WORK When the force is constant ..... and only when the force is constant: Work done = Force x distance W = Fd Units: Joules, J Newtons, N metres, m Work is only being done when the object ________ in the direction of the force Example Calculate the work done in each of the following situations: __________________ 20 N 20 N __________________ __________________ __________________ 3m 20 20 __________________ N N 20o 20o __________________ __________________ __________________ 3m Monday, 7 June 2010
20. 20. LET’S DIG DEEPER By the SI definition of the joule: “One joule is the amount of work done when a one Newton force acts over the distance of one metre.” GRAPHS The definitive rule: Work done is always equal to the area under the force - distance graph For a constant force: For a non-constant force: A1 A2 F F W = Area = F.d W = Area = A1 + A2 d d Monday, 7 June 2010
21. 21. Examples 1. A moving mass is brought to rest by 50N of friction over a distance of 4m. __________________________________________________________________ 2. A builder lifts a piece of timber whose weight is 100N, through 1.2 m. __________________________________________________________________ 3. A 5 kg box drops to the floor from a shelf of 3 m high. __________________________________________________________________ 4. A girl lifts an 18 kg suitcase 1.2 m above the floor. __________________________________________________________________ 5. The girl holds the suitcase for 5 minutes. __________________________________________________________________ 6. The suitcase is carried a horizontal distance of 5 m. __________________________________________________________________ The energy that results in each of the above examples: (also, where no work is done, an explanation why) 1. 4. 2. 5. Complete Q.1 & 2 - 3. 6. “Work Exercises” Monday, 7 June 2010
22. 22. DIFFERENT FORMS OF ENERGY Chemical (stored in _______ between ________ ) Gravitational (stored as a result of Potential (or _______) an object’s __________ ) Energy Elastic (stored in materials that can ____________ ) What are Kinetic (depends on __________ ) they? Sound (produced when __________ __________) Heat (the total internal energy) Light (produced when objects become very _____ ) Electrical (produced from the relative position or motion of _____________ ) Monday, 7 June 2010
23. 23. KINETIC ENERGY • When work is done to move or accelerate an object the object gains kinetic energy. • For an object of mass, m travelling at speed, v kinetic energy, Ek can be calculated using the following formula: Ek = 1mv2 2 The unit of Ek is the joule, J We do not treat Ek as a vector quantity since it relies on v2 Examples A 500g trolley travelling at 1 ms-1 accelerates to 2 ms-1 (a) Compare the Ek at 2 ms-1 to the Ek at 1 ms-1 _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ (b) Compare the Ek at 3 ms-1 to the Ek at 1 ms-1 _________________________________________________________________ _________________________________________________________________ Complete Q.1 to 5 - “Energy Transfer Exercises” Monday, 7 June 2010
24. 24. THE KINETIC ENERGY - SPEED RELATIONSHIP Ek Ek v v2 The kinetic energy of an object is proportional to the speed squared: Ek α v2 This means that when v doubles then Ek will quadruple If v trebles then Ek will multiply by a factor of nine ... and so on Question Explain why a relatively small increase in speed for a motor vehicle say from 100 kmh-1 to 110 kmh-1 (a 10% increase) results in a disproportionately higher risk of injury. __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ Monday, 7 June 2010
25. 25. GRAVITATIONAL POTENTIAL ENERGY When work is done to lift an object the object gains gravitational potential energy. Consider: A mass, m is lifted off the ground to a height, h m m h Before After • The object nows has gravitational potential energy. • Work has been done because a lifting force has been applied (to overcome gravity) over a distance, h. • This lifting force is a constant force (because it overcomes gravity which is a constant force) W = Fgrav x h (Remember that Fgrav = mg) therefore W = mgh so Ep = mgh (since Work has been done to give the object gravitational potential energy) Monday, 7 June 2010
26. 26. Examples 1. An object 5 m above the ground has a gravitational potential energy of 120 J with respect to ground level. (a) What is the object’s mass? __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ (b) What is the object’s potential energy if it is lowered to 2.5 m above the ground? __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ 2. An object weighing 50 N falls a distance of 7 m. Calculate its loss of potential energy? __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ Complete Q.1 & 2 - “Gravitational Potential Energy Exercises” Monday, 7 June 2010
27. 27. ELASTIC POTENTIAL ENERGY Materials which have elasticity such as springs or rubber bands can store energy as elastic potential energy. Consider: Adding a mass, m to the end of a hanging spring. The spring stretches through a distance, x x m Before After When work is done to stretch the spring the spring gains elastic potential energy, Ep elast Monday, 7 June 2010
28. 28. Theory The force required to stretch the spring increases as the extension, x increases . The graph clearly illustrates this trend between force and extension: F Fαx Force is proportional to extension x In summary: F = kx F = the force required to expand or compress a spring (given in Newtons, N) x = the compression or extension of the spring (given in metres, m) k = gradient of the graph or the spring constant (in Nm-1) Monday, 7 June 2010
29. 29. Remember • Work done is given by the area under the force - distance graph. • It follows then that for a spring the work done equals the area under the force against extension (or compression) graph. F kx But since F = kx the graph could be drawn as shown x x W = Area of a ∆ = 1.x.kx 2 = 1kx2 2 Since the work done represents elastic potential energy gained by the spring: Ep elast = 1 kx2 2 Monday, 7 June 2010
30. 30. Examples 1. A spring is 66 cm long. When a 500g mass is attached to the spring its length increases. The new length is 96 cm. What is the extension of the spring? 66 cm 96 cm 500 g 2. A spring of length 50 cm has a mass of 1 kg added to it. The spring compresses and is now 25 cm long. Calculate the compression of the spring. 1 kg 50 cm 25 cm Monday, 7 June 2010
31. 31. 3. A spring, which is part of the suspension of a car has a spring constant of 100000 Nm-1. It is one of four identical springs. (a) If the car has a mass of 1200 kg then calculate the weight of the car. (b) How much of this weight acts on the spring. (assume that the cars weight is evenly distributed across all four springs). (c) If the uncompressed length of the spring is 300 mm then calculate how much the spring has compressed as a result of the car’s weight. (d) Consider a situation where the car is loaded with four people and that the mass of the car increases by 320 kg as a result. Calculate how much further the spring compresses. Monday, 7 June 2010
32. 32. 4. In an exercise in the school lab, students determine the spring constant of a spring. Each spring is tested using the equipment below. The mass hanging on each spring is increased by adding masses and with the addition of each new mass, the length of the spring is measured. (a) Complete the results table to show the force Length of Mass, m Force, F Extension on the spring and its extension. spring (kg) (N) (m) (m) 0 0.13 0.02 0.15 0.04 0.17 0.06 0.19 0.08 0.21 0.10 0.23 0.12 0.25 (b) Graph the force against the extension. (c) Use the graph to calculate the spring constant. Monday, 7 June 2010
33. 33. 5. A toy catapult has a spring constant of 50 Nm-1. (a) What is the force required to pull the elastic band back 0.15 m? ________________________________________________________________ ________________________________________________________________ (b) What elastic potential energy is stored in the catapult at that extension? ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ 6. A 50 kg child stands on a trampoline and causes the trampoline to sag by 30 cm. (a) What is the child’s weight? ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ (b) What is the trampoline’s spring constant? ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ Complete Q.1 to 2 - “Energy & Springs Exercises” Monday, 7 June 2010
34. 34. Clickview - “The Conservation of Energy” Ch1: part 1 to 3 CONSERVATION OF ENERGY Demo: the pendulum Gravitational potential, elastic potential and kinetic energy are forms of mechanical energy since they depend on an object’s position. When an object moves and no energy is converted to heat, light or sound then the mechanical energy of an object remains constant. in other words... The total of Ep and Ek is always the same or Ep + Ek = a constant value 1. Enter the URL below into the address bar of your web browser. 2. Study the animation carefully and at each critical position of the trolley state the predominant forms of energy that the trolley has. http://surendranath.tripod.com/Applets/Dynamics/Coaster/CoasterApplet.html Monday, 7 June 2010
35. 35. Examples 1. A 150 g cricket ball is hit to a vertical height of 30 m. (a) Calculate the ball’s original kinetic energy? _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ (b) Calculate the ball’s potential energy 10 m up. _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ Explain why its kinetic energy here is 30 J. _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ (c) Calculate the ball’s speed at this height. _______________________________________________________________ _______________________________________________________________ Monday, 7_______________________________________________________________ June 2010
36. 36. 2. A 2 kg stone is thrown horizontally from the top of a cliff 45 m high at a speed of 10 ms-1. (a) Calculate the total energy at point X, 45 m up. ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ____________________________________________________________ (b) Hence write down the total energy at point Y ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ____________________________________________________________ (c) Calculate the kinetic energy and speed at point Y. ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ Complete Q.1 to 3 - “Conservation of Energy - Exercises” Monday, 7 June 2010
37. 37. POWER Power is the rate at which work is done P = power (in joules per second, Js-1 or Watts, W) P=W W = work (in joules, J) t t = time (in seconds, s) Since work done is energy transferred, then Power can be thought of as the rate at which energy is: (a) used or produced or ... (b) converted from one form to another Example The power output of a 40 kg student is 800 W. She runs up the stairs in 10 seconds (a) Calculate the force that the student exerts in order to climb the stairs _________________________________________________________________ _________________________________________________________________ (b) Calculate the height of the stairs. _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ Complete Q.1 to 3 - “Power Exercises” Monday, 7 June 2010
38. 38. Momentum & Impulse EXERCISES 3. A tennis ball of mass 0.08 kg approaches a racket at a right angle to the strings with a speed 10 ms-1. The person holding the racket strikes the ball causing it to rebound along the same path at 20 ms-1. a. Draw the situation. b. Let the initial velocity of the ball be a positive velocity and the final velocity be negative. Calculate the initial and final momentum of the ball. c. Hence determine the ball’s impulse. d. Given the collision occurs over a time interval of 0.1 s, calculate the average force that the racket exerts on the ball. Answers: 3.a shows 10ms-1 vector to the right and 20 ms-1 vector in opposite direction 3.b pi = 1kgms-1 pf = -2kgms-1 3.c -3kgms-1 3.d -30 N Monday, 7 June 2010
39. 39. 4.Marama is driving her car home after her event, when she collides with a stationary van. Assume there are no outside horizontal forces acting during the collision. (a) Name the physical quantity that is conserved in this collision. The mass of the car is 950 kg and the mass of the van 1700 kg. The car is travelling at 8.0 m s–1 before the collision and 2.0 m s–1 immediately after the collision, as shown in the diagram above. (b) Calculate the size and direction of the car’s momentum change. (c) Calculate the speed of the van immediately after the collision. (d) If the average force that the van exerts on the car is 3 800 N, calculate how long the collision lasts. (e) Marama had a bag resting on the front seat. Use relevant physics concepts to explain why the bag fell onto the floor during the collision. (f) The front of modern cars is designed to crumple or gradually compress during a collision. Use the idea of impulse to explain why this is an advantage for the people in the car. Monday, 7 June 2010
40. 40. Monday, 7 June 2010
41. 41. Work EXERCISES 1. A weightlifter holds weights steady, at shoulder level, for 30 seconds before dropping them. (i) Has any work been done by the weightlifter (explain your answer)? _______________________________________________________________ _______________________________________________________________ (ii) Has any work been done at all in this situation (explain your answer)? _______________________________________________________________ It takes 0.7 s for the weights to reach the floor from when they dropped. The weights have a total mass of 75 kg and they fall through a distance of 1.3 m. (iii) Calculate the work done on the weights. _______________________________________________________________ 2. A car of mass 1000 kg travels at 25 ms-1 along the open road. The driver who sees an obstacle in his path brakes suddenly to bring the car to a halt over a distance of 25 m. (i) Explain why work has been done on the car? _______________________________________________________________ _______________________________________________________________ (ii) Name the force that is responsible for doing this work. ___________________ (iii) Calculate the size of this force. _______________________________________________________________ (iv)Describe the energy transformations (changes) that are taking place during the braking process. Monday, 7_______________________________________________________________ June 2010
42. 42. Energy transfer EXERCISES 1. How much work is done by a motorcyclist pushing his motorcycle with a force of 1000 N through a horizontal distance of 20 m? __________________________________________________________________ __________________________________________________________________ 2. Not all the energy that the motorcyclist uses is converted to kinetic energy. Discuss this statement. __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ __________________________________________________________________ 3. How much work is done by a swimmer who pushes off from the wall in the swimming pool at the start of a race. She applies a force of 500 N over a distance of 50 cm. __________________________________________________________________ 4. Once the swimmer’s feet have lost contact with the wall she decides not to move her body any further. Explain why she slows down and eventually stops in the water. __________________________________________________________________ __________________________________________________________________ 5. How much work is done by a crane which lifts a car weighing 1200 kg through a vertical distance of 2 m? __________________________________________________________________ __________________________________________________________________ Monday, 7 June 2010
43. 43. Gravitational Potential Energy EXERCISES 1. A student climbs a flight of stairs on her way to the first floor of the school gymnasium. The student’s mass is 56 kg and the vertical height climbed is 14 m. (i) Explain why work has been done by the student. ________________________________________________________________ ________________________________________________________________ (ii) Calculate the gravitational potential energy that the student has once she has reached the first floor of the gymnasium. ________________________________________________________________ 2. A second student makes his way to the first floor of the gymnasium and gains 56000J of gravitational potential energy. (i) Calculate the mass of the second student. ________________________________________________________________ ________________________________________________________________ (ii) Calculate the height that the second student would need to be at to have the same gravitational potential energy as the first student when the first student is on the first floor. ________________________________________________________________ ________________________________________________________________ (iii) Explain why the second student is more likely to cause damage to himself and to the ground if he fell from the first floor than if the first student had a similar fall from the first floor. ________________________________________________________________ ________________________________________________________________ Monday, 7 June 2010
44. 44. Energy and Springs EXERCISES Monday, 7 June 2010
45. 45. Power EXERCISES 1. A girl uses 200J of energy to push someone up onto a wall. It takes her 2 seconds to do this. What is her power rating? _________________________________________________________________ 2. A boy of mass 60 kg runs up a flight of stairs. The vertical distance is 20 m and he takes 8 s to reach the top. Calculate the boy’s power output. __________________________________________________________________ 3. A rugby team pushes against the scrum machine with a force of 10000N over a distance of 7 m. It takes 22 s to cover this distance. (i) Calculate the work done by the team. ________________________________ (ii) Calculate the power output of the team. _______________________________________________________________ Conservation of Energy 1. A 200g (0.2 kg) apple falls 3m to the ground below the tree. How fast was it going just before it hit the ground? Monday, 7 June 2010
46. 46. 2. A 160g (0.16 kg) cricket ball is hit straight up at 20 ms-1. What height will it reach before falling back? ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ 3 Monday, 7 June 2010
47. 47. Work - answers Energy transfer - answers 1. 20000 J 2. In reality work done is greater than the increase in kinetic energy because some of that kinetic energy is transformed to heat (due to friction) 3. 250 J 4. Friction (water resistance) acting over a distance in the opposite direction to which the swimmer moves slows the swimmer to a stop. 5. 24000 J Gravitational Potential Energy - answers 1. (i) The student is exerting a force against gravity. This force acts over a distance of 14 m so work is being done by the student. (ii) 7840 J 2 (i) 400 kg (ii) 1.96 m (iii) Whilst they both hit the ground with the same speed, the second student has much more mass, therefore has much more kinetic energy. More work has to be done by the ground to change this kinetic energy to heat. Monday, 7 June 2010
48. 48. Power exercises 1. 100 W 2. 1500 W 3. (i) 70000 J (ii)3182 W Monday, 7 June 2010
49. 49. 12 PHYSICS ENERGY ASSIGNMENT Name 1. A 50 kg girl swings freely on a 5.0 metre long rope tied to a branch of a Pohutukawa tree overhanging the water. The diagram shows the rope at the extremes of the swing arc and the path of the swing. Point A is 1.0 metres vertically above point C. (use g = 9.8 ms-2) (a) On the diagram, draw arrows to show the direction of the nett or total force on the girl at points A and C. (deals with concepts in forces and in circ. motion topic. (b) Use the principle of energy conservation to calculate the speed of the girl at point C. _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ Monday, 7 June 2010
50. 50. 2. A dart of mass 250 g is loaded into a dart gun as shown, by compressing the main spring by 4.4 cm. The elastic constant of the main spring is 5 kNm-1. (a) What force is required to load the gun? _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ (b) How much potential energy is stored in the main spring when compressed? _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ (c) What is the kinetic energy of the dart as it leaves the gun? _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ (d) What is the speed of the dart as it leaves the gun? _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________ Monday, 7 June 2010
51. 51. 3. The following diagram represents a track which has been eroded to demonstrate certain aspects of the energy of a body. A small cart of mass 4 kg moves without friction on the track. 10 ms-1 2m D E A B 5m C (a) What is the kinetic energy of the cart as it moves along AB? _______________________________________________________________ (b) At which point on the track is the potential energy at a maximum? __________ (c) What is the change in potential energy of the cart between D and B? _______________________________________________________________ _______________________________________________________________ (d) What is the kinetic energy of the cart as it moves along DE? _______________________________________________________________ _______________________________________________________________ (e) Calculate the speed of the cart as it passes the point C. _______________________________________________________________ _______________________________________________________________ Monday, 7 June 2010
52. 52. 12 PHYSICS MOMENTUM MINI ASSIGNMENT Name ___________________ 1. A Peugeot (mass 750kg) is travelling at 30ms-1 and collides head on with a Mercedes Benz (mass 1600kg) travelling at 20ms-1 in the opposite direction. (a) Draw the situation and calculate the magnitude of the momentum of each car before crashing. (b) If the two cars lock together in the crash, in which direction will they be moving immediately after the collision? (c) Calculate the initial speed of the combined wreck immediately after the collision. (d) Why does this speed quickly reduce to zero? 8 kgms-1 5 kgms-1 A B 2. Two balls A and B are about to collide and the momentum of each ball is shown in the diagram. After the collision both balls move in the opposite directions, ball A -1 having a momentum of magnitude 1.5 kgms . Calculate the momentum of ball B after the collision. (Hint: draw a vector diagram) Monday, 7 June 2010
53. 53. 3. A trolley rolls along a bench at a constant speed. As it passes a student, she drops a block of wood, at a time t1, vertically down onto the trolley. Sketch a speed-time graph which best represents the speed before and after the block of wood was dropped. Show your reasoning to the left of the graph. Monday, 7 June 2010