UNIT 3. Work, Energy & Power

Transcription

1 Name: Regents Physics Date: Mr. Morgante UNIT 3 Work, Energy & Power

2 Work Work is equal to the force applied to an object that results in the object s displacement. Displacement is a vector! So again, direction and sign convention are important. Eq: W = F x d Units: J = N x m This J is a unit, it is not impulse! Joules W = Work (Joules OR N m) F = Force (Newtons) d = displacement (meters) Joules is a unit of energy, therefore we must input energy into moving an object to do work. If I do work on an object, I have put energy into the object! I push a lawnmower, I put energy into moving a lawnmower. Can we derive Kinetic Energy equations from work and Newton s 2 nd Law! W = F Net d AND F Net = m a W = m a d where v 2 = 2a d from kinematics equations therefore v 2 / 2 = a d W = m (v 2 / 2) W = Joules = energy KE = Joules = energy KE = ½ m v 2 a = v/ t v = d/t Typically W = F d Fapp. = 10N d=10 m Fapp.=10N W = F d = 10N x 10 m = 100 N m = 100 J 2

3 Kinetic Energy of an Object Kinetic means moving, therefore object has to be moving. Does it have Kinetic Energy (KE)? Yes it moves, therefore it has KE. KE = ½ mv 2 KE = Kinetic Energy (Joules) m = mass (kg) v = Velocity (m/s) [has direction & magnitude] OR speed (m/s) [has only direction] Ex. v = 10 m/s m = 2kg KE = ½ mv 2 = ½ (2kg)(10m/s) 2 = 100 Joules Different Forms of Energy Gravitational Potential Energy (PEg) When work is done against gravity i.e. lifting a box, climbing stairs, climbing a mountain, etc. PE = mg h PE = change in potential energy (Joules) m = mass (kg) g = gravity (m/s 2 ) h = change in height OR elevation (m) mg = weight = (N) SKETCH h g m F 3

4 Work Against Friction Trick Question - Object moves at constant speed of 2 m/s for a distance of 5m. What work is done on the object? [Ans: NONE b/c constant velocity = no accel.=no Force] Sketch: F N Ff Fapplied F g =m g Elastic Potential Energy mg = F g Hooke s Law = F = k x SKETCH x (N)=(N/m)(m) k = spring constant (N/m) When we stretch a spring, we input stored energy (PEs) Potential Energy of Spring into the spring. We know this because when the spring is released, it moves and when it moves it transforms PEs into KE. Eq. for PEs PEs = ½ k x 2 This is energy Please note this is NOT F = K x This is force k = spring constant (N/m) x = displacement (m) **If you use F=k x, you can first get k and then k plug into PEs = ½ k x 2 ** PEs = stored energy (J) or (N m) 4

5 Area Under Graphs and Work & Energy F d Area of triangle = ½ b h Units for energy Joules or N m Slope = spring constant UNITS ANALYSIS Y axis N X axis m Therefore looking at units for the area under line ½ Base Height OR ½ Force distance = F d Units Analysis = N m = J which is energy! 5

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7 Pendulum- Period T=2Π l/g Time to complete 1 full swing No friction, pendulum will keep swinging Period depends on length (l) and gravitational acceleration (g) Period is independent of mass of the bob h v=0 here so MAX PE g! Equilibrium point V max is here so MAX KE! Period is the time taken by the bob to go from one end of its swing to the opposite end and then return to the starting point - Stick different masses on pendulum and determine T - Set different length and determine T Total Energy= KE + PE + Internal Energy We will talk about forms of energy in motors, generators, photocell, battery. Power Power is the rate at which work is done, or the rate at which energy is used transferred. The SI unit for power is the watt (W). A power of 1W means that work is being done at the rate of 1 J/s. Larger units for power are the kilowatt kw (1kW = 1000 W = 10 3 W) and the megawatt MW (1 MW = W = 10 6 W). 7

8 If work is being done by a machine moving at speed v against a constant force, or resistance, F, then since work doe is force times distance, work done per second is Fv, which is the same as power. Example 1 A constant force of 2 kn pulls a crate along a level floor a distance of 10 m in 50s. What is the power used? Solution Alternatively we could have calculated the speed first and then calculated power 8

9 Example 2 A hoist operated by an electric motor has a mass of 500 kg. It raises a load of 300 kg vertically at a steady speed of 0.2 m/s. Frictional resistance can be taken to be constant at 1200 N. What is the power required? Solution From the Previous Power Equation 9

10 Name Regents Physics Energy Notesheet, Part I Definitions: 1. Energy Date Mr. Morgante 2. Work 3. Joule 4. Power 5. Watt 6. Potential Energy 7. Gravitational Potential Energy Equation Variables/ constants Units Can be used to find Vector/scalar ΔPE ΔPE = mgδh m g Δh W = Fd = ΔE T W F d ΔE T P P = W = Fd =F v W t t F d t v A θ A x A y A y = A sin θ A x = A cos θ 10

11 +y 8. Work and gravitational potential energy examples +x Case 1 Case 2 Case 3 F F F mass mass mass no friction μ static μ kinetic a = a= 0 a = 0 v= v = v = d = d = d = F f = F f = F f = W = W = W = Summary Case 4 Case 5 Case 6 (frictionless) F θ h μ kinetic a = h θ v= d = F f = W = Summary: 11

12 Name Regents Physics Energy Notesheet, Part II Date Mr. Morgante 9. Force versus displacement graph The area under a Force versus displacement graph can be used to find Calculate the work done in each case: F F F F disp disp disp disp Work = 10. Definitions: Forms of Energy/Devices for converting energy Internal energy: Nuclear energy: Electromagnetic energy: Photocell Generator Motor Battery 12

13 Name Regents Physics Definitions: 1. Compression 2. Elastic Potential Energy 3. Elongation 4. Hooke s Law 5. Spring constant 6. Equilibrium position Date Mr. Morgante Energy Notesheet, Part III, Elastic Potential Energy Equation Variables/ constants Units Can be used to find Vector/scalar F s F s F s F s = kx k k k x x x PE s PE s PE s PE s = ½ kx 2 k k k x x x Hooke s Law: Sketch the graph of an elastic material that is being elongated according to F s = kx. a)what is the slope of this graph? F s b)what are the units of k? c)what quantity can be computed for the area under an F versus displacement graph? x d)what is the equation for the area of a triangle? e) Calculate the work done on a spring if the endpoints of the graph are (0m,0N) & (1.7m,20N) 13

14 Elastic Potential Energy: a) Using PE s = ½ kx 2, and k = 15 N/m, complete the table below: x value 0m 0.25m 0.5m 0.75m 1m 2m PE s b) Sketch the graph of an elastic material that is being elongated according to F s = kx. PE s X c) Using PE s = ½ kx 2 Solve for k solve for x d) Prove that PE s is equivalent to Work is equivalent to ΔPE using units: 14

15 Name Regents Physics Definitions: 1. Kinetic energy 2. Potential energy 3. Momentum Date Mr. Morgante Energy Notesheet, Part IV, Kinetic Energy Equation Variables/ constants Units Can be used to find Vector/scalar KE KE KE KE = ½ mv 2 m m m v v v ΔPE = mgδh ΔPE ΔPE ΔPE m m m g g g Δh Δh Δh p = mv p p p m m m v v v Algebra review: 1. If KE = ½ mv 2, solve for: m =, v = 2. If the velocity of an object is doubled, the KE is 3. If the velocity of an object is halved, the KE is Graph review: Sketch the basic shapes of the graphs below(mass remains constant): KE p velocity velocity 15

16 Unit Review: a)show how Work = KE with units Practice Problem: A 2-kg object falls from rest from a 490 m cliff. Ignore air resistance. Use g = 9.8 m/s 2 Time (s) Velocity Displacement PE g KE Momentum (Not to scale) +x +y 16

17 Name Regents Physics Definitions: 4. Conservative force 5. Nonconservative force 6. Closed system 7. Law of conservation of energy: 8. Mechanical energy 9. Ideal mechanical system 10. Simple pendulum 11. Nonideal mechanical system 12. Total energy Date Mr. Morgante Energy Notesheet, Part V, Conservation of Energy Equation Variables/ constants Units Can be used to find Vector/scalar E T E T E T E T =PE+KE+Q PE PE PE KE KE KE Q Q Q ΔPE = mgδh ΔPE ΔPE ΔPE m m m g g g Δh Δh Δh KE = ½ mv 2 KE KE KE m m m v v v 17

18 Algebra review: 1. Given: KE = ½ mv 2, ΔPE = mgδh, W = Fd, PE s = ½ kx 2 a) If ½ mv 2 = mgδh, solve for v: b) If ½ mv 2 = mgδh, solve for Δh: a) b) c) If mgδh = ½ kx 2, solve for k: d) If mgδh = ½ kx 2, solve for x: c) d) e) If mgδh = ½ kx 2, solve for Δh: f ) If mgδh = ½ kx 2, solve for m: e) f) g) If ½ mv 2 = ½ kx 2, solve for v: h ) If ½ mv 2 = ½ kx 2, solve for m: g) h) i) If ½ mv 2 = ½ kx 2, solve for k: j) If ½ mv 2 = ½ kx 2, solve for x: i) j) 18

19 Conservation of Energy Systems: Case 1 Case 2 Object in free-fall above ground to h = 0 Object projected vertically (+y) from ground to v i = 0, h top of arc +y +y h = 0 h = 0 PE i = KE i = PE i = KE i = PE f = KE f = PE f = KE f = What Energy transformation occurs? What energy transformation occurs? Case 3 Case 4 Object on inclined plane Object launched vertically from spring v i = 0 System: h h = 0 PE i = KE i = PE i = KE i = PE f = KE f = PE f = KE f = What Energy transformation occurs? What energy transformation occurs? 19

20 Name: Date: Regents Physics Mr. Morgante Work Worksheet 1. What is the spring constant of a spring of negligible mass which gained 8 joules of potential energy as a result of being compressed 0.4 meters? (1 ) 100N/m (2 ) 50N/m (3 ) 0.3N/m (4 ) 40N/m 2. Work is done when a force (1 ) acts vertically on a cart that can only move horizontally (2 ) exerted by one team in a tug of war when there is no movement (3 ) is exerted while pulling a wagon up a hill (4 ) of gravitational attraction acts on a person standing on the surface of the Earth 3. A spring of negligible mass with a spring constant of 200 newtons per meter is stretched 0.2 meters. How much potential energy is stored in the spring? (1 ) 40 J (2 ) 20 J (3 ) 8 J (4 ) 4 J 4. An object gains 10 joules of potential energy as it is lifted vertically 2.0 meters. If a second object with one-half the mass is lifted vertically 2.0 meters, the potential evergy gained by the second object will be (1 ) 10. J (2 ) 20. J (3 ) 5.0 J (4 ) 2.5 J 5. A cart of mass M on a frictionless track starts from rest at the top of a hill having height h1, as shown in the diagram below. What is the kinetic energy of the cart when it reaches the top of the next hill, having height h2? (1 ) mgh1 (2 ) mg(h1-h2) (3 ) mg(h2-h3) (4 ) 0 20

21 6. A force is applied to a block, causing it to accelerate along a horizontal, frictionless surface. The energy gained be the block is equal to the (1 ) Work done on the block (2 ) power applied to the block (3 ) impulse applied to the block (4 ) momentum given to the block 7. A 1.0 x10 3 -kilogram car is moving at a constant speed of 4.0 meters per second. What is the kinetic energy of the car? (1 ) 1.6 x 10 3 J (2 ) 2.0 x 10 4 J (3 ) 8.0 x 10 3 J (4 ) 4.0 x 10 3 J 8. When a spring is stretched meter from its equilibrium position, it possesses a potential energy of 10.0 joules. What is the spring constant for this spring? (1 ) 100. N/m (2 ) 125 N/m (3 ) 250. N/m (4 ) 500. N/m 9. A constant force of 2.0 newtons is used to push a 3.0-kilogram mass 4.0 meters across the floor. How much work is done on the mass? (1 ) 6.0J (2 ) 8.0J (3 ) 12J (4 ) 24J 10. A student rides a bicycle up a 30 hill at a constant speed of 6.00 meters per second. The combined mass of the student and bicycle is 70.0 kilograms. What is the kinetic energy of the student-bicycle system during this ride? (1 ) 210. J (2 ) 420. J (3 ) 1,260 J (4 ) 2,520 J 11. If the distance a spring is stretched is doubled, the potential energy is: (1) four times as great (2) one fourth as great (3) twice as great (4) the same 12. A 5-kg cart is rolling along on the ground when an additional 5-kg mass is placed on the cart. The KE of the cart is now: (1) four times as great (2) one fourth as great (3) twice as great (4) the same 13. In raising an object vertically at a constant speed of 2.0 meters per second, 10 watts of power is developed. The weight of the object is (1) 5.0 N (3) 40. N (2) 20. N (4) 50. N 14. An object moving at a constant speed of 25 meters per second possesses 450 joules of kinetic energy. What is the object s mass? (1) 0.72 kg (3) 18 kg (2) 1.4 kg (4) 36 kg 21

22 Name: Regents Physics Work and Power Worksheet Date: Mr. Morgante Priscilla and Larry begin to climb the stairs at the end of the science wing in WHS to travel to physics class. The vertical rise of the stairs is 4.0 meters. Priscilla s mass is 45.0 kg, while Larry has a mass of 60.0 kg. Priscilla makes the climb in 2.0 seconds, while Larry takes 30.0 seconds to climb the same distance. 1. Calculate Larry s weight (metric) 2. Calculate the work done by Priscilla in climbing the stairs? 3. Calculate Priscilla s power rating. Larry normally takes 30.0 seconds to climb the stairs, on a particular day he is the recipient of verbal help from a teacher. With the help he manages to climb the stairs in 2.0 seconds. 4. Compare the work he did climbing the stairs on a normal day to this special day. 5. Compare his usual power rating to his power rating on that special day. Name: Regents Physics 22 Date: Mr. Morgante

23 Work, Power, KE, and PE Problems Work and Power A) What work is done by a girl who pushes a box along a floor with a force of 52.0 N for a distance of 11.0 m? B) A boy raises a 20.0 Kg rock 2.3 meters: -What is the force that the boy uses to raise the rock? -Calculate the amount of work that he does? C) A student is pulling on a wagon handle with a force of 40.0 N. The handle is at a 30- degree angle with the horizontal. The wagon moves 8 meters in 10 seconds. Find the work done by the student and the power exerted by the student. Kinetic Energy A) What is the kinetic energy of an object who s mass is 5.0 Kg and is moving a 4.0 m/s? If the object was accelerated from rest for a distance of 10.0 m, what was the force applied to it? (OVER) B) A force of 10 N is applied to a body on a practically frictionless table over a distance of 8.0 m, what is the Kinetic energy it imparts to the body? If the body starts at rest 23

24 and has a mass of 4.0 kg, what velocity does the force impart? C) When the brake is applied to a car having a mass of 1000 Kg, its speed is reduced from 30 m/s to 20 m/s. How much work does the brake do on the car? If the brake is applied for a distance of 25 m, what force does it exert on the car? Potential Energy A) A 5.0 Kg rock is located on a ledge 10 meters above the ground, calculate the potential energy of the rock relative to the ground. Name: Regents Physics Date: Mr. Morgante 24

25 Force (N) Work and Energy Graph Worksheet 1. Calculate the work done on the cart by the force shown in the diagram below. 30N 60 o 25 m 2. The force on an object varies as shown in the graph below. Force (N) vs. Distance (m) Distance (m) Series1 What is the work done on the object in the first 1.1 meters? 3. How many joules of energy are produced by a 60 watt light bulb in 2 minutes? (OVER) 25

26 4. The coefficient of friction between a 5.0 kg mass and a desktop is An unbalanced force of 50.0 N acts horizontally on the mass to move it along the desktop as shown below. 5.0 kg a. What is the weight of the mass? 50 N +X b. What is the size and direction of the frictional force acting on the mass? c. What is the value and direction of the unbalanced force acting on the mass? d. What is the acceleration experienced by the mass? e. The unbalanced force is reduced to zero by lowering the outside push to 9.81N after the mass has reached a speed of 6 m/s. At what power is work being done on the mass if this is true? 26

27 Name: Date: Regents Physics Mr. Morgante More Work, KE, PE in Springs & Pendulum Problems 1. A spring is stretched for a distance of 1m by 10N force. What is the potential energy stored in the spring (Think F=kx)? 2. A spring with a spring constant of 3 N/m is stretched a distance of 4m. What is the PE s? 3. A 30-kg box is pulled at constant velocity of 4 m/s across a rough surface. 15 N θ = 25º +x a) Calculate the horizontal component of the pulling force, F x. (Show mag. & dir.) b) Calculate the friction force, F f Sketch the vector on the diagram(show mag. & dir.) c) Calculate the work against friction in 90 seconds (Show mag. & dir.): d) Calculate the work done by friction in 90 seconds (Show mag. & dir.): (OVER) 27

28 4. Answer the following questions based on the diagram below: Pt. B h Pt. A mass of pendulum ball = 2 kg h = 2 m length of string = 4 m a) What is the PEmax? b) What is the maximum velocity of the ball when it reaches Pt. A after being released from Pt. B? c) What is the KEmax? 5. Find the potential energy stored in the spring below. The mass of the object is 40 dg and the distance the spring is elongated 2m. Show all of your work. Spring m h=2m m a) What is the max. velocity and KEmax of the mass? b) What is the max PEg of the mass? 28

29 NAME Regents Physics DATE Mr. Morgante Nonideal Mechanical Systems Objective: Investigators will analyze nonideal mechanical system and develop solutions based on evidence. Definition: Nonideal mechanical system: Sketch: vi = 0 m/s m = 40 kg L = 3 m Point A 40 O h = 0 1. A 40-kg box initially at rest slides down a 3 m long inclined plane that is elevated 40º to the horizontal. At point A, the bottom of the plane, the velocity of the block is found to be 4 m/s. a) Calculate the gravitational potential energy of the box at the top of the inc. plane b) What is the grav. potential energy of the box at the bottom of the plane? a) c) What is the kinetic energy of the box at the bottom of the plane? b) c) d) Has E T been conserved in this system? Yes No Explain: e) If E T = PE + KE + Q, What is the probable value of Q in this system? (over) e) 29

30 f) What condition probably caused the increase in Q? f) g) How much work was done by friction in this system? g) h) Calculate the average friction force acting on the box: Magnitude h) Direction i) Sketch the box on the plane and show friction force direction, Normal force exerted on the box by the plane, F g on box: Calculate F g Magnitude Direction j) Neglecting friction on the inclined plane, calculate the theoretical speed of the box at the bottom of the plane: j) k) What is the magnitude of the normal force acting on the box? k) l) Additional comments 30

31 NAME Regents Physics DATE Mr. Morgante Law of Conservation of Energy Practice 1. A 3.0-kg mass free-falls from rest a distance of 10m to the ground (h=0) Use g = 10 m/s 2 ; neglect air resistance; Complete the table below Time Dist. from ground (m) PE g KE Velocity 2. Using the strip of graph paper provided, Label x-axis 0 to 10m, y-axis Energy Using RED pencil plot PE g, BLUE pencil KE, GREEN pencil E T Attach graph here 3. Explain how this exercise helps illustrate the Law of Conservation of Energy 31

32 KE (J) Name: Regents Physics Date: Mr. Morgante Energy Stored in Head-On Collisions The graph below shows the kinetic energy of a moving cart vs. time as it collides with the spring bumper of a fixed cart. The mass of the moving cart is 1.0 kg. KE (J) vs. Time (s) Time (S) KE (J) 1. Determine the time at which the spring reaches its maximum compression. 2. The graph shows that the kinetic energy of the cart on rebounding from the spring bumper is less than before the collision. Explain a possible cause. 3. The cart compresses the spring and then rebounds. Why is the graph not drawn as the graph shown below? (OVER) 32

33 Force (N) KE (J) KE (J) vs. Time (s) Time (s) Series1 4. If the KE of the cart at t=1.0 seconds is 8 J calculate the speed of the cart. The graph below relates the force exerted on a spring to its compression. Force (N) vs. Compression (m) Compression (m) Series1 5. Use the graph to find potential energy stored in the spring when it is compressed by 0.04 m. 33

34 Force (N) Force (N) Force (N) Force (N) Name: Date: Regents Physics Graphs and Work Worksheet Mr. Morgante Find the work done in each of the cases pictured below. Show All Work!!!!!! Displacement (m), Left Series Displacement (m), North Series Displacement (m), West Series Series1 Spring Elongation (m) Z:\Physics\Regents Physics\Class Material\Unit 3 Work & Energy doc 34