Work Work has a variety of meanings (taking out the trash is hard work; the toaster doesn t work; Mom goes to work)

Transcription

1 Physics Work, Power, and Energy Notes (Chapter 8 in Textbook) Key Terms Work Power Energy Potential Kinetic Mechanical Energy Law of Conservation of Energy Work-Energy Theorem Joule Watt Work Work has a variety of meanings (taking out the trash is hard work; the toaster doesn t work; Mom goes to work) In physics, work has a specific meaning work is what is accomplished when a force acts on an object and the object moves through a distance Work = component of force parallel to the distance object moved multiplied by magnitude of distance I.e. push a cart with a horizontal force [W= Fcosθ(d)] F W = Fd F = magnitude of constant force d = distance object moves d Work is a scalar quantity has only magnitude and no direction Work is measured in N m or Joules Demo: a) Pick up stool vertically, supporting so force is also vertical did I do work on the stool? YES! b) Carry the stool across the room with constant velocity, still supporting vertically. Am I doing work on the stool? NO! because the force is perpendicular to the displacement c) Hold the stool still in front of you Am I doing work on the stool? No because there is no displacement (there is work being done on your muscles because they are undergoing many displacements and that s why they get tired, but there is no work done on the stool) What about waiters carrying the tray at the restaurant? No work done! 1

2 When looking at work need to specify whether the work is done BY the object or done ON the object Also specify if work is done due to one particular force or due to net force Sign convention: + work if force is in same direction as displacement (force is trying to speed object up) - work if force is in opposite direction as displacement, ex. Friction (force is trying to slow object down) A weightlifter lifts a 100 kg weight 0.25 meters over his head. How much work was done on the weight? Power Power: the rate at which work is done or the rate at which energy is transformed P = W/t = energy transformed/time Measured in J/s = Watts (W) The English unit is horsepower (1 hp = 746 W) Ex. Power rating of an engine how much chemical or electrical energy can be transformed into mechanical energy per unit of time Electrical devices (i.e. light bulb) rate at which light bulb changes electrical energy into light or rate at which heater changes electrical energy into thermal energy Work vs. Power: If climb stair while walking, you can climb for long time, but if run up stairs, run out of energy much faster you are limited by power Car engines do work to overcome the force of friction, to climb hills and to accelerate a car is limited by the rate at which it can do work why cars are rated in hp (increased hp means more power to climb hills and accelerate) Oftentimes, convenient to look at power in terms of force and velocity P = W/t = Fd/t = Fv A Ford Mustang can apply Newtons over 20 meters in 2 seconds. What is its power rating? How much horsepower is that? Energy Energy is a very important concept in science The 6 main types of energy: Mechanical energy energy of moving objects Radiant energy travels in waves light, sound Chemical energy stored in food and fuels Heat energy thermal Electrical energy movement of electrons Nuclear energy from nucleus of atom fission and fusion 2

3 Energy = the ability to do work Law of Conservation of Energy total energy before a process equals total energy after the process [ E o = E f ] We are going to focus on mechanical energy in the forms of kinetic energy and potential energy [ME = ME`] A moving object can do work on another object that it strikes a cannonball does work on a brick wall it knocks down, a hammer does work on a nail it drives into wood In both cases, a moving object exerts a force on a 2 nd object which moves a distance An object in motion has the ability to do work and therefore has energy kinetic energy the energy of motion KE = ½ mv 2 Measured in Joules Scalar quantity Depends on mass and velocity Relationships KE directly related to mass if m x2 KE x2 KE directly related to square of velocity if v x2 KE x4 A 100 kg football player is running down the field. If he has 1000 J of kinetic energy, how fast is he running? Potential Energy energy associated with object s position relative to its surroundings We will look at two types 1. gravitational potential energy (GPE) 2. elastic potential energy (EPE) Most common PE is gravitational PE has PE because of object s position relative to the Earth Ex. Heavy brick held high in the air or balanced boulder on top of a cliff A raised sledge hammer has the ability to do work if it is released, it will fall to the ground due to the gravitational force and can do work on a stake, driving it into the ground GPE = mgh mg = object s weight (N) h = height above some reference level The higher an object is above the reference level, the more PE it has The work done by external forces (W ext ) is equal to change in PE W ext = ΔPE 3

4 Changes in PE only depend on change in vertical height and not on path taken, so if lift something up 4 m or push up an incline a vertical distance of 4 m, PE is still the same due to change in vertical height A 1000 kg concrete crusher has J of potential energy. How high is it above the ground? Elastic potential energy potential energy a spring has when compressed (or stretched) When it is released, it can do work on a second object A spring has a natural (unstretched) length, if you want to change the spring s length, it requires a force, F p = kx k = spring constant a measure of the stiffness of the particular spring, remains the same for a particular spring, but is not the same for ALL springs x = distance the spring is stretched or compressed The stretched/compressed spring exerts an equal and opposite force, F s = -kx known as Hooke s law or spring equation F s is the restoring force the spring exerts trying to return the spring to its original position (natural length) As you stretch a spring, F p is not constant, it varies over the distance it is stretched the further you stretch, the more force it requires EPE = ½ kx 2 k = spring constant (N/m) x = distance spring is stretched or compressed from its natural length A 5 kg mass is hanging on a spring scale. The spring is stretched 0.02 meters. How much energy does the spring have.. In all cases looked at PE is stored energy that can be used later Mechanical Energy = KE + PE Total Mechanical energy (E) is a conserved quantity. It remains constant as long as there are no external forces acting on the system (i.e. friction, air resistance) (KE + PE) 1 = (KE + PE) 2 All PE KE and PE are inversely related Ex.: a. Pendulum: Increase KE Decrease PE b. Rock falling due to gravity from a height, h All PE, if rock is dropped from rest All KE As falls, PE decreases (h decreases) and KE increases (gain in velocity) All KE, just before hits ground 4

5 At any point along the path, E = KE + PE = ½ mv 2 + mgh Mechanical energy is conserved if ignore air resistance, so can pick any 2 points along the path and E 1 = E 2 c. Rollercoaster: All PE at hills, all KE in valleys, changing KE/PE going up and down hills [draw example of rollercoaster make sure hills and valleys are same heights] d. Toy dart gun elastic PE and KE We mentioned other forms of energy before with atomic theory, these other forms of energy can be considered KE or PE at the atomic or molecular level i.e. thermal energy = KE (particles moving faster when heated) chemical energy = PE (stored in food and fuels) Energy can be transformed from one form to another i.e. rock falling: PE KE water at top of dam, falls to bottom of dam, caused turbine to move, forms electricity: PE KE electrical energy Work-energy Theorem: W net = ΔKE = KE 2 KE 1 = ½ mv f 2 ½ mv o 2 or W=1/2m(V f -V i ) 2 The net work done on an object is equal to the change in the object s kinetic energy This principle is only valid if work is the net work (total work) done on the object If + W net done on an object object s KE increased (velocity increased) If W net done on an object object s KE decreased (velocity decreased) A net force exerted on an object opposite to the object s direction of motion decreases its speed and its KE Ex. Moving hammer striking a nail When hammering a nail, hammer does work on the nail (applies a force to the nail that causes the nail to move a certain distance) The hammer has a change in its KE (it decreases moving to come to a stop on impact) and that change in KE equals the work done on the nail [workenergy principle] transfer of energy is accompanied by the performance of work (work is done when energy is transferred from one object to another) If a 900 kg car does 20,000 J of net work to speed up from rest, what is its final velocity? 5

6 Work and Power and Energy Problems Complete in GUESS format on a separate piece of paper. 1. A 196 N suitcase is raised 3.0 m above a platform by a crane at constant velocity. How much work is done on the suitcase? [588 J] 2. A tugboat pulls a ship with a constant net horizontal force of 5000 N and causes the ship to move through the harbor. How much work is done on the ship if it moves a distance of 3000 m? [1.50 x 10 7 J] 3. A weight lifter lifts a set of weights a vertical distance of 2.00 m. If a constant net force of 350 N is exerted on the weights, what is the net work done on the weights? [700 J] 4. A loaded sled requires a force of 250 N applied horizontally to push it across wet snow. How far can it be pushed with 800,000 J of work? [3200 m] 5. A worker pushes a 1500 N crate with a horizontal force of 345 N a distance of 24.0 m. If the force of friction is 330 N, find: a. How much work is done by the worker on the crate? [8280 J] b. How much work is done by the floor on the crate? [-7920 J] c. What is the net force on the crate? [15 N] d. What is the net work done on the crate? [360 J] e. If the mass of the crate is kg, what is the crate s acceleration? [0.098 m/s 2 ] 6. A delivery clerk carries a 34 N package from the ground to the fifth floor of an office building, a total height of 15 m. How much work is done by the clerk? [510 J] 7. What work is done by a forklift raising a 583 kg box 1.2 m.? [ J] 8. You and a friend each carry identical boxes to a room one floor above you and down the hall. You choose to carry it first up the stairs, then down the hall. Your friend carries it down the hall, then up another stairwell. Who does more work? Why? [same amount] 9. A rock climber wears a 7.5 kg knapsack while scaling a cliff. After 30 minutes, the climber is 8.2 m above the starting point. a. How much work does the climber do on the knapsack? [602.7 J] b. If the climber weighs 645 N, how much work does she do lifting herself and the knapsack? [ J] c. What is the average power developed by the climber? [3.27 W] 10. An electric motor develops 65 kw of power as it lifts a loaded elevator 17.5 m is 35.0 seconds. How much force does the motor exert? [130,000 N] 11. A 60 kg jogger runs up a long flight of stairs in 4.0 s. The vertical height of the stairs is 4.5 m. What is the jogger s power output? [661.5 W] 12. A student with a mass of 80 kg runs up three flights of stairs in 12 seconds. The student has gone a vertical distance of 8 meters. a. Determine the amount of work done by the student to elevate his body to this height. [6272J] b. Determine the power exerted by the student. [ W] 13. Ben and Will are in the weight room. If Ben lifts the 75 N barbell over his head 11 times in 45 seconds and Will lifts the same barbell over his head 11 times in 35 seconds. a. Who has more work? Why? b. Who demonstrates more power? Why? 6

7 14. How long does it take a 19 kw steam engine to do 6.8 x 10 7 J of work? [ s] 15. What work is done if a boy pushes a box that has a mass of 30 kg with a force of 50 N over a distance of 6 meters in 4 seconds? [300 J] 16. A girl pushes a 6 kg box for a distance of 3 meters with a force of 4 N in 2 seconds. What is the power of the girl? [6 W] Energy 17. A comet with a mass of 7.85 x kg strikes Earth at a speed of 25,000 m/s. What is the kinetic energy of the comet? [2.45 x J] 18. A rifle can shoot a kg bullet at a speed of 965 m/s. a. What is the kinetic energy of the bullet? [ J] b. How much work is done on the bullet if it starts from rest? [ J] c. If the work is done over a distance of 0.75 m, what is the average force on the bullet? [ N] 19. A 6.0 kg cat runs after a mouse at 10 m/s. What is the cat s kinetic energy? [300 J] 20. A 7.00 kg bowling ball moves at 3.00 m/s. How much kinetic energy does the bowling ball have? [31.5 J] b. How fast must a 2.45 g table-tennis ball move in order to have the same kinetic energy as the bowling ball? [ m/s] 21. Calculate the speed of an 8.0 x 10 4 kg airliner with a kinetic energy of 1.1 x 10 9 J. [ m/s] 22. Two bullets have masses of 3.0 g and 6.0 g, respectively. Both are fired with a speed of 40.0 m/s. Which bullet has more kinetic energy? 23. A car has a kinetic energy of 4.32 x 10 5 J when traveling at a speed of 23 m/s. What is its mass? [ kg] 24. If the velocity of a car is doubled, how is its kinetic energy affected? Why? 25. Larry, who weighs in at 630 N, climbs up a ladder to a height of 5.0 m. a. Does Larry do work? b. How much work does Larry do? c. What is Larry s gravitational potential energy before he starts climbing? d. What is Larry s gravitational potential energy at the top of the ladder? 26. A 90 kg rock climber climbs 45 m upward to the top edge of Enchanted Rock. a. What is his gravitational potential energy at the top of his climb? [39690 J] b. He climbs back down to the ground, 85 m below the top of Enchanted Rock. Using his initial height as the reference point, calculate his gravitational potential energy at the bottom of his climb. (Hint: Draw a sketch - it is ok to have a negative PE g ) [ J] 27. A spoon is raised 21.0 cm above a table. If the spoon and its contents have a mass of 30.0 g, what is the gravitational potential energy associated with the spoon at that height relative to the surface of the table? [ J] 7

8 28. Calculate the increase in gravitational potential energy of a 75 kg hiker who climbs a 1500 m peak. [1.103 x 10 6 J] 29. If 2.0 J of work is done in raising a 180 g apple, how far is it lifted? [1.134 m] 30. If a force of 15 N is used to drag the loaded cart along the incline for a distance of 1.2 m. a. How much work is done on the loaded cart?[18 J) b. What is the cart s mass, if it reached a height of 0.9 meters?(considering no work done by friction)[2.04 kg] c. If more work is done on a cart then the potential energy it has due to its height, what happened to the energy? 31. A spring with a force constant of 5.2 N/m has a relaxed length of 2.45 m. When a mass is attached to the end of the spring and allowed to come to rest, the vertical length of the spring is 3.57 m. Calculate the elastic potential energy stored in the spring. [3.261 J] 32. The staples inside a stapler are kept in place by a spring with a relaxed length of m. If the spring constant is 51.0 N/m, how much elastic potential energy is stored in the spring when its length is m? [0.031 J] 33. A bike rider approaches a hill with a speed of 8.5 m/s. The total mass of the bike and rider is 85 kg. a. What is the kinetic energy of the bike and rider at the base of the hill? [ J] b. The rider coasts to the top of the hill. What is his kinetic energy at the top of the hill? Explain your answer. [0 J] c. How much work does the rider do? [ J] d. Assuming there is no friction, at what height will the bike come to a stop? [3.67 m] 34. Starting from rest, a child zooms down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide? Assume she has a mass of 25 kg. [7.668 m/s] 35. A pendulum bob is released from some initial height such that the speed of the bob at the bottom of the swing is 1.9 m/s. What is the initial height of the bob? [0.184 m] 36. What is the potential energy of a pendulum that hangs 4 meters above the ground and has a mass of 2 kg? b. If the pendulum starts to move. At the bottom of the swing it is going 5 m/s. What is its kinetic energy at that point? c. At the bottom of the swing of the pendulum, the pendulum hits a brick. The brick moves 3 meters. With what force did the pendulum hit the brick? 37. Draw a diagram of a pendulum, label the points where there is the maximum potential energy, the maximum kinetic energy, zero potential energy, zero kinetic energy and where there are both kinetic and potential energy present. How is work related? 8

9 Physics Work, Power & Energy Review Key Terms Work Power Energy Potential Kinetic Mechanical Energy Law of Conservation of Energy Work-Energy Theorem Joule Watt 1) For work to be done an object must have moved a distance due to a force exerted on it. a. True b. False 2) Work is a quantity in which direction does not matter. 3) The units for work are 4) If positive work is done on an object, the force must be applied in the direction as the distance the object moves. 5) If work is done on an object, the force was applied in the opposite direction as the distance the object moved. 6) A common force that causes negative work to be done on an object is. 7) What is power? 8) The units for power are 9) You are limited by your power output not by the amount of work you can do. a. True b. False 10) If a neighbor pushes a lawnmower four times as far as you do but exerts only half the force, which one of you does more work and by how much? [neighbor, twice] 11) What is energy? 12) Energy is a conserved quantity. a. True b. False 13) Mechanical energy is the sum of what 2 types of energy? 14) The unit for energy is. 15) A moving object can do work on a second object. Explain why this statement is true. 16) What does the work-energy principle tell us? 17) If positive net work is done on an object, the object s kinetic energy. a. increased b. decreased c. stayed the same d. is zero 18) If negative net work is done on an object, the object s kinetic energy a. increased b. decreased c. stayed the same d. is zero 19) The work done on an object is equal to its change in gravitational potential energy. a. True b. False 20) The further an object gets from the earth s surface as it is thrown upwards, the gravitational potential energy it has. a. more b. less c. same amount 21) Kinetic energy is only found in objects that are a. still b. at rest c. moving d. high above the ground 9

10 22) If a car starts moving 4 times faster, what is the new kinetic energy of the car? a. 4 times faster b. 16 times faster c. 4 times slower d. 16 times slower 23) How can a rollercoaster demonstrate conservation of energy? 24) Can the speed of an object change if the net work done on it is zero? Why? [No] 25) Draw a sketch of a pendulum and describe the changes in the energy as it moves back and forth. 26) A person lifts a 4.5 kg cement block a vertical distance of 1.2 m. Determine the work done on the block by the person. [53 J] 27) What amount of work can a 600-W electric motor do in 240 seconds? [ J] 28) A 40-kg boy runs up the staircase to a floor 5.0 m higher in 7.0 seconds. What is his power output? [280 W] 29) What is the kinetic energy of a 50 kg boy who is sprinting at 7.5 m/s? [ J] 30) What is the gravitational potential energy of a pendulum that hangs 1.0 m above the ground and has a mass of 1.5 kg? [14.7 J] 31) Assuming the law of conservation of mechanical energy holds true, calculate the velocity of a roller coaster at the following points. The roller coaster has a starting hill 50 m tall and the second hill is 25 m tall. If a car starts from rest, what is its velocity at a. the bottom of the first hill? [31.3 m/s] b. at the top of the second hill? [22.14 m/s] 32) Starting from rest, a 20 kg child zooms down a frictionless slide from an initial height. If her speed at the bottom of the slide is 3.8 m/s, how high above the ground did she start? [0.74 m] 33) If it takes 10 J of work to raise a book 2 m, what is the mass of the book?[0.51kg] 34) If it takes 15,000 J of work for a 100 kg student to walk up the stairs. How high are the stairs? [15.31m] 35) 30,000 J of positive net work are used to accelerate a 1000 Kg car from rest. What is its final velocity?[7.75 m/s] 36) A 200 kg pyramid stone is pushed up an incline by Egyptian slaves with a 1000 N net force for 10 meters. a. How much work was done?[10,000 J] b. If the stone moved 2 vertical meters, what is the change in potential energy?[3920 J] c. Why is there a difference? d. What is the efficiency of the incline?[39.2%] 10