DULLES HIGH SCHOOL Chapter 10-Work, Energy & Power Energy Transformations Judy Matney 1/12/2016 In this chapter, we will study the concepts of force and work; we will understand the transformations of various energy forms such as potential, kinetic, chemical, nuclear, and thermal into work, and the relationship of The Law of Conservation of Energy and the Energy Model. 0
I. FORMS OF ENERGY 1. Energy. Three types: 2. Other forms of energy: 3. Definitions of Energy: (K) is energy of motion. (U g ) is stored energy with an object s height above the ground. (U sp ) energy when a spring or other elastic body is stretched. (E T ) is the sum of the kinetic and potential energy of the molecules of a substance. (E C ) is the energy stored in the bonds of molecules. (E n ) is the energy stored in the mass of molecules. II. Work and Energy 1. Work: Work is done by a force on an object if the force causes the object to move in the direction of the force. The SI unit for Work is: Named in honor of. One Joule of work is done when 1.0 N of force is applied through a distance of 1 m. 2. Graphically- Work is area under a Force vs Displacement graph. 1
Example: In pushing a load, a woman exerts a force as given by the graph below. The total work done by the woman is: 3. Work Done by a Constant Force: Work is the Dot Product of the Force and Displacement: Work is a scalar that can be positive, negative, or zero depending on the angle between the force and the displacement. Work Done at an angle: Suppose a man pulls a suitcase with a 50 lb Force at an angle of 30 0 angle above the horizontal for 30 feet. How much work does he do? 2
Example: Calculate the amount of work down in lifting a 5 kg mass 2m? Example: Calculate the amount of work that friction does in sliding a box 2 m to the right. The box has a mass of 2 kg, and the coefficient of kinetic friction is 0.2 Example: Calculate the work done in moving the block 3.0 m to the right by the 40 N force exerted at an angle of 35 0 to the horizontal? 3
Example: A crate having a mass of 100 kg is pulled to the right 20 m with a constant velocity across the floor by a rope that makes an angle of 35 0 with the horizontal. Find (a) the tension in the rope and (b) the work done by F, F f, F N, and F mg. (c) the total work done on the box. 4. Work Done by a Variable Force: The force needed to stretch spring is : F = kx HOMEWORK: P. 5, PROBLEMS 1-9 4
PROBLEM SET 1: WORK 1. A person weighing 750 N climbs a flight of stairs that is 5.0 m high. What work does the person do? 2. What work is done when a person lifts a 2.5 kg package and places it on a shelf 2.2 m high? 3. How much work must be done to roll a metal safe, mass 116 kg, a distance of 15.0 m across a level floor? The coefficient of kinetic friction is 0.050. 4. A sled is pulled over level snow a distance of 0.500 km by a force of 124 N applied to a rope that makes an angle of 35 0 with the snow. How much work is done? 5. A force of 18 N is required to stretch a spring 0.25 m from its equilibrium position. (a) Compute the amount of work done on the spring. (b) How much force is required to stretch the spring 0.50 m (assuming that the elastic limit of the spring is not exceeded)?. (c) Compute the amount of work done when stretched the 0.50 m? 6. A loaded trunk has a mass of 35 kg. The coefficient of friction between the trunk and the floor is 0.20. How much work is done in moving the trunk with a constant velocity, 8.0 m across a level floor and then lifting it into a truck 1.3 m above the ground? 7. A 75 kg crate is to be pushed up an inclined plane at a constant velocity, 3.00 m long that makes an angle of 20 0 with the horizontal. If the coefficient of kinetic friction between the crate and the inclined plane is 0.150, how much work must be done? 8. An unbalanced force of 5.0 N acts on a mass of 2.0 kg that is initially at rest. How much work is done (a) during the first two seconds, and (b) during the tenth second? 9. A loaded sled is pulled by a rope that makes an angle of 45 0 with the horizontal. If the mass of the sled is 60.0 kg, and the coefficient of friction is 0.020, how much work is done in pulling the sled along a level road at a constant velocity for a distance of 1.00 km? 5
III. Work Done by Conservative and Non-Conservative Forces 1. Conservative force: The work it does is stored in the form of energy that can be released at a later time. Example: 2. The work done by a conservative force in moving an object around a closed path is. 3. Non-conservative force: Part of the work done by a non-conservative force is lost. Example: 4. Definition of Potential Energy: W = U U = ( U U ) = U c i f f i The SI Unit for Energy is: 5. Gravitational Potential Energy: W = U = U U = mgy c i f 6. Example: What is the potential energy gained when a 100 kg barrel is raised 4m? 7. Work done by a Conservative Force Spring 1 Wc = Ui U f = kx 2 Example: 2 A force of 12 N stretches a spring and makes it 0.15 m longer. What is the spring constant, k, and what is the elastic potential energy stored in the spring? IV. Kinetic Energy and the Work-Energy Theorem: 1. When positive work is done on an object, its speed increases. 2. When negative work is done on an object, its speed decreases.: 6
1. Definition of Kinetic Energy: The energy of. 1 2 1 2 Wt = mv f mvi 2 2 2. Work-Energy Theorem: All types of energy before the event = All types of energy after the event. The net work done on an object is equal to its change in kinetic energy. W = K 3. Dropped Object loses Potential Energy as it gains kinetic energy. E 4. Example: A brick with a weight of 0.5 lb is dropped from the top of a 10-story high building (100 ft). What is the kinetic energy of the brick as it hits the man below? HOMEWORK: P. 8, PROBLEMS 1-7. 7
PROBLEM SET 2: ENERGY PROBLEMS 1. A mass of 2.00 kg is lifted from the floor to a table 0.80 m high. Using the floor as a reference level, what potential energy does the mass have because of this change of position? 2. A large rock with a weight of 1470 N rests at the top of a cliff 40.0 m high. What potential energy does it have using the bottom of the cliff as a reference level? 3. What is the kinetic energy of a baseball having a mass of 0.14 kg when thrown with a speed of 18 m/s? 4. A meteorite weighing 1860 N strikes the Earth with a velocity of 45.2 m/s. What is its kinetic energy? 5. A spring scale is calibrated from zero to20 N. The calibrations extend over a length of 0.10 m. (a) What is the elastic potential energy of the spring in the scale when a weight of 5.0 N hangs from it? (b) What is the elastic potential energy when the spring is fully stretched. 6. The force constant of a spring is 150 N/m. (a) How much force is required to stretch the spring 0.25 m? (b) How much work is done on the spring in that case? 7. A stone having a mass of 50.0 kg is dropped from a height of 197 m. What is the potential energy and the kinetic energy of the stone (a) at t = 0 seconds; (b) at t = 1.00 second (c) at t = 5 seconds; (d) when it strikes the ground? HOMEWORK, P 9, PROBLEMS 1-8 8
PROBLEM SET 3: ENERGY PROBLEMS 1. A car weighing 2.00 x 10 5 N is accelerated on a level raod from 45.0 km/hr to 75.0 km/hr in 11 seconds. (a) What is the increase in kinetic energy? (b) What force produces the acceleration? 2. What is the kinetic energy, in Joules, of an electron that has a mass of 9.11 x 10-31 kg and that moves at a speed of 1.0 x 10 7 m/s? 3. A 2.5 kg Ping-Pong ball at rest is set in motion by the use of 1.8 J of energy. If all the energy goes into the motion of the ball, what is the ball s maximum speed? 4. With what speed would a 50 kg girl have to run to have the same kinetic energy as a 1000 kg automobile traveling at 2.0 km/hr? 5. How far does a 1.0 kg stone with a kinetic energy of 3.0 J go in 2.0 seconds if it is moving in a straight line? 6. How much potential energy with respect to the ground does a 10 kg lead weight have when it is 2.00 m above the surface of the ground? 7. A 900 N crate slides 12 m down a ramp that makes an angle of 35 0 with the horizontal. If the crate slides at a constant speed, how much thermal energy is created? 8. A 1000 kg wrecking ball hangs from a 15 m long cable. The ball is pulled back until the cable makes an angle of 25 0 with the vertical. By how much has the gravitational potential energy of the ball has changed? HOMEWORK P. 10, PROBLEMS 1-9 9
PROBLEM SET 4: CONSERVATION OF ENERGY 1. A 1.00 kg mass is placed at the free end of a compressed spring. The force constant of the spring is 115 N/m. The spring has been compressed 0.200 m from its neutral position. It is now released. Neglecting the mass of the spring and assuming that the mass is sliding on a frictionless surface, how fast will the mass move as it passes the neutral position of the spring? 2. With what speed does a hammer dropped from a height of 23 m strike the ground? Neglect air friction. 3. A block slides on a semicircular frictionless track as shown below. If it starts from rest at position A, what is its speed at the point marked B? 4. A 4.0 kg box of books is pulled up a 4.0 m long inclined plane to a height of 1.5 m. A force of 20 N parallel to the incline is needed to pull the box up the inclined plane. (a) How much energy is used and (b) What percent of that energy is lost to friction? 5. A 50 kg gymnast stretches a vertical spring by 0.50 m when she hangs from it. How much energy is stored in the spring? 6. From what height must a car be dropped to give it the same kinetic energy just before impact that it has when traveling at 60 km/hr? 7. A 40 kg child sits in a swing suspended with a 2.5 m long rope. The swing is held aside so that the rope makes an angle of 15 0 with the vertical. If let go, what speed will the child have at the bottom of the arc? 8. A 55 kg skateboarder wants to just make it to the upper edge of a half pipe with a radius of 3.0 m, as shown below, what speed v i does he need at the bottom if he is to coast all the way up? 9. The sledder shown below starts from the top of a frictionless hill and slides down into the valley. What initial speed v i does the sledder need to just make it over the next hill? 10
V. Power 1. is the time rate of doing work or the time rate transfer of energy. 2. The SI unit for Power is the named in honor of James Watt. W F d 3. P= = = F v t t 4. In the BES, the unit for power is the. 1 HP= 550 ft lbs s 5. Example: Find the power of engine capable of lifting 200 lb to a height of 55 ft in 10 seconds? HOMEWORK, P. 12, PROBLEMS 11
PROBLEMS SET 5: POWER PROBLEMS 1. What power is required to raise a mass of 47 kg to a height of 12 m in 15 seconds? 2. A loaded elevator has a mass of 2.50 x 10 3 kg. If it is raised in 10.0 seconds to a height of 50.0 m, how many kilowatts are required? 3. The mass of a large steel ball is 1500 kg. What power is used in raising it to a height of 33m if the work is performed in 30.0 seconds? 4. A pump can deliver 20.0 liters of gasoline per minute. What power, in kilowatts, is expended by the pump in raising gasoline a distance of 6.00 m? One liter of gasoline has a mass of 0.700 kg. (The kinetic energy acquired by the gasoline may be disregarded.) 5. A motor is rated to deliver 10.0 KW. At what speed in m/min, can this motor raise a mass of 2.75 x 10 4 kg? 6. What power will be required to move a locomotive weighing 1.00 x 10 6 N up a grade that rises 1.50 m for each 100 m of track, so that it will move at a speed of 40.0 km/hr if the frictional force opposing the motion is 2.00 x 10 3 N? 12
VI. Simple Machines 1. Simple Machines are devices that are used to manipulate the amount and/or direction of force when work is done. 2. A common misconception is that machines are used to do a task with less work than would be needed to do the task without the machine. In fact, one actually does work. 3. The major benefit of a machine is the work can be done with less applied force, but at the expense of the through which the force must be applied. 4. Efficiency of a Machine: Wout % Efficiency = x100% Win 5. Types of Simple Machines: HOMEWORK: P. 14, PROBLEMS 1-4 13
PROBLEM SET 6: SIMPLE MACHINES 1. A force of 545 N is exerted on the rope of a pulley system, and the rope is pulled in 10.0 m. This work causes an object weighing 2520 N to be raised 1.50 m. What is the efficiency of the machine? 2. Two people use a wheel-and-axle to raise a mass of 750 kg. The radius of the wheel is 0.50 m, and the radius of the axle is 0.040 m. If the efficiency of the machine is 62%, and each person exerts an equal force, how much force must each person apply? 3. The raised end of an inclined plane 4.0 m long is 0.90 m high. Neglecting friction, what force is required to push a steel box weighing 750 N up this plane? 4. A jackscrew has a lever arm 0.75 m long. The screw has 1.5 threads to the centimeter. If 320 N of force must be exerted in order to raise a load of 6.0 x 10 3 kg, calculate the efficiency of the machine? 14