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Work, Power, & Energy

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Work, Power, & Energy In physics, work is done when a force acting on an object causes it to move a distance. There are several good examples of work which can be observed everyday - a person pushing a grocery cart down the aisle of a grocery store, a student lifting a backpack full of books, a baseball player throwing a ball. In each case a force is exerted on an object that caused it to move a distance. Work (Joules) = force (N) x distance (m) W = f d The metric unit of work is one Newton-meter ( 1 N-m ). This combination of units is given the name JOULE in honor of James Prescott Joule (1818-1889), who performed the first direct measurement of the mechanical equivalent of heat energy. The unit of heat energy, CALORIE, is equivalent to 4.18 joules, or 1 calorie = 4.18 joules. Work has nothing to do with the amount of time that this force acts to cause movement. Sometimes, the work is done very quickly and other times the work is done rather slowly. The quantity which has to do with the rate at which a certain amount of work is done is known as the power. The metric unit of power is the WATT. As is implied by the equation for power, a unit of power is equivalent to a unit of work divided by a unit of time. Thus, a watt is equivalent to a joule/second. For historical reasons, the horsepower is occasionally used to describe the power delivered by a machine. One horsepower is equivalent to approximately 750 watts. Power (watts) = work (joules) / time (seconds) P = w / t Objects can store energy as the result of its position. For example, the heavy ram of a pile driver is storing energy when it is held at an elevated position. Gravitational potential energy is the energy stored in an object as the result of its height above the ground. The energy is stored as the result of the gravitational attraction of the Earth for the object. The gravitational potential energy of the heavy ram of a pile driver is dependent on two variables - the mass of the ram and the height to which it is raised. GPE (joules) = mass (kg) x gravitational acceleration (9.8 m/s/s) x height (m) GPE = m g h A second form of potential energy is elastic potential energy. Elastic potential energy is the energy stored in elastic materials as the result of their stretching or compressing. Elastic potential energy can be stored in rubber bands, bungee chords, trampolines, springs, or the stretched strings of a tennis racket and the compressed tennis ball. The amount of elastic potential energy stored in such a device is related to the amount of stretch or compression of the device - the more stretch or compression, the more stored energy. Kinetic energy is the energy of motion. An object which has motion - whether vertical or horizontal motion - has kinetic energy. There are many forms of kinetic energy. The amount of kinetic energy which an object has depends upon two variables: the mass (m) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object. KE (joules) = ½ mass (kg) x velocity (m/s)2 KE = ½ m v2 Work, Power & Energy 1 PART I: LEG POWER A person, like all machines, has a power rating. Some people are more powerful than others; that is, they are capable of doing the same amount of work in less time or more work in the same amount of time. Whenever you walk or run up stairs, you do work against the force of gravity. The work you do is simply your weight times the vertical distance you travel, i.e., the vertical height of the stairs. WORK = (YOUR WEIGHT IN NEWTONS) X (HEIGHT OF STAIRS IN METERS) PROCEDURE While your partner times you, run up a flight of stairs as fast as you can. Measure the vertical height of the stairs, and using your weight (no cheating!) calculate the work done and power developed. Then, walk up the flight of stairs. Record the information in the tables provided and calculate the work and power necessary to walk and run up the stairs. Your Weight Height of Stairs Time Activity (Newtons) (meters) (seconds) Running 60.0 kg = 588 N 2.30 m 2.25 Walking 60.0 kg = 588 N 2.30 m 4.50 WORK POWER Activity Joules calories Watts Horsepower Running 1350 323 600. 0.828 Walking 1350 323 300. 0.414 How does the work compare walking up the stairs vs. running up the stairs? 1. The work running or walking up the stairs is equal. Since the mass of the student and the height of the stairs is constant then the work is constant. ____ How does the power compare walking up the stairs vs. running up the stairs? 2. Power is inversely proportional to time. Given that work is constant, performing the same amount of work in less time produces a greater power output. PART II: POTENTIAL & KINETIC ENERGY IN A PENDULUM A pendulum is a simple mechanical device consisting of an object (a mass called a bob) that is suspended by a string from a fixed point and that swings back-and-forth under the influence of gravity. In 1581, Galileo, while studying at the University of Pisa in Italy, began his study of the pendulum. According to legend, he watched a suspended lamp swing back and forth in the cathedral of Pisa. Timing the swing with the beat of his pulse, Galileo noted that the time that the pendulum swings back-and-forth does not depend on the arc of the swing. Eventually, this discovery would lead to Galileo's further study of time intervals and the development of his idea for a pendulum clock. Work, Power & Energy 2 If a pendulum is pulled to some angle from the vertical but not released, potential energy exists in the system. When the pendulum is released, the potential energy is converted into kinetic energy as the pendulum bob descends under the i nfluence of gravity. The faster the pendulum bob moves, the greater its kinetic energy. The higher the pendulum bob, the Maximum greater its potential energy. This change from potential to Maximum GPE kinetic energy is consistent with the principle of conservation GPE of mechanical energy which states that the total energy of a system, kinetic plus potential, remains constant while the system is in motion. Maximum KE When you pull the pendulum to the side, you increase the gravitational potential energy of the pendulum by an amount equal to the change in height times the mass times the acceleration of gravity. So we can write GPE=m g h, where GPE is the change in potential energy, m is the mass in kilograms, h is the vertical distance that the pendulum has been raised, and g is 9.80 m/s² as before. Kinetic energy of motion is given by the formula K E= ½ m v², where m is mass in kilograms, and v is the velocity of the pendulum in m/s. If the energy is conserved, all of the potential energy at the top of the swing should be converted to kinetic energy at the bottom of the swing where the velocity is greatest. Let's test this. PROCEDURE In this portion of the experiment, you will test whether energy is conserved in a pendulum by using a photogate timer that measures the time it takes the falling bob to pass through a narrow beam of light. From this the speed of the falling bob can then be calculated. Comparing the kinetic energy at the bottom of the swing with the amount of potential energy at the release point will test the conservation of energy of the pendulum. Make the following measurements for your pendulum and record the data in the table below: Mass of bob: 58.10 g 0.05810 kg Diameter of bob: 2.00 cm 0.0200 m Height of bob at rest above table: 9.00 cm 0.0900 m You will collect the time it takes for the bob to pass through the photogate for 3 trials at two different release heights. Pull back the pendulum and measure the height of the bob above the table using a ruler. Try to keep the height of the bob the same for each of the three trials. Reset the timer between trials. Release Height Time: Trial 1 Time: Trial 2 Time: Trial 3 Average 30.0 cm 0.0100 sec 15.0 cm 0.01850 sec How much higher (vertically) is the pendulum at each release height than it was when it was hanging at rest? Convert this distance to meters and calculate the gravitational potential energy, GPE, of the bob. 30.0 cm Release Height 15.0 cm Release Height 30.00 cm – 9.00 = 21.00 cm (0.02100 m) 15.00 cm – 9.00 = 6.00 cm (0.0600 m) (0.05810 kg) x (9.80 m/s2) x (0.2100 m) (0.05810 kg) x (9.80 m/s2) x (0.0600 m) 0.1196 joules 0.03311 joules Work, Power & Energy 3 Calculate the velocity of bob at the bottom of the swing: diameter of bob (m) = speed of bob (m / s ) average time (sec) 30.0 cm Release Height 15.0 cm Release Height 0.0200 m / 0.0100 sec = 2.00 m/s 0.0200 m / 0.01850 sec = 1.08 m/s Calculate the kinetic energy of the bob at the bottom of the swing 30.0 cm Release Height 15.0 cm Release Height 2 ½ (0.05810 kg) (2.00 m/s)2 ½ (0.05810 kg) (1.08 m/s) 0.1162 joules 0.03388 joules Compare the values for the gravitational potential energy and kinetic energy of the pendulum.
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