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) or 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) or 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 string of a bow. 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 or KE = ½ m v 2 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. Activity Your Weight (Newtons) Height of Stairs (meters) Time (seconds) Running 588 2.75 3.25 Walking 588 2.75 6.60 WORK POWER Activity joules calories watts horsepower Running 1620 388 498 0.656 Walking 1620 388 245 0.323 How does the work compare walking up the stairs vs. running up the stairs? Same amount of work for either running or walking. How does the power compare walking up the stairs vs. running up the stairs? Power is greater for running: Work is done in a shorter amount of time. (Power and time are inversely proportional when work is constant) What changes would you make in the experiment in order to increase the amount of work? Climb two flights of stairs (increase height) or carry a box (increase mass). What changes would you make in the experiment in order to increase the amount of power? Run faster (decrease time) or increase the work but in the same amount of time. 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-andforth 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 influence of gravity. The faster the pendulum bob moves, the greater its kinetic energy. The higher the pendulum bob, the greater its potential energy. This change from potential to kinetic energy is consistent with the principle of conservation of mechanical energy which states that the total energy of a system, kinetic plus potential, remains constant while the system is in motion. Maximum GPE Maximum KE Maximum GPE 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: 1.90 cm 0.0190 m Height of bob at rest above table: 7.00 cm 0.0700 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 0.00890 s 15.0 cm 0.01580 s Work, Power & Energy 3
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 Gravitational Potential Energy at Release Point 15.0 cm Release Height (0.05810 kg) x (9.80 m/s 2 ) x (0.230 m) 0.131 J (0.05810 kg) x (9.80 m/s 2 ) x (0.080 m) 0.0455 J Calculate the velocity of bob at the bottom of the swing: diameter of bob (m) average time (sec) 30.0 cm Release Height 0.0190 m 0.00890 s = 2.13 m/s = velocity of bob (m/s) Velocity at the Bottom 15.0 cm Release Height 0.0190 m 0.0158 s = 2.13 m/s Calculate the kinetic energy of the bob at the bottom of the swing. 30.0 cm Release Height ½ x (0.05810 kg) x (2.13 m/s) 2 0.132 J Kinetic Energy at Bottom 15.0 cm Release Height ½ x (0.05810 kg) x (1.20 m/s) 2 0.0418 J Compare the values for the gravitational potential energy and kinetic energy of the pendulum. Was energy conserved? That is, were they equal? If not, how might you account for the difference in energies? At 30.0 cm the speed of the pendulum is greater and so is the velocity. The GPE and KE at 30.0 cm is greater than at the lower height. The GPE at the top is similar to the KE at the bottom which means very little energy is lost during the swing. Work, Power & Energy 4
PART III: ENERGY TRANSFORMATION POTPOURRI Located in the laboratory are several objects that transforms one form of energy to another. Complete the table to identify the object that represents the energy transformation in the chart. Electrical Energy 3 Chemical Energy 1 7 6 4 2 8 5 Mechanical Energy Radiant Energy 1 ELECTRIC MOTOR 5 PLANT Part IV: The Inclined Plane 2 ELECTRIC GENERATOR 6 MY DOG (ANIMALS) 3 BATTERY 7 LIGHT BULB 4 CANDLE 8 SOLAR CELL 1, Complete the data table below using the appropriate number of digits for the measurement. Length of the Inclined Plane Height of the Inclined Plane Mass of Car 120.00 cm 20.00 cm 47.00 g 1.2000 m 0.2000 m 0.4700 kg 2. Use the stopwatch to determine the time for the car to roll down the length of the track. Trial 1 Trial 2 Trial 3 Average Time 2.35 s Work, Power & Energy 5
For calculations below express your answer with the appropriate number of significant figures. 3. Determine the gravitational potential energy of the car at the top of the ramp. GPE = (0.04700 kg) x (9.80 m/s 2 ) x (0.2000 m) = 0.09212 Joules 4. Determine the speed of the car at the end of the ramp. Final Speed = [ (1.2000 m) (2.35 s) ] x 2 = 1.02 m/s 5. Determine the kinetic energy of the car at the bottom of the ramp. KE = ½ x (0.04700 kg) x (1.02 m/s) 2 = 0.0244 Joules 6. Determine the acceleration of the car along the ramp. a = 1.02 m/s 2.35 s = 0.434 m/s 2 7. Determine the accelerating force for the car. F = (0.04700 kg) x (0.434 m/s 2 ) = 0.0204 Newtons 8. Compare the GPE at the top of the ramp with the KE at the bottom. Which is greater? How do you account for any differences in the two values? The GPE at the top is greater than the KE at the bottom. When the car is moving along the ramp, some of the GPE is converted to heat energy through the friction of the wheels the track. on 9. If a more massive car were used, what changes, if any, would there be in the following (increase, decrease, stays the same)? Gravitational Potential Energy at the top of the ramp - Increased Final speed of the car at the bottom of the ramp No change Kinetic energy at the bottom of the ramp - Increased The acceleration of the car No change The accelerating force for the car No change Work, Power & Energy 6
10. If the height of the track was increased to 40.00 cm, what changes, if any, would there be in the following (increase, decrease, stays the same)? Gravitational Potential Energy at the top of the ramp - Increased Final speed of the car at the bottom of the ramp - Increased Kinetic energy at the bottom of the ramp - Increased The acceleration of the car - Increased The accelerating force for the car - Increased POSTLAB CALCULATIONS 1. The calories that we watch in our diet are actually kilocalories, or 1000 calories (usually designated as 1 C "big calories"). If a "Snickers" bar has 250 Calories (big calories), how many flights of stairs would you need to climb to burn off the energy from the candy bar? Show your work. 250 Calories = 250,000 calories = 1,045,000 Joules / 1620 Joules = 645 flights! 2. Consider the following: You are holding a small (about 100 g) rubber ball held at arm s length in front of you and you drop it (you decide on the height). It hits the floor and bounces to the height of your waist (you decide on the height) and you catch it. What is the potential energy of the ball before you drop it? GPE = (0.100 kg) (9.80 m/s 2 ) (1.50 m) = 1.47 Joules What is the kinetic energy of the ball at the instant it hits the floor? KE = 1.47 Joules (no energy is lost while the ball is falling) What is the potential energy of the ball where you catch it? GPE = (0.100 kg) (9.80 m/s 2 ) (1.00 m) = 0.980 J How much energy is unaccounted for from the point of dropping it and the point of catching it after it bounces? 0.49 Joules has been converted to heat energy when the ball impacted the floor. An instant after the ball hits the floor and before the ball begins to bounce, the ball has stopped moving. Therefore the potential energy is zero (its height above the floor is zero) and its kinetic energy is zero (its velocity is zero). If the Law of Conservation of Energy is true, how is the energy stored in the ball? (Hint: Read page one of this lab manual!) Energy is stored in the ball as elastic potential energy. (much like the energy stored in a rubber band when stretched.) Work, Power & Energy 7