Work and Energy Lab - University of Michigan
Work and EnergyA. Tomasch 01/10Pre-Lab QuestionIf moving objects have energy due to their motion (called Kinetic Energy (KE)), what is the source of kinetic energy for a ball that starts at rest and rolls down a hill?EXPLORATIONExploration MaterialsDedicated Components1 Pitsco PC Sportster car1 ? inch x 2” steel hex bolt with nut 1 10’ steel wall stud ramp8 ? inch cut steel washers1 Homer bucket ramp support1 Guide Wire Assembly1 spring scale– Ohaus 2000g/20N 1 clear plastic ruler1 meter stick1 digital scale1 stop watch1 calculator1 2” long thin rubber bandMechanical WorkPitsco Car Number______________For the following series of experiments, load your car with the bolt and eight washers, seven washers on the top and one on the bottom of the car.Definition: If a force acts on an object parallel to its direction of motion, the product of the force and the distance the object moves is called mechanical work. Work is a scalar quantity which can be positive, negative or zero. Mechanical work is positive if the force acts in the direction of motion and negative if it acts in opposition to the direction of motion. A force perpendicular to the direction of motion does zero mechanical work. A zero net force also does zero work. Definition: Energy is defined as the ability to do mechanical work.Using your spring scale, determine the force due to gravity on the car acting down the incline of your ramp. Use a long rubber band to attach the scale to the small metal loop at the rear of the car. Drag the car slowly up the ramp at a constant speed and read the scale. Your scale reads in grams and we want to state forces in Newtons, so you must convert grams to kilograms and multiply by the acceleration of gravity (g = 9.8 m/s2) get the force in Newtons. Show your calculation.Force of Gravity Acting Down the Ramp (N)Assuming that the length of the ramp is 2.74 meters, use your answer to question 1 to estimate the amount of work done by gravity on the car as it rolls down the ramp. A force of one Newton pushing on an object parallel to its direction of motion for one meter does one Joule of work. Show your calculation.Work Done by Gravity for a Car Rolling Down a Ramp (Joules)How does the work done by gravity on a car released half way up the ramp compare to the work done by gravity on a car released at the top of the ramp? Estimate the amount of work in Joules for a car released half way up the ramp. Show your calculation.Work Done by Gravity for a Car Rolling Half Way Down a Ramp (Joules)If we release a car from rest at the top of a ramp we can measure the final speed of the car at the bottom of the ramp by measuring the average speed of the car. The average speed (m/s) is length of the ramp (m) divided by the time it takes the car to roll to the bottom (s): Average Speed = (Ramp Length)/(Time to Roll Down Ramp).Since the car starts at rest (zero initial speed):Average Speed = ? (Initial Speed + Final Speed)Average Speed = ? (0 + Final Speed) = ?(Final Speed).So the final speed of the car at the bottom of the ramp is simply twice the average speed:Final Speed = 2(Average Speed)Release your car from rest approximately half way up the ramp and measure the time to reach the end of the ramp with the stop watch. Compute the average speed of the car as half the ramp length divided by the measured time. Estimate the final speed of the car at the bottom of the ramp from the measured average speed. Show your calculation for one trial.Distance = ?(2.74 m)Time(s)Average Speed (m/s)Final Speed (m/s)Trial #1Trial #2Trial #3Average Final SpeedRepeat the experiment, but this time release the car from the top of the ramp and again compute the average speed as the total length of the ramp divided by the time. Again estimate the final speed of the car at the bottom of the ramp. Show your calculation for one trial.Distance = (2.74 m)Time(s)Average Speed (m/s)Final Speed (m/s)Trial #1Trial #2Trial #3Average Final SpeedQualitatively, how is the average speed down the ramp related to the distance the car rolls down the ramp?Qualitatively, how is the average speed down the ramp related to the amount of work done by gravity as the car rolls down the ramp?Kinetic Energy and Gravitational Potential EnergyDefinition: Kinetic Energy (KE) is defined as one half the product of an object’s mass m and its speed v squared: KE ≡ ? mv2Definition: Gravitational Potential Energy (GPE) is defined as the product of an objects weight W and its height h above an arbitrary horizontal reference elevation: GPE ≡ mgh = Wh All heights must be measured consistently relative the chosen reference elevation when calculating GPE.Determine the mass of your car using one of the digital scales provided and record it here in kilograms (show your conversion from grams to kilograms): Mass of Car (kg)Let’s choose the bottom of the ramp to be our reference level for calculating gravitational potential energy, where we will define the height zero. Hold the car in its starting position at the top of the ramp. With your meter stick measure the height of the top surface of the ramp above the table top where the rail rests on the edge of the support bucket. Next measure the height of the top surface of the ramp where the ramp enters the bottom “car catcher” bucket. The difference between these two measured heights is the distance the car will descend vertically as it rolls down the ramp, that is, how much higher the car is at the top of the ramp than at the bottom. Record all your measurements in the table below and convert the final height difference to meters. Show your final conversion from centimeters to Height of Ramp at Car Center (cm)Bottom Height of Ramp at Car Center (cm)Difference Between Top and Bottom Height of Ramp (cm)Difference Between Top and Bottom Height of Ramp (m)Calculate the gravitational potential energy of your car’s mass using the difference in height determined in question (9) and report it along with the work done by gravity on the car you calculated in question (2). Also calculate the kinetic energy of your car at the bottom of the ramp using the average final speed you determined in (5) for the car rolling the entire length of the ramp. Show your calculations (g = 9.8 m/s2).Gravitational Potential Energy at Top of Ramp (Joules)Work Done by Gravity Rolling Down Ramp (Joules)Final Kinetic Energy of Car at Bottom of Ramp (Joules) How does the number of Joules of work done by gravity that you estimated in question (2) compare with the gravitational potential energy and the final kinetic energy you calculated in question (9)? Can we use gravitational potential energy as an alternative to measuring the force down the ramp and the length of the ramp to account for work done by gravity? If we define gravitational potential energy to be zero at the bottom of the ramp, do your results support the conclusion that total energy (gravitational potential energy plus kinetic energy) is conserved? Explain.Theorem: The Work-Energy Theorem states that the work done on an object by a net force Fnet acting parallel to a displacement d equals the change in the object’s kinetic energy: ΔKE ≡ Fnet x d = Wnet ΔKE ≡ KEfinal – KEinitial = ? mvf2 - ? mvi2If positive work is done on an object (the net force acts in the direction of motion), its speed increases.If negative work is done on an object (the net force acts in opposition to the direction of motion, its speed decreases.If zero net work is done on an object its speed remains constant.Assuming the car starts at rest (zero initial speed) the Work-Energy Theorem predicts that the final kinetic energy at the bottom of the ramp is ? (Mass of Car)×(Final Speed)2. At the top of the ramp the gravitational potential energy is the product of weight and height = (Mass of Car)×(Ramp Height)×(Acceleration of Gravity).In symbols we can state these relationships very simply: Let’s apply the Work-Energy Theorem to our car rolling down the ramp, assuming that only gravity does work on the car. Using the expressions for kinetic energy (KE) and gravitational potential energy (GPE) given above, conserve energy, that is, set the final kinetic energy equal to the initial gravitational potential energy at the top of the ramp (that is, at height h) and solve for the final speed of the car. Show your calculation below. Does the result of your calculation in (13) depend on the mass of the car? Why? Is this consistent with the results we obtained previously for cars of different masses rolling down the ramp? What single factor determines the final speed at the bottom of the hill, assuming that only gravity does work on the car? Using the difference in height you determined for your car at the top of the ramp in (8) and the expression you derived in (12) calculate the speed of your car at the bottom of the ramp and compare it to the average final speed you measured at the bottom of the ramp in (5) for the car rolling down the entire length of the ramp. Show your calculation below (g=9.8 m/s2).Calculated Final Speed at the Bottom of the Ramp (m/s)Measured Final Speed at the Bottom of the Ramp (m/s) Our work-energy analysis of the car’s motion assumes that only the force of gravity does positive work on the car and all of the energy gained by the car contributes to increasing its final speed. Cite one additional force that acts on the car that does negative work on the car and therefore causes the car to be moving more slowly at the bottom of the ramp. Cite one additional way the car has gained kinetic energy that we have not accounted for in our analysis. Will this make the car move faster or slower at the bottom of the ramp? (Hint: What parts of the car are moving and therefore have kinetic energy we have not accounted for?).ApplicationMaterialsDedicated Components1 Hot Wheels Car1 calculatorShared Components1 8’ steel wall stud ramp with Hot Wheels Track2 Homer bucket ramp supports1 Homer bucket car-catcher1 50 gram digital scale w/pulley and Homer Bucket Support to measure force of gravity down the ramp1 clear plastic ruler1 meter stick1 digital scale for weighing carsPacking tape to secure rampData acquisition system for cars: ring stand photo gate support, laptop PC running Logger Pro “speed trap” application and MS ExcelConservation of EnergyWe will now make a quantitative study of energy conservation for Hot Wheels cars rolling down a ramp. We will collect our data together as a class using the same “speed trap” that we used to study Newton’s Second Law with the rocket-powered Pitsco cars to measure the speed of cars at the bottom of the ramp. We’ll enter our measurements directly into an Excel spreadsheet and discuss the results as a class. The spreadsheet results will be posted on CTools for you to print out and include in your lab notebook. Record the data for your car below. Be sure to convert the car mass in grams to kilograms and the force parallel to the ramp to Newtons. Show your conversions for grams to kilograms and grams to Newtons of force below. Finally, please report your values to the entire class on the front black board.Data: g=9.8 m/s2Hot Wheels Car Number________Car Mass_________ (g) Car Mass_________ (kg)Force of gravity Parallel to Ramp Framp ___________ (g)Force of Gravity Parallel to Ramp Framp ___________ (N)Time Between Photo Gates Δt __________________(s)Speed at Bottom of Ramp = (0.35 m)/ Δt =_____________m/sThe Hot Wheels cars will descend a height of 0.56 m as they roll down the ramp. Use the expression you derived in (13) to predict the final speed of the Hot Wheels cars, assuming that only gravity does work as they roll down the ramp. Show your calculation (g= 9.8 m/s).Predicted Final Speed at Bottom of Ramp (m/s)Record the data for the class measurements below:Car NumberCar Mass (kg)Force of Gravity Parallel to Ramp (g)Force of Gravity Parallel to Ramp (N)Time Between Photo Gates Δt (s)Measured Final Speed = (0.35 m)/ Δt (m/s)#1#2#3#4#5#6#7#8Average Final Speed at the Bottom of the Ramp (m/s)Compare the average measured final speed for the class measurements to the final speed you predicted in (18). In light of your answers to (15) and (16), discuss what might account for any difference you observe. You may also suggest additional factors that might cause the predicted and measured values to differ, but be specific.Based on your measurements and analysis, can work-energy analysis be used as an alternative to Newton’s Second Law (F = ma) to predict the final speed of a car rolling down a ramp? Give your overall assessment of how well your measured values and calculations support this conclusion.Everyday ApplicationsAPPLICATIONAirplane pilots have an expression “Altitude is speed.” Explain what this means using the concepts of gravitational potential energy, kinetic energy and energy conservation. Neglect any energy lost to air resistance.Summary:A net force which acts parallel to an object’s direction of motion does mechanical work on the object.The work done by individual forces can be added together to get the work done by the net force.Positive work is done when the force acts in the direction of motion.Negative work is done when the force acts in opposition to the direction of motion.Zero work is done if a force acts perpendicular to the direction of motion or if the net force is zero.Kinetic Energy (KE) is energy due to motion and is equal to half the product of an object’s mass and multiplied by its speed squared: KE ≡ ? mv2A conservative force does the same work between any two points in space irrespective of the path taken between the points, or equivalently, zero work for a closed loop path in space. For conservative forces it is possible to characterize the work done by the force by means of a potential energy function.Gravitational Potential Energy is defined as the product of an object’s weight and its height above an arbitrarily chosen reference height: GPE ≡ mgh = Wh.The work done by gravity can be accounted for by differences in the gravitational potential energy, and hence changes in an object’s height. This is possible because gravity is a conservative force.The Work-Energy Theorem states that the work done by the net force is equal to the change in an object’s kinetic energy.If positive work is done on an object, its speed increases.If negative work is done on an object, its speed decreases.If zero work is done on an object, its speed remains constant.If only gravity does work the final speed of an object descending a height h down a frictionless ramp is given by CleanupPlease attach the Washers and bolt to your Pitsco car, one washer on the bottom and seven on top. ................
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