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Work and Energy UM Physics Demo Lab 07/2013 Pre-Lab Question If 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? EXPLORATION Exploration Materials Dedicated Components 1 Pitsco PC Sportster car 1 ½ inch x 2” steel hex bolt with nut 1 10’ steel wall stud ramp 8 ½ inch cut steel washers 1 Homer bucket ramp support 1 Guide Wire Assembly 1 spring scale– Ohaus 2000g/20N 1 clear plastic ruler 1 meter stick 1 digital scale 1 stop watch 1 calculator 1 2” long thin rubber band Shared/Consumable Components: Additional rubber bands 8’ Dual use ramp for speed trap measurements 3 Homer Buckets, 2 with lids—2 ramp supports and one car catcher Clear package tape Scissors Data acquisition system for Pitsco cars: ring stand photo gate support, laptop PC running Logger Pro “speed trap” application and MS Excel Mechanical Work Pitsco 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. Property of LS&A Physics Department Demonstration Lab Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109 1 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. 1. 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 = 9.81 m/s2) get the force in Newtons. Show your calculation! Force of Gravity Acting Down the Ramp (N) 2. 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! Property of LS&A Physics Department Demonstration Lab Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109 2 Work Done by Gravity for a Car Rolling Down a Ramp (Joules) 3. 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 = ½ (Initial Speed + Final Speed) Average Speed = ½ (0 + Final Speed) = ½(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) Property of LS&A Physics Department Demonstration Lab Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109 3 4. 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 = ½(2.74 m) Time (s) Trial #1 Trial #2 Trial #3 Average Speed (m/s) Final Speed (m/s) Average Final Speed 5. Repeat 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 #1 Trial #2 Trial #3 Average Final Speed Property of LS&A Physics Department Demonstration Lab Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109 4 6. Qualitatively, how is the average speed down the ramp related to the distance the car rolls down the ramp? 7. 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 Energy Definition: Kinetic Energy (KE) is defined as one half the product of an object’s mass m and its speed v squared: KE ≡ ½ mv2 Definition: 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. 8. 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) Property of LS&A Physics Department Demonstration Lab Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109 5 9. 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 meters. Top 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) Property of LS&A Physics Department Demonstration Lab Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109 6 10.Calculate the gravitational potential energy of your car’s mass at the height of the ramp measured in question (9) and compare it with the work done by gravity on the car you calculated in question (2). Show your calculation! Don’t forget the units. Gravitational Potential Energy at Top of Ramp (Joules) Work Done by Gravity Rolling Down Ramp (Joules) 11. How does the number of Joules of work done by gravity that you estimated in question 2 compare with the gravitational potential energy in Joules you calculated in question 9? Property of LS&A Physics Department Demonstration Lab Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109 7 12. 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? 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 = ½ mvf2 - ½ mvi2 If 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 ½ (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: 2 KE 21 mvfinal GPE mgh Property of LS&A Physics Department Demonstration Lab Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109 8 13. Considering your answer to question 5, are your observations regarding the amount of work done by gravity and the average speed of your car rolling down the ramp qualitatively consistent with the work Work-Energy Theorem? Explain. (Hint: a larger average speed means that the car is moving faster at the bottom of the ramp). Application Materials Dedicated Components 1 Hot Wheels Car 1 calculator Shared Components 1 8’ steel wall stud ramp with Hot Wheels Track 2 Homer bucket ramp supports 1 Homer bucket car-catcher 1 50 gram digital scale w/pulley and Homer Bucket Support to measure force of gravity down the ramp 1 clear plastic ruler 1 meter stick 1 digital scale for weighing cars Packing tape to secure ramp Data acquisition system for cars: ring stand photo gate support, laptop PC running Logger Pro “speed trap” application and MS Excel Conservation of Energy We will now make a quantitative study of energy conservation for 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 Car Number________ # of Washers __________ Car Mass_________ (kg) Car Weight Parallel to Ramp Framp ___________ (N) Property of LS&A Physics Department Demonstration Lab Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109 9 Everyday Applications APPLICATION 1. Airplane 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. Property of LS&A Physics Department Demonstration Lab Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109 10 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 ≡ ½ mv2 A 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 vfinal = 2 gh Cleanup Please remove the washers and bolt from your car and store the washers on the bolt, retained with the nut. Property of LS&A Physics Department Demonstration Lab Copyright 2006, The Regents of the University of Michigan, Ann Arbor, Michigan 48109 11