College of Education – University of Florida



Crash CourseDefinitionspotential energy (PE): stored energy due to the relative position or condition of an object, measured in joules (J)kinetic energy (KE): the energy of motion, measured in joules (J)conservation of energy law: in every interaction of any kind (in a closed system) the total energy afterwards is always the same as the total energy at the beginningKey question(s)Does throwing a ball higher give it more energy?How does the ball’s energy level change throughout the flight?How is the energy level of the thrown ball related to its final crashing speed?Why does a small change in a car’s speed produce a more dangerous crash? Grade levels: 9-12Time required: 50 - 55 minutesObjectivesStudents will:measure the time in the air of an upwardly thrown ball.calculate the time an upwardly thrown ball travels to the top of its flight.calculate the ball’s maximum height during the flight.calculate the ball’s maximum gravitational PE gained during the flight.determine the maximum KE gained by the ball during the flight.calculate the ball’s maximum velocity using the Law of Conservation of Energyexplain the relationship between the ball’s maximum velocity and the maximum KE gained during the flight.site evidence to support the statement that KE is transferred or transformed during a car crash.describe how small changes in a car’s speed produce exponentially more energetic, and possibly more dangerous, crashes.Next Generation Science StandardsDisciplinary Core IdeasHS-PS2 Motion and Stability: Forces and InteractionsMS-PS2 Motion and Stability: Forces and InteractionsScience and Engineering PracticesPlanning and Carrying Out InvestigationsConstructing Explanations and Designing SolutionsAnalyzing and Interpreting DataEngaging in Argument from EvidenceBackground informationReview the Background Information in Teacher Lesson 4 “Conservation: It’s the Law.” Energy is defined as the ability to do work. And work is the ability to apply a force (push or pull) over a distance. One of my students simply defined energy as "the stuff that makes things move." Underlying all forms of energy and motion is a basic law of physics: the law of conservation of energy. This fundamental law has nothing to do with saving energy but what happens to energy when it is used. The law states that energy cannot be created or destroyed; it may be transformed or transferred, but the total amount of energy never changes. Energy is a tough concept to illustrate and explain because the only time it can really be seen, felt, or heard is when it is being transferred or transformed. For us to concretely observe the effects of energy, something has to happen (like throwing a ball upward as high as possible). In this activity, we will discuss mechanical energy. Mechanical energy is easier to see and discuss since it deals with larger, visible objects. Thermal, electrical, chemical, and electromagnetic energies are associated with the molecules that form the objects. Nuclear energy involves the energy within the nucleus of individual atoms. To better describe an energy transfer or transformation, scientists consider all energy in one of three conditions: 1) kinetic energy, which is energy of motion; 2) potential energy, which depends on relative position or condition; or 3) field energy, which is energy contained within a field, such as electromagnetic waves. For mechanical energy, an object’s total mechanical energy is the sum of its potential and kinetic energy. Since work is required to lift objects against Earth’s gravity, the mechanical or gravitational potential energy of an object is calculated by multiplying the mass of the object (m) times the acceleration due to gravity (g) times its direct height (h) above the ground (PE = mgh) or by calculating the work it took to lift the object to its resting height (PE=W=Force to elevate object to resting height x vertical distance above ground). Since energy is defined as the ability to do work then releasing energy does work and doing work on something adds energy to it. So, energy and work are actually equivalent concepts. This is known as the work-energy theorem (Work = ?E). The work required to bring an object up to a speed from rest equals its gain in KE. That also means that the kinetic energy of a moving object is equal to the work the object can do while being brought to rest. In equation form, Work = ?KE or Fnetd = ? mv2. Note that kinetic energy is dependent upon the square of the speed (KE = ? mv2). This means that doubling the speed quadruples the kinetic energy. Tripling the speed increases the KE by a factor or nine. And for a fourfold increase in speed, the KE increases by a factor of 16. In vehicle crashes, a small increase in speed results in an exponentially large increase in KE. It is this kinetic energy that can cause injuries if it reaches the occupants.Materials neededEssential: (per group of 2-3 students)ball (1, use a relatively soft ball, i.e., tennis ball or racquetball)stopwatch (1)calculator (1)clipboard (1)“Ball of Energy” Student Activity sheet (1 per student)Supplemental: (per class)pan balance with masses or electronic balancedocument camera or computer projectorcomputer with web accessProcedureLocate an area on the school grounds with a large open field. Assemble the materials for the groups. Make copies of student activity sheet. Introduce the activity with the key questions. Does throwing a ball higher give it more energy?How does the ball’s energy level change throughout the flight?How is the energy level of the thrown ball related to its final crashing speed?Why does a small change in a car’s speed create a big change in its crash energy?Divide students into groups of two or three and distribute materials. If pan balances or electronic balances are available, ask students to measure the mass of their ball and record it in Table 1 of their activity sheet. If balances are not available, the approximate mass of a tennis ball is 58 g (0.058 kg) and for a racquetball is 40 g (0.040 kg).If possible, project an image of the student activity sheet using a document camera or computer projector to facilitate the discussion of the sheet’s data tables. Inform students that while they are outside they are responsible for making only one type of measurement, that is the total time the ball is in the air (Table 2, column #2). Using the stopwatches provided, students will measure the total time the ball is in the air by starting the stopwatch the instance the ball leaves a thrower’s hand and stopping it as soon as the ball hits the ground. The remaining values in the data table are calculated using ? of the total time (time up = ? of total time). Determine a safe upward-throwing procedure with students. For example: All students must stay behind a common line during the throws. If sufficient space is available, have the groups spread across the field to allow enough space for the thrown balls to land without hitting other group members. Do not throw balls at others. Use relatively soft balls that would not injury a student if accidently hit (i.e., tennis balls rather than golf balls). Students may choose their own throwing-style. Balls can be thrown under-hand (i.e. softball-pitch style) or over-hand (i.e. baseball-pitch style). Proceed to the open field area and call on a few students to restate the safety procedures. Ask students to disperse and begin their trials (throws) and recording the total times in their data plete as many trials as time permits. Suggestion: Make each student responsible for recording five trials.If some groups finish before others, ask them to move to a safe spot along the perimeter and begin calculating the values in the data table (see Table 2 below with sample data and Table 3).Upon returning to the classroom, discuss teams’ results and address the Analysis and Crash Questions (see answers below). Inform students that to help simplify this activity, we are ignoring the release height of the ball from the thrower’s hand to the ground, and the effects of air resistance on the ball, consequently there is no change in the ball’s total amount of the mechanical energy. The energy is conserved. The sum of the kinetic and potential energy at any position along the ball’s path is the same. As the thrown ball rises, gravity opposes its motion, doing negative work and decreasing the ball’s KE. When the ball’s KE is depleted, it begins to fall back to earth, as gravity does positive work on it, increasing its kinetic energy. Once the finishing height matches the starting height (the ground, in this simplified case), the KE upon landing equals the KE of the ball the instant it is thrown upward. The equation simplifies to: KEi + PEi = KEf + PEf(i=initial, f=final)During the Crash Question discussion, help students understand that kinetic energy is dependent upon the square of the speed (see Background). Relate this to vehicle crashes – a small increase in speed results in an exponentially large increase in KE. In terms of work, a car that has doubled its speed requires four times as much work to stop.Conclude the lesson with a discussion of the potentially large amounts of energy transfers and transformations in vehicle crashes and how engineers design vehicles to prevent the crash energy from injuring occupants. If possible, have students visit to watch video clips of various crash tests and explore the test details and technical measurements to gather evidence for their arguments.Data tables Table 1Ball typeMass (kilograms)Tennis ball0.058Table 2MeasureCalculateTrial #Total time(s)tup(s)tdown(s)dup= ? gtup2(m)PEmax = mghmax(J)KEmax = PEmax(J)Vmax(m/s)12.301.151.156.493.693.6911.323.061.531.5311.56.546.5415.032.751.381.389.345.315.3113.543.381.691.6914.08.008.0016.653.501.751.7515.08.538.5317.2Table 3SymbolDefinitionFormulaDescription and unitstupTime up? total timeDivide the total time by 2. tup = total time ÷2 Measured in seconds (s)tdownTime down? total timetup = tdown (neglecting air resistance)dupMaximum distance up? gtup2Use half of the total time (time up or time down) to calculate the maximum distance upward or height the ball achieves. Measured in meters (m).gAcceleration due to gravity9.81 m/s2The acceleration for any object moving under the sole influence of gravity, also know as free fall. Measured in meters per second per second (m/s2).PEmaxMaximum potential energymghmaxPotential energy (PE) is energy due to the relative position of an object, measured in joules (J). PEmax = mghmax where m=mass of the ball in kilograms, g = acceleration due to gravity, and h = maximum height above ground. For the ball, its maximum potential energy is at the top of it flight, use the value for maximum distance up (dup ) for hmax. KEmaxMaximum kinetic energyKEmax = PEmaxKinetic energy (KE) is energy of motion, measured in joules (J). KEmax is equal to half the mass multiplied by the final maximum velocity squared (KEmax = ? mvmax2). The maximum potential energy gained by the ball on its upward journey is converted entirely to kinetic energy during its downward journey (neglecting air resistance) therefore PEmax = KEmaxVmaxMaximum crash velocity√2ghVmax is calculated from KEmax = PEmax. Measured in meters/second (m/s). The change or loss in potential energy is equal to the change or gain in kinetic energy. Solving algebraically for the final velocity:?KEmax = ?PEmax? mvmax2 = mghmaxvmax = √2ghAnswers to Analysis Questions: Describe how work was done on the ball to increase its potential energy. Work was done on the ball by the person’s muscles applying a force through their range of throwing motion until they released the ball upward.Identify the point in the ball’s flight where the following occur:Maximum PE at the ball’s maximum heightMaximum KEthe instant before the ball hits the groundDescribe the relationship between the ball’s final velocity and the maximum kinetic energy gained during the flight.In general, as the ball’s kinetic energy increased the ball’s final crashing velocity increased. However, under closer review, they each did not increase by the same amount. While the KE more than doubled going from 3.69 J to 8.53 J (increasing by a factor of 2.3) at the same time, the final crashing velocity changed from 11.3 m/s to 17.2 m/s (increasing by a factor of 1.5). In other words, a small change in velocity creates a big change in kinetic energy.Answers to Crash Questions Write an argument to support the claim that when the kinetic energy of a car changes during a crash test with a crash barrier, energy is transferred or transformed during the crash? If possible, watch video clips of IIHS frontal crash testing (either small or moderate overlap) at and use your observations and/or data from the site as evidence to support your argument.A large portion of the kinetic energy is either transferred transformed during the crash test. In reviewing the video of for the Acura RL moderate overlap frontal crash test the car’s front end and the crash barrier were severely deformed. Small parts of the car and crash barrier were seen breaking and flying away from the crash area. A loud crashing sound was also heard upon the collision. The technical measurements taken after the collision of intrusion into the occupant on the driver’s side show footwell intrusion up to 14 cm and a brake pedal intrusion of 13 cm.Why do small changes in a car’s speed produce exponentially more energetic, and possibly more dangerous, crashes?A car’s crashing energy or KE is dependent upon the square of it speed (KE = ? mv2). This means that doubling the speed quadruples the KE. Therefore a small increase in speed results in an exponentially large increase in KE. It is this KE that can cause injuries if it reaches the occupants. In terms of work, a car that has doubled its speed requires four times as much work (or KE) to stop.Extension(s)Have students investigate how to calculate the forces in a car crash by visiting the Georgia State University’s HyperPhysics website at students to visit the IIHS website () and search “side crash test.” Ask students to explore why and how the side crash test is conducted. Have students share their observations and compare the engineering challenges of protecting occupants in a side crash versus a moderate overlap frontal crash test.91440068008500209550-558800Name __________________________________________ Period _______ Date____________00Name __________________________________________ Period _______ Date____________4682066-12700000A Ball of EnergyCrash test question(s) Does throwing a ball higher give it more energy?How does the ball’s energy level change throughout the flight?How is the energy level of the thrown ball related to its final crashing speed?Why does a small change in a car’s speed produce a more dangerous crash? 413893011239500Purpose To calculate the final crashing speed of a thrown ball.To explore the effects of kinetic energy during a car crash test.Materials Per group of 2-3 students:ball (1), use a relatively soft ball, i.e., tennis ball or racquetballstopwatch (1)calculator (1)clipboard (1)Discussion Engineers at the IIHS’s Vehicle Research Center consider three factors to determine how a vehicle rates in the frontal crash tests: structural performance, injury measures, and dummy movement. To assess a vehicle’s structural performance, engineers measure the amount of intrusion into the occupant compartment. The less intrusion the better the occupant is protected. In this lesson, you will explore the relationship between an objects kinetic energy and it final crashing velocity.ProcedureIf a scale is available, before you go outside measure the mass of the ball and record it in Table 1. If a scale is not available, your teacher will provide the mass of the ball.Once you are outside and have reviewed the safety procedures, use the stopwatch to time the ball from the instant you release it to the instant it hits the ground. Record this time in seconds as the Total Time in the Table 2 below. Complete 5 trials per team member.After the trials are completed, move to a safe spot and begin your calculations.To find time up, divide the total time the ball was in the air by two (time up = total time ÷ 2).Refer to Table 3 for the formulas needed to calculate the maximum height (dup), maximum potential energy (PEmax), and the final crashing velocity of the ball (vmax).Data tablesTable 1Ball type (i.e., tennis)Mass of ball (kilograms)Table 2MeasureCalculateTrial #Total time(s)tup(s)tdown(s)dup= ? gtup2(m)PEmax = mghmax(J)KEmax = PEmax(J)Vmax(m/s)12345Table 3SymbolDefinitionFormulaDescription and unitstupTime up? total timeDivide the total time by 2. tup = total time ÷2 Measured in seconds (s)tdownTime down? total timetup = tdown (neglecting air resistance)dupMaximum distance up? gtup2Use half of the total time (time up or time down) to calculate the maximum distance upward or height the ball achieves. Measured in meters (m).gAcceleration due to gravity9.81 m/s2The acceleration for any object moving under the sole influence of gravity, also know as free fall. Measured in meters per second per second (m/s2).PEmaxMaximum potential energymghmaxPotential energy (PE) is energy due to the relative position of an object, measured in joules (J). PEmax = mghmax where m=mass of the ball in kilograms, g = acceleration due to gravity, and h = maximum height above ground. For the ball, its maximum potential energy is at the top of it flight, use the value for maximum distance up (dup ) for hmax. KEmaxMaximum kinetic energyKEmax = PEmaxKinetic energy (KE) is energy of motion, measured in joules (J). KEmax is equal to half the mass multiplied by the final maximum velocity squared (KEmax = ? mvmax2). The maximum potential energy gained by the ball on its upward journey is converted entirely to kinetic energy during its downward journey (neglecting air resistance) therefore PEmax = KEmaxVmaxMaximum crash velocity√2ghVmax is calculated from KEmax = PEmax. Measured in meters/second (m/s). The change or loss in potential energy is equal to the change or gain in kinetic energy. Solving algebraically for the final velocity:?KEmax = ?PEmax? mvmax2 = mghmaxvmax = √2ghAnalysisDescribe how work was done on the ball to increase its potential energy. ____________________________________________________________________________________________________________________________________________________________Identify the point in the ball’s flight where the following occur:Maximum PE ________________________________________________________Maximum KE ________________________________________________________Describe the relationship between the ball’s final velocity and the maximum kinetic energy gained during the flight.__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Crash QuestionsWrite an argument to support the claim that when the kinetic energy of a car changes during a frontal crash barrier test, energy is transferred or transformed during the crash? If possible, watch IIHS video clips of frontal crash tests (either small or moderate overlap frontal crash test) at and use your observations and/or data from the site as evidence to support your argument.______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________Why do small changes in a car’s speed produce exponentially more energetic, and possibly more dangerous, crashes?__________________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ................
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