The same piece of film is exposed every time thestrobe light flashes so you can see many steps in a process atthe same time.

Photographs taken with a strobe light, such as theimage of the golf swing in Figure 5.14, give youa sensation of motion. Strobe lights flash manytimes a second, allowing you to capture steps inthe motion of objects.

Stroboscopic photographs also allow you toanalyze the motion and the energy involved in themotion. For example, Figure 5.14 shows that thegolfer is doing work on the golf club, thus makingit move. Since it is moving, it has kinetic energy.Then the golf club exerts a force on the golf ballover a short distance, thus doing work on the ball.The club did work on the ball, making it move.Since the distances between the images of the ballare all nearly the same, the ball is moving with aconstant velocity or uniform motion. In this case,the energy given to the ball was the energy of motion or kinetic energy.You have learned how to calculate the amount of work done on an object.How do you calculate kinetic energy?

Stroboscopic photographyis not the only way to studyrapidly moving objects.Repeating motion, such asthe rotation of a fan or areciprocating (back-and-forth)movement, can appear muchslower when you look througha hand stroboscope like the onepictured here. As you turn thestroboscope wheel, its slotsreveal a brief glimpse of themoving object every fewhundredths of a second. If yourschool does not have a handstroboscope, it is not difficultto make one from particleboard or thin plywood.

Calculating Kinetic EnergyOn what properties of an object does its kinetic energy depend? An objectmust move in order to have kinetic energy. Therefore, the amount of kineticenergy must depend on the speed of the object. Think of another propertythat might contribute to kinetic energy. Imagine that a bowling ball and abilliard ball are both rolling toward you at the same speed. Which onewould be the most difficult to stop? Since their speed is the same, what elsecould be contributing to their kinetic energy? An object's mass contributesto its kinetic energy. You can calculate the kinetic energy of an object byusing the formula below.

In every formula, the units must agree. Agreement means that the units onone side of the equation must be equivalent to the units on the other side.If you substitute the units for each quantity into the formula for kineticenergy, you will get the following result.

(m)2 m2

J=kg-;- =kg-;z-

Chapter 5 Energy and Motion. MHR 197

A joule is equivalent to a kilogram times a metre squared divided by a secondsquared. Including units in problem solving will often help you discover errors.For example, if the units do not agree, you know that there is an error in yoursolution. The incorrect units will usually lead you to the misplaced or missingvalue. To develop your problem-solving skills, study the Model Problems below.Then complete the Practice Problems.

Part AA car with a mass of 1500 kg is moving at a speed of 14 m/s (about 50 km/h).What is the kinetic energy of the car?

Givenmass of the car, m = 1500 kg speed of the car, v = 14 m/s

Requiredkinetic energy of the car, Ek

AnalysisThe speed and mass of the car are given so you can substitute directlyinto the formula for kinetic energy.

SolutionEk = fmv2

Ek = t(1500 kg) ( 14 ~)2

Ek = t(1500 kg)( 196~)

m2Ek = 1.47 X 105 kg 2s

Ek = 1.5 x 105J

ParaphraseThe kinetic energy of the 1500 kg car travelling at 14 m/s is approximately1.5 X 1051.

Part BA hockey puck has a mass of 0.21 kg. If the hockey puck has 73 J ofkinetic energy, what is its speed?

Givenmass of the hockey puck, m = 0.21 kgkinetic energy of the hockey puck, Ek = 73 J

Requiredspeed of the hockey puck, v

AnalysisYou can approach this problem in two different ways. You can rearrangethe formula by using the rules of algebra to solve for speed. You can alsosubstitute the numerical values into the equation and then solve for thespeed. Both methods are shown on the next page.

198 MHR . Unit 2 Energy Flow in Technological System

SolutionSolve for the speed in theformula first. Then substitutethe numerical values into themodified formula.

Substitute numerical values intothe formula first and then solvefor the speed.

1 m"695.24 2

s-vv = 26.367 ~

s26m

ParaphraseA 0.21 kg hockey puck that has 73 J of kinetic energy has a speedof approximately 26 rn/s.

,4KUse the knowledge that you have gained about kinetic energy tocomplete the following problems.

32. A wrecking ball, similar to the one shown in the diagram, hasa mass of 315 kg. If it is moving at a speed of 5.12 mis, whatis its kinetic energy?

/ .33. A freight elevator with a mass of 120 kg is moving with

a speed of2.50 mls. What is its kinetic energy? -.&.

34. A student with a mass of 55 kg is jogging at a speed of1.6 mls. What is the student's kinetic energy?

35. Anelectronwithamassof9.11 x 10-31 kg is moving at a speedof2.19 x 107 mls. What is the kinetic energy of the electron?

199Chapter Motion . MH~Iler~

To a baseball fan,the pitcher is pitching the ball.To a physicist, the pitcher isdoing work on the ball.

Work and Kinetic EnergyThe pitcher in Figure 5.15 is exerting a force on a baseball over a distanceof about 1 m. The pitcher is doing work on the ball and thus transferringkinetic energy to the ball. If all of the work goes into kinetic energy, you couldpredict the speed of the ball when it leaves the pitcher's hand. The method isidentical to the problems above. You determined the speed of an object giventhe mass and kinetic energy of the object.

In many transformations, however, not all of the work goes 'into kineticenergy. In fact, in some situations, doing work on an object reduces its kineticenergy. For example, consider the situation shown in Figure 5.16. The baseballhad kinetic energy. However, the work done by the catcher's mitt removedthe kinetic energy. Where did the energy go?

If you have ever caught a fast ball, you will have a clue to the answer to thequestion above. The mitt and your hand felt a little warm. When you caughtthe ball, the kinetic energy of the ball was converted into thermal energy, mosdyin the mitt and your hand. Notice that when kinetic energy is removed froman object, the force doing the work is directed opposite to the direction ofthe motion of the object. When work removes kinetic energy from an object,physicists call this negative work.

Catching a baseball is just one example ofnegative work, that is, work that removes kineticenergy from an object. In the Find Out Activityon the next page, you will examine a situation inwhich your life might depend on removing thekinetic energy of an object. The object is the carin which you are a passenger. In the investigationthat follows the activity, you will have a chance todesign your own system that does negative work.

~ When the catcher catches a baseball, thecatcher's mitt does negative work on the ball. Explainthe meaning of negative work as it applies to the baseball.

200 MHR . Unit 2 Energy Flow in Technological Systems

'ind OutDriving SafelyTo drive safely, you must be able to stop withinthe distance between your car and the car infront of you. The distance required varies with thespeed at which your car is moving. The force thatdoes negative work on your car to transform allof the kinetic energy into thermal energy is theforce of friction within the brakes and betweenthe tires and the road. The thermal energy is thenshared among the brakes, tires, and the road. Fora car with a mass of about 1500 kg, it would bereasonable to expect that the force of friction wouldbe approximately 12 000 N. Your challenge is tofind the distance needed for stopping at severaldifferent speeds.

6. Make a graph of stopping distance in metresversus speed in kilometres per hour. Putdistance (d) on the vertical axis and speed (v)on the horizontal axis.

Procedure

1. Develop an equation to calculate thestopping distance for any speed byfollowing these steps.

(a) Start with the information that the workdone on the car by the force of frictionmust be equal to the kinetic energy ofthe car. Write that relationship in mathe-matical form.

(b) Substitute Fi1.d for work and substitutetmv2 for kinetic energy.

(c) Solve the equation for i1.d.

2. Make a table similar to the one shown here.Leave space for seven different speeds.

3. Fill in the first speed column with 5, 1O, 15,20, 25, 30, and 35 m/s. 2. What does this graph tell you about

stopping at high speeds compared tostopping at lower speeds?

4. Calculate the stopping distance for each of thespeeds. Place the answers in the last column.

3. What, if anything, surprised you the mostabout your results?

5. Convert the speeds to kilometres per hourand fill in the second speed column.

llergyandMotion . MHR 201flapter

1. Describe the shape of the curve on yourgraph. Is it a straight line or not? (Hint: If it isa straight line, doubling the speed will doublethe stopping distance. For example, is thestopping distance at 100 km/h twice thestopping distance at 50 km/h? If not, therelationship between speed and stoppingdistance is not a straight line.)

Slowing down a heavy, fast-moving aircraft or racingcar in a short distance can be too much for drumor disc brakes, like those used on most vehicles.Although the brakes could be made powerful enoughto stop the wheels from turning, the skidding tireswould be quickly worn away or destroyed as theyscraped across the ground. Air brakes are parachutesor surfaces that can turn or pivot to increase drag(air resistance) and help stop the vehicle.

ChallengeDesign and construct an effective air brake for asmall vehicle, and measure its stopping distance.

Plan and Construct L-0 Work in a small group to brainstorm possible

designs for an air brake. Possibilities includeparachutes, movable sails, or spoilers thatchange the shape of the vehicle to increaseair resistance. Consider how to keep your airbrake from slowing the vehicle as it goes downthe ramp. How will your air brake fold orturn when activated? How will you attach itto the vehicle? What sort of trigger mechanismwill you use?

Materialssmall moving vehicle, such as a lab cart or a large toy carstarting ramp to get the vehicle movingconstruction materials, such as wood, cardboard,

cloth, string, glue, and fasteners

stopwatchmetre stick or tape

. Obtain the materials you need, and constructa prototype of your air brake.

Design CriteriaA. Your vehicle must gain initial speed by moving

down the ramp without any braking action.B. The air brake might be a separate structure that

the vehicle runs into, but it must end up attachedto the vehicle.

C. The air brake must not cause the vehicle to tipover~ spin, or turn significantly.

D.ConstfU{;t your air brake. Then conduct severaltrials to determine the shortest distance requiredto stop the vehicle. Start measuring at the endof the ramp,

. Conduct preliminary trials. Modify yourair brake until it satisfies the design criteria.

0 Create a data table for your observations.

0 Conduct several trials, so that you can averageyour results to increase their reliability.

202 MHR . Unit 2 Energy Flow in Technological Systems

Race car driver David Purley survived a crash in which his car wentfrom 173 km/h to zero in a distance of 66 cm. Using calculations ofwork done to stop the vehicle, scientists estimated that he experienceda force 179.8 times his body weight. It's no wonder he suffered29 broken bones and three dislocations.

Section 5.2 SummaryIn this section, you learned how to calculate the kinetic energy of a movingobject. You learned that when a force does work on an object and increasesthe object's speed, the work transfers kinetic energy to the object. You alsodiscovered that doing work on an object can reduce its kinetic energy. In thesecases, the force doing the work is opposite to the direction of the motion ofthe object. When the kinetic energy of an object is reduced, the energy isoften transformed into thermal energy.

Chapter 5 Energy and Motion. MHR 203

Check Your Understanding

1. What properties of an object affect its kinetic energy?

2. Since work equals force times distance, the units are newtons times metres(N8m). A newton is equivalent to a kilogram times a metre divided byseconds squared (kg8m1s2). Show that the units of work are the sameas the units for kinetic energy.

3. The SR71 Blackbird - the fastest jet airplane ever built - is flying at

a speed of 3200 km/h. lfthe mass of the Blackbird is 36000 kg, whatis its kinetic energy? (Hint: Remember to convert km/h to mls.)

4. A neutron travelling at a speed of 2200.0 mls has 4.048 X 10-21 Jof kinetic energy. What is its mass?

5. (a) A pool cue exerted an average force of 160 N on a cue ball overa distance of 0.012 m. How much work did the cue do on the ball?

(b) lfall of the work done (a) was transformed into kinetic energy ofa 0.200 kg cue ball, what was the speed of the ball?

6. Describe three different examples of negative work.

7. Apply To stop a car that is moving at 45 km/h, a specific amount ofwork must be done on the car by some force. The same amount ofwork must be done to stop the car whether it is on a dry road ora wet road. Why is it safer to stop on a dry road?

8. Apply In the first section of this chapter, you learned how to relatethe direction of an object's acceleration to the change in the velocity ofan object. In this section, you learned that a force can either increasethe kinetic energy of an object or reduce the object's kinetic energy.Create examples that involve both (a) increasing and (b) reducing thekinetic energy of an object. Visualize the forces acting on the objectin both cases. Determine the direction of the acceleration of the objectin both cases. Formulate a relationship between the direction of aforce acting on an object and the direction of the object's acceleration.

9. Critical Thinking As you know, a force must do work on a car toreduce the car's kinetic energy to zero, thus stopping the car. You alsoknow that an object's kinetic energy is related to the square of its velocity.Use this knowledge to prepare a presentation to convince people thatwhen the speed of a car doubles, the distance needed to stop the carincreases by a factor of four.

204 MHR . Unit 2 Energy Flow in Technological Systems