1

Science and the Science and the RoadRoadK M ChengK M Cheng

Department of Physics, Department of Physics, CUHKCUHK

Time Allocation: 6 hoursTime Allocation: 6 hours

2

ContentContent

Measuring motionMeasuring motion Speeding up and slowing downSpeeding up and slowing down Tyre/road frictionTyre/road friction （摩擦力）（摩擦力） Stopping a carStopping a car The speed formulaThe speed formula CollisionCollision Travelling round a bendTravelling round a bend Driving safetyDriving safety

3

Measuring motionMeasuring motion SpeedSpeed （速率）（速率） tells us how fast an tells us how fast an

object moves. object moves.

The speed at a particular instant of The speed at a particular instant of time is found bytime is found by taking the average taking the average speed over a very short time interval.speed over a very short time interval.

VelocityVelocity （速度）（速度） tells us the speed tells us the speed of the object as well as its direction of the object as well as its direction of travel. of travel.

t

sv

taken timetotal

travelleddistance totalspeed Average

4

An object accelerates when its speed An object accelerates when its speed increases and decelerates when its increases and decelerates when its speed decrease.speed decrease. Acceleration Acceleration （加速（加速度）度） is the rate of change of velocity. is the rate of change of velocity.

For motion in a straight line, For motion in a straight line,

When When tt becomes very small, the becomes very small, the average acceleration approaches the average acceleration approaches the acceleration at a particular time acceleration at a particular time instant.instant.

t

va

change for the time

speedin changeonacceleratiAverage

5

For uniformly accelerating motion in For uniformly accelerating motion in a straight line: a straight line:

where where

t

uva

vuv

and

2

initial velocity,

final velocity,

average velocity,

acceleration,

time.

u

v

v

a

t

6

From these two expressions, the three From these two expressions, the three equations of motionequations of motion can be can be deduced: deduced:

Note that Note that ss is the is the displacementdisplacement （位（位移）移） which is the distance travelled which is the distance travelled along the straight line.along the straight line.

asuv

atuts

atuv

2

2

1

22

2

7

Speeding up and slowing Speeding up and slowing downdown

We may change the motion of a moving We may change the motion of a moving object by pushing or pulling it. Scientists object by pushing or pulling it. Scientists call this pull or push to be a call this pull or push to be a forceforce （力）（力） . . The unit of force is newton (N - The unit of force is newton (N - 牛頓牛頓 ).).

Newton formulated three laws of motion Newton formulated three laws of motion describing the properties of force. In describing the properties of force. In NewtonNewton’’s first law, it states that: s first law, it states that:

A body continues in a state of rest or uniform motion in a straight line, unless an unbalanced force acts on it.

8

What does the term unbalanced What does the term unbalanced force really mean? force really mean?

These forces balance. The block does not move.

These forces does not balance. The block moves as if it was being pulled by a force of 10 N to the right.

10 N

10 N

10 N

20 N

9

Newton's first law of motion tells us Newton's first law of motion tells us that all objects resist change in their that all objects resist change in their state of motion. All objects have this state of motion. All objects have this tendency, i.e. they have tendency, i.e. they have inertiainertia （慣（慣性）性） . .

10

The The massmass （質量）（質量） of an object is a of an object is a measure of its inertia. An object with measure of its inertia. An object with a larger mass has more inertia and a larger mass has more inertia and thus has larger tendency to resist thus has larger tendency to resist changes in its state of motion. The changes in its state of motion. The mass of an object is usually given in mass of an object is usually given in unit of g (gram) or kg (kilogram).unit of g (gram) or kg (kilogram).

11

If an object is dropped, it falls to the If an object is dropped, it falls to the ground at increasing speed. The free ground at increasing speed. The free falling objectfalling object （ 自 由 落 體 ）（ 自 由 落 體 ） accelerates accelerates due to the pull of the Earthdue to the pull of the Earth’’s gravitys gravity （重（重力 ）力 ） . When air resistance is negligible, . When air resistance is negligible, all free falling objects fall with the same all free falling objects fall with the same uniform acceleration (approximately) uniform acceleration (approximately) known as the known as the acceleration due to acceleration due to gravity ggravity g. The value of . The value of gg is independent is independent of the mass of the body, and is usually of the mass of the body, and is usually taken as 10 m/staken as 10 m/s22..

12

PUSH

To Move

FRICTIONAL FORCE to Resist Motion

A car will eventually stop if the A car will eventually stop if the engine is turned off. It is due to the engine is turned off. It is due to the frictionfriction （摩擦力）（摩擦力） which slows down which slows down the carsthe cars’’ motion. motion.

Friction arises whenever an object Friction arises whenever an object slides or tends to slide over another slides or tends to slide over another object. It always acts against the object. It always acts against the motion.motion.

13

Friction is due to the irregularities Friction is due to the irregularities on a surface. Even a smooth surface on a surface. Even a smooth surface has these has these ““peaks and valleyspeaks and valleys””. If two . If two surfaces rub over each other, the surfaces rub over each other, the irregularities on the two surfaces irregularities on the two surfaces would crush together, resulting in an would crush together, resulting in an opposing force.opposing force.

14

What does friction depend on?What does friction depend on? Friction does not depend on the area of Friction does not depend on the area of

contact, but depends only on the contact, but depends only on the naturenature of the contact surface. of the contact surface.

Friction is much reduced if the contact Friction is much reduced if the contact surface is lubricated with water or oil, surface is lubricated with water or oil, and if rollers and bearings are placed and if rollers and bearings are placed between the contact surface.between the contact surface.

The greater is the weight of the object, The greater is the weight of the object, the greater is the friction.the greater is the friction.

15

Tyre/road frictionTyre/road friction According to NewtonAccording to Newton’’s Third Law, the car is s Third Law, the car is

driven by the driven by the forward frictional pushforward frictional push of the of the ground on tyres.ground on tyres.

If we apply the brakes (very hard), the wheels If we apply the brakes (very hard), the wheels are locked and thus prevent from rotating.are locked and thus prevent from rotating.

As a result, the car skids and decelerates. The As a result, the car skids and decelerates. The decelerating force is actually the decelerating force is actually the sliding sliding frictionfriction （滑動摩擦）（滑動摩擦）–– a backward push of the a backward push of the ground on tyres.ground on tyres.

Anti-lock braking system (ABS - Anti-lock braking system (ABS - 防鎖死煞車系防鎖死煞車系統統 )): a system on motor vehicles which prevents : a system on motor vehicles which prevents the wheels from locking while braking. the wheels from locking while braking.

16

Tyre/road frictionTyre/road friction

On a level road, this force is given by On a level road, this force is given by

where where is the coefficient of tyre/road is the coefficient of tyre/road friction and friction and mgmg is the weight of the car. is the weight of the car.

The The value changes only slightly with value changes only slightly with speed. However, if the road surface is speed. However, if the road surface is wet, the wet, the value depends significantly on value depends significantly on tyre conditions, speed, weight of vehicle tyre conditions, speed, weight of vehicle and degree of wetness.and degree of wetness.

F mg

17

Tyres and tread patternsTyres and tread patterns Various tread patterns are designed to provide a Various tread patterns are designed to provide a

firm grip on the road surfacefirm grip on the road surface

Groove on the thread are for pushing out water on Groove on the thread are for pushing out water on

a wet road so that the tyres and the road are still in a wet road so that the tyres and the road are still in

direct contact and are not lubricateddirect contact and are not lubricated

Tread pattern on a car tyre Tread pattern on a mountain bicycle tyre

(Wikimedia commons)

18

Tyres and tread patternsTyres and tread patterns

Worn-out tyres are dangerous and illegalWorn-out tyres are dangerous and illegal By law, tread depth must not be less than By law, tread depth must not be less than

1 mm over three-quarters of the tread area1 mm over three-quarters of the tread area A penny can be used to check tyre A penny can be used to check tyre

tread (Penny test, USA):tread (Penny test, USA): Take a penny and put Abe's head into Take a penny and put Abe's head into

one of the grooves of the tyre treadone of the grooves of the tyre tread If part of his head is covered by the If part of his head is covered by the

tread, you're driving with the legal tread, you're driving with the legal amount of tread amount of tread

If you can see all of Abe's head, it's If you can see all of Abe's head, it's time to replace the tyretime to replace the tyre

(Wikimedia commons)

19

Slick tyre Slick tyre A type of tire that has no tread pattern A type of tire that has no tread pattern

Used mostly in auto racing Used mostly in auto racing By eliminating any grooves cut into the tread, such By eliminating any grooves cut into the tread, such

tyres provide the largest possible contact patch to tyres provide the largest possible contact patch to the roadthe road

Can be very dangerous if the racing track is wet!Can be very dangerous if the racing track is wet!

(Wikimedia commons)

20

The skid marks The skid marks When a car skids, particularly on a tarmac road When a car skids, particularly on a tarmac road

surface, clearly visible skid marks are usually left surface, clearly visible skid marks are usually left

on the roadon the road

The speed of a vehicle prior to skidding can be The speed of a vehicle prior to skidding can be

estimated from the estimated from the skid mark lengthskid mark length and the and the

coefficient of frictioncoefficient of friction （摩擦係數 ）（摩擦係數 ） between the between the

tyres and the road surfacetyres and the road surface

(Wikimedia commons)

21

Skidding over different Skidding over different surfaces surfaces

Very often, a skid mark may extend over Very often, a skid mark may extend over

different surfaces, e.g., tarmacdifferent surfaces, e.g., tarmac （柏油碎（柏油碎石）石） , concrete, concrete （混凝土）（混凝土） , gravel, gravel （砂礫）（砂礫） , ,

grass, etc. grass, etc.

In these cases, the speed of a vehicle In these cases, the speed of a vehicle

prior to skidding can be estimated from prior to skidding can be estimated from

the the skid mark lengthsskid mark lengths on different on different

surfaces and the surfaces and the coefficient of frictionscoefficient of frictions

between the tyres and different surfaces between the tyres and different surfaces

22

Skidding on slopes Skidding on slopes

When the road surface is not level, When the road surface is not level,

the skidding distance is affected. It the skidding distance is affected. It

will be shorter for going uphill and will be shorter for going uphill and

longer for going downhill. longer for going downhill.

One may define the One may define the gradient gradient ee （斜（斜率）率） of a non-level road byof a non-level road by

He

L

H

L

23

Skidding on slopes Skidding on slopes

us e

If the If the coefficient of frictionscoefficient of frictions of a level of a level

surface is surface is , then, then the the effective valueeffective value for for

an up-slope or down-slope of gradient an up-slope or down-slope of gradient e e

and the same road type is approximately and the same road type is approximately

given by given by

ds e

Up-slope:

Down-slope:

24

Skidding on slopes Skidding on slopes

Proof of the formulae: Proof of the formulae:

sinF N mg cos tanmg

mg

mgsinN

N = mgcos

H

L

cosmg e mg e

if is small

Force diagram for the case of down-slope

25

Stopping a carStopping a car

When a driver sees a hazard, he hits When a driver sees a hazard, he hits the brake to stop the car. The time the brake to stop the car. The time taken for the driver to react is called taken for the driver to react is called the the reaction timereaction time (or (or thinking thinking timetime). Reaction time varies from ). Reaction time varies from person to person but is, on average, person to person but is, on average, about 0.2 s. The distance travelled about 0.2 s. The distance travelled by a vehicle during reaction time is by a vehicle during reaction time is called called reaction distancereaction distance, i.e., i.e.reaction distance reaction time

average speed during this time

26

Measuring reaction time by the ruler Measuring reaction time by the ruler drop techniquedrop technique

Your partner holds a ruler between your Your partner holds a ruler between your fingers. The ruler is released suddenly. As fingers. The ruler is released suddenly. As soon as you see it, close your finger to soon as you see it, close your finger to catch the ruler. Record how far the ruler catch the ruler. Record how far the ruler drops before you catch it. The faster you drops before you catch it. The faster you react, the less the ruler will drop before react, the less the ruler will drop before being caught.being caught.

Remark: the reaction times are much longer in the case of unexpected events – in the range 1.5 to 2.5 seconds!

27

Once the driver applied the brakes, Once the driver applied the brakes, the car slows down. The distance that the car slows down. The distance that the car moves during braking is called the car moves during braking is called the the braking distance braking distance (can be (can be estimated by the skid mark length). estimated by the skid mark length).

Stopping distanceStopping distance is the distance is the distance taken to stop a car, i.e.taken to stop a car, i.e.

And the time taken to stop a car is And the time taken to stop a car is called the called the stopping timestopping time..

distance brakingdistancereaction distance stopping

28

0 m/s

12 m/s

0.75 s 2.5 s

Stop signalStarts to brake

Slowing down

Stopped

time

Sp

ee

d

Thinking time = 0.75 s Distance Travelled during thinking time = 12 m/s 0.75 s = 9

m Distance Travelled during braking = ½ 2.5 s 12 m/s = 15

m Total stopping distance = 9 m + 15 m = 24 m

ExampleExample

29

The stopping distance depends on The stopping distance depends on the following factors:the following factors:

the speed of the carthe speed of the car

the driverthe driver’’s reaction times reaction time

the road surfacethe road surface

the condition of the carthe condition of the car’’s brakes s brakes and tyresand tyres

30

The speed formulaThe speed formula

Suppose a vehicle of mass Suppose a vehicle of mass mm travel on a travel on a level road at a speed level road at a speed uu prior to skidding. prior to skidding. The kinetic energy of the vehicle is The kinetic energy of the vehicle is given bygiven by

21

2kE mu

kE

s

u

21

2kE mu0kE

u = 0

31

The speed formulaThe speed formula

After skidding a distance After skidding a distance ss, the vehicle , the vehicle stops. The decelerating force is the stops. The decelerating force is the tyre/road friction and is given bytyre/road friction and is given by

The work done The work done WW against friction is against friction is

F mg

s

uu = 0

F mg0F

W Fs mgs

32

The speed formulaThe speed formula

When the vehicle stops, its kinetic energy When the vehicle stops, its kinetic energy is reduced to zero. The change of kinetic is reduced to zero. The change of kinetic energy is equal to the work done against energy is equal to the work done against the friction, i.e.the friction, i.e.

21

2mu mgs

2

2

us

g OROR 2u gs

So the skid-to-stop distance depends only So the skid-to-stop distance depends only on theon the coefficient of tyre/road frictioncoefficient of tyre/road friction (()) and theand the speed of the vehicle (speed of the vehicle (uu) ) prior to prior to skidding.skidding.

33

Some Learning PointsSome Learning Points

In braking , a carIn braking , a car’’s kinetic energy (KE) s kinetic energy (KE) must be dissipated (usually as heat)must be dissipated (usually as heat)

KE = work done in stopping the car = KE = work done in stopping the car = mgsmgs

Braking distance is proportional to the Braking distance is proportional to the speed squaredspeed squared

The effective coefficient of friction is The effective coefficient of friction is not the same for all carsnot the same for all cars

The coefficient of friction decrease by The coefficient of friction decrease by about 40% in wet conditions (assuming about 40% in wet conditions (assuming the tyres are in good condition) the tyres are in good condition)

34

CollisionCollision

Traffic accidents almost always involve Traffic accidents almost always involve collisions of one kind or anothercollisions of one kind or another

The principle of The principle of conservation of linear conservation of linear momentummomentum （動量守恆）（動量守恆） can be applied:can be applied: The total momentum of the objects before The total momentum of the objects before

collision is equal to the total momentum collision is equal to the total momentum after collision, provided that there is no after collision, provided that there is no external force acting on the colliding external force acting on the colliding objects. objects. (Newton(Newton’’s First Law)s First Law)

35

CollisionCollision

The momentum of an object is defined The momentum of an object is defined as the product of its mass as the product of its mass mm and and velocity velocity vv. For two colliding vehicles . For two colliding vehicles of masses of masses mmAA and and mmBB travelling along travelling along the the same straight pathsame straight path, their , their velocities are velocities are uuAA and and uuBB before impact before impact and and vvAA and and vvBB after impact. Then the after impact. Then the total momentumtotal momentum before and after before and after impact is relatedimpact is related

A A B B A A B Bm u m u m v m v

36

Collision (remarks)Collision (remarks) Momentum is a Momentum is a vector quantityvector quantity. If the . If the

collision occurs at an angle, the vector sum of collision occurs at an angle, the vector sum of the momentum before impact is equal to that the momentum before impact is equal to that after impact.after impact.

Vehicles exert force on one another on impact Vehicles exert force on one another on impact (Newton(Newton’’s Third Law)s Third Law). The force of impact . The force of impact causes damage to the vehicles and changes causes damage to the vehicles and changes their velocities (and hence momenta).their velocities (and hence momenta).

In fact, the force of impact, In fact, the force of impact, FF, is related to the , is related to the momentum, momentum, PP, by, by dP mv mu

Fdt t

NewtonNewton’’s Second Law!s Second Law!

37

Travelling round a bendTravelling round a bend

A vehicle travelling A vehicle travelling round a bend on a round a bend on a level road can be level road can be viewed as moving viewed as moving along a circular along a circular pathpath

The centripetal The centripetal forceforce （向心力）（向心力） is is pointing towards pointing towards the centre of the centre of circular motioncircular motion

Centripetal force2mv

rCentre of circular path

r

v

38

Travelling round a bendTravelling round a bend The centripetal force is provided by the The centripetal force is provided by the

sideway friction between the tyres and the sideway friction between the tyres and the road surface:road surface:

Equating the two forces, we getEquating the two forces, we get

vv is called the is called the critical curve speedcritical curve speed for the for the bendbend

2mvmg

r

v gr

F mg

39

Travelling round a bendTravelling round a bend When the speed of the vehicle is When the speed of the vehicle is smaller thansmaller than

the critical curve speed of a bend, the vehicle the critical curve speed of a bend, the vehicle has has no difficulty in negotiating the bendno difficulty in negotiating the bend..

When the vehicle is When the vehicle is just at the critical curve just at the critical curve speedspeed, it is travelling at the limit of adhesion to , it is travelling at the limit of adhesion to the road. It the road. It cannot brake or steer onto a cannot brake or steer onto a tighter coursetighter course to avoid an unexpected hazard to avoid an unexpected hazard without risking side-slipping.without risking side-slipping.

When the speed of the vehicle is When the speed of the vehicle is greater thangreater than the critical curve speed, the frictional force is the critical curve speed, the frictional force is not large enough to provided the necessary not large enough to provided the necessary centripetal force. As a result, the vehicle centripetal force. As a result, the vehicle side-side-slipsslips. .

40

Travelling round a bendTravelling round a bend

If the bend is banked, the vehicle may If the bend is banked, the vehicle may negotiate a bend at a higher speed negotiate a bend at a higher speed because a component of the normal because a component of the normal reaction contributes to the centripetal reaction contributes to the centripetal force as shown:force as shown:

41

Travelling round a bendTravelling round a bend

When a bicycle (or motorcycle) travel When a bicycle (or motorcycle) travel round a bend, it is necessary to lean it round a bend, it is necessary to lean it into the turn. Otherwise the centrifugal into the turn. Otherwise the centrifugal forces will throw the bicycle (or forces will throw the bicycle (or motorcycle) over on its side.motorcycle) over on its side.

42

Driving safetyDriving safety Major reasons of car accidents [3]:Major reasons of car accidents [3]:

Following too closely to vehicle in Following too closely to vehicle in front.front.

Losing control of vehicle. Losing control of vehicle.

Careless lane changing. Careless lane changing.

Improper or illegal turn. Improper or illegal turn.

Starting negligently. Starting negligently.

43

Many people are injured or even killed Many people are injured or even killed by traffic accidents in each year. by traffic accidents in each year. Whether as pedestrian, driver or Whether as pedestrian, driver or passenger, we should be aware of passenger, we should be aware of road safety to avoid traffic accidents. to avoid traffic accidents.

Almost all modern cars are equipped Almost all modern cars are equipped with some with some safety featuressafety features which can which can help to protect the driver and help to protect the driver and passengers during an impact (see next passengers during an impact (see next page figure). page figure).

44

DonDon’’t drink and drive!t drink and drive! Alcohol Affects Your Driving Alcohol Affects Your Driving

AbilityAbility Impairs judgment of speed and Impairs judgment of speed and

distance distance Slows down reaction time Slows down reaction time Affects the co-ordination of the Affects the co-ordination of the

body's movements body's movements Blurs vision Blurs vision Gives a false sense of confidence Gives a false sense of confidence

http://www.td.gov.hk/road_safety/drink_driving/index.htm

45

DonDon’’t drink and drive!t drink and drive! The effect of blood alcohol The effect of blood alcohol

content (BAC)content (BAC)

No. of No. of standard standard drinksdrinks

BACBAC

(mg/100 (mg/100 ml)ml)

EffectsEffects

11 20 - 3020 - 30 noticeable effects (on noticeable effects (on perception etc.)perception etc.)

55 100 to 150100 to 150 intoxicationintoxication

2424 240 to 360240 to 360 unconsciousnessunconsciousness

3636 360 to 480360 to 480 coma or deathcoma or death

BAC < 50 ml/100 ml under the law in Hong Kong!http://www.sciencetechnologyaction.com/lessons/53/NCT.pdf

46

References:References:1.1. G. Bethell and D. Coppock, G. Bethell and D. Coppock, Physics firstPhysics first. .

Oxford: Oxford University Press, 1999.Oxford: Oxford University Press, 1999.

2.2. G. Alderton, D. Berrington, and M. G. Alderton, D. Berrington, and M. Brimicombe, Brimicombe, Revise for GCSE Science: Revise for GCSE Science: SaltersSalters. Oxford: Heinemann, 1999. . Oxford: Heinemann, 1999.

3. http://www.roadsafety.gov.hk/eng/index.html

4.4. P. K. Tao, P. K. Tao, The Physics of Traffic Accident The Physics of Traffic Accident InvestigationInvestigation: Oxford University Press, 1987: Oxford University Press, 1987

5. http://www.td.gov.hk..6. http://www.sciencetechnologyaction.com/lesso

ns/53/NCT.pdf

47

Example 1Example 1

A car skids with all four wheels A car skids with all four wheels locked and leaves skid marks of 19.3 locked and leaves skid marks of 19.3 m on a tarmac road surface, 5.6 m on m on a tarmac road surface, 5.6 m on a concrete pavement and 15.4 m on a concrete pavement and 15.4 m on grass. The coefficients of friction of grass. The coefficients of friction of the tarmac, concrete pavement and the tarmac, concrete pavement and grass are 0.74, 0.82 and 0.46 grass are 0.74, 0.82 and 0.46 respectively. Estimate the speed of respectively. Estimate the speed of the car at the start of skidding.the car at the start of skidding.

48

Example 1Example 1

The kinetic energy of the skidding The kinetic energy of the skidding car is equal to the total work done car is equal to the total work done against friction over different against friction over different surfaces. Hencesurfaces. Hence

where where 11, , 22, , 33 are the coefficients are the coefficients of friction of the tarmac, concrete of friction of the tarmac, concrete pavement and grass respectively. pavement and grass respectively.

21 1 2 2 3 3

1

2mu mgs mgs mgs

49

Example 1Example 1

The speed of the car at the start of The speed of the car at the start of skidding is given byskidding is given by

1 1 2 2 3 3

1

1

2 2 2

22.6ms

81.2 kmh

u gs gs gs

50

Example 2Example 2

A car skids with all four wheels locked A car skids with all four wheels locked for 38.5 m and then runs into a tree. for 38.5 m and then runs into a tree. The impact speed of the car is The impact speed of the car is estimated from the damage to be 40 estimated from the damage to be 40 kmhkmh-1-1. The coefficient of tyre/road . The coefficient of tyre/road friction is found to be 0.76. Estimate friction is found to be 0.76. Estimate the speed of the car prior to skidding.the speed of the car prior to skidding.

51

Example 2Example 2

The car decelerated on skidding. The The car decelerated on skidding. The decelerating force decelerating force FF is given by is given by

If the average deceleration over a If the average deceleration over a skidding distance is skidding distance is aa, then, then

F mg

F ma mg a g

(Newton(Newton’’s Second Law)s Second Law)

52

Example 2Example 2

Applying the equation of uniform Applying the equation of uniform acceleration,acceleration,

2 2 2 2v u as gs 2 2u v gs

2

1 1

40 3.6 2 0.76 9.81 38.5

26.4 ms 95.1 kmh

u

53

Example 3Example 3A car skidded 12.6 m before hitting a A car skidded 12.6 m before hitting a parked van on its side. The two vehicles parked van on its side. The two vehicles became locked together and skidded a became locked together and skidded a distance of 3.6 m before coming to a stop. distance of 3.6 m before coming to a stop. The coefficient of tyre/road friction was The coefficient of tyre/road friction was found to be 0.71. Total mass of the car and found to be 0.71. Total mass of the car and its passengers was 1,260 kg and total mass its passengers was 1,260 kg and total mass of the van and its load was 2,100 kg. What of the van and its load was 2,100 kg. What was the speed of the car before impact? was the speed of the car before impact? What was its speed at the start of skidding?What was its speed at the start of skidding?

54

Example 3Example 3

Since the car and the van were Since the car and the van were locked together after impact, they locked together after impact, they had a common post-impact velocity had a common post-impact velocity vv. From the skid mark, we get. From the skid mark, we get

1 1

2 2 0.71 9.81 3.6

7.08 ms 25.5 kmh

v gs

55

Example 3Example 3

Applying the principle of Applying the principle of conservation of momentum, we haveconservation of momentum, we have

1260 2100 0 1260 2100 7.08Au

A A B B A A B B A Bm u m u m v m v m m v

1 11260 21007.08 18.9 ms 68.0 kmh

1260Au

The pre-impact speed of the carThe pre-impact speed of the car

56

Example 3Example 3

The speed of the car at the start of The speed of the car at the start of skidding isskidding is

2

2

1 1

2

18.9 2 0.71 9.81 12.6

23.1 ms 83.1 kmh

Au u gs