tiII t H AID ICENTRIPETAL ACCELERATIONAN OBJECT MOVING AT ACONSTANT SPEED IN A CIRCLEEXPERIENCES CENTRIPETALACCELERATION

5 PEF.DE

DlREN.tfdYEIRERAT1ONCHANGING CONSTANT

fEIFLER Eff CONSTANT CHANGING

THE VELOCITY AT ANY INSTANT 15TANGENT TO THE CIRCLEFORCE AND ACCELERATION AREPERPENDICULAR TO THE VELOCITYDIRECTED INWARD TOWARDS THECENTRE OF THE CIRCLE

r

DERIVINGCENTRIPETALACCELERATIOT

air

it

V Vz V R RER

SIMILAR TRIANGLESz

R

V

a Ef f v

a 2fII4 R v2 4M

ac CENTRIPETALACCELERATION Ft

a YI 4I v TANGENTIALVELOCITY F

R RADIUS OFCURVATURE m

T PERIOD

IF THE NET FORCE ON AN OBJECTCAUSES UNIFORM CIRCULARMOTION WE CALL THIS NETFORCE THE CENTRIPETAL FORCE

mac E CENTRIPETALFORCE N

m MASS 1kgai CENTRIPETALACCELERATION Fst

EXAMPLETA CAR IS TRAVELLING AT 10 s 136 FAND MAKES SEVERAL TURNSCALCULATE THE CENTRIPETALACCELERATION FORa A CURVE OF RADIUS 50 m

HIGHWAY EXIT

b A CURVE OF RADIUS 10 mPARKING LOT

C A CURVE OF RADIUS 4MCITY STREET

EXAMPLETA CAR IS TRAVELLING AROUND ACIRCULAR TRACK OF RADIUS 80.0 m

THE COEFFICIENT OF FRICTION IS0.80 IN DRY WEATHER ETHEL'SNEPROVIDES

a DETERMINE THE MAXIMUMTRACK SPEED

DRAW A FREEBODY DIAGRAM

WRITE DOWNNEWTON'S SECONDLAW Fc Mad

REPLACE E WITHTHE VECTOR SUMOF ALL FORCESCONSIDER INWARDSTO BE THE POSITIVEDIRECTION

b WHAT IS THE LAP TIME AT THISSPEED

c IF THE TRACK IS WET THECOEFFICIENT OF FRICTION IS0.50 DOES THE MAXIMUMVELOCITY INCREASE DECREASEOR STAY THE SAME

EXAMPLETCIVIL ENGINEERS DESIGN EXITRAMPS AND CURVES TO ASSISTDRIVERS CONSIDER A CAR TRAVELLINGAT 60 T AROUND A 50M RADIUSCURVE WHAT ANGLE SHOULD THEROADBED HAVE TO ACCOMODATETHIS TURN BY BANKING TILTING THE ROADBED

THE NORMAL FORCE PROVIDESTHE INWARD Fc

I.IEoi

EXAMPLETA 4.0kg BUCKET OF WATER IS SWUNGIN A VERTICAL CIRCLE OF RADIUS 1.5 m

IF THE PERIOD OF REVOLUTION IS0.75 s WHAT IS THE TENSION INTHE ROPE AT

a THE BOTTOM OFTHE CIRCLE i l I

I 11.52I

b THE TOP OF THE CIRCLE

c WHAT IS THE MINIMUM SPEEDAT THE TOP OF THE CIRCLEIF THE WATER DOES NOTSPILL FROM THE BUCKETMINIMUM SPEED OCCURS WHEN IT IS AT AMINIMUM THIS IS THE CASE IF TENSION IS ZERO