Solutions to Force - Worksheet 1

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(c) Pressing on the brakes: The hydraulic system transfers pressure to the pads that grip the discs or ... The problem is that constant hard braking can cause theĀ ...
ANSWERS TO FORCES _ WORKSHEET 1

Question L: Describe the typical effects of external forces on bodies including: - friction between surfaces - air resistance Let us considerhow externalforces affect the motion of cars. When dealing with friction and carsthere are different types of friction to consider. (i) Static friction: This is the friction betweenthe tyre and the road when the car is stationary or when the tyre rolls without slipping. It is this static friction force that provides the reaction force that causesthe wheel to roll and the car to move. When it is removed(e.9. a carboggedin mud or trying to drive on ice) the wheelsrotate but becausethere is no reaction force betweenthe tyres and the surface,the car will not move. Static friction is also the force that holds a car in place when it is parked on a slope. (ii) Kinetic friction: This is the friction betweentwo surfacesthat are moving with respectto eachother. It applies,for instance,when hard-brakingstopsthe wheels from turning and the car skids to a stop. (iiD Rolling friction: There is someloss of energyand somedecelerationfrom friction for any real wheel in motion, and this is sometimesreferredto as rolling friction. It is partly friction at the axle and can be partly due to flexing of the wheel which will dissipatesomeenergy. (iv) Internal friction: this is the friction that occursbetweenmoving parts of a car such as the pistonsand cylinders. When an object moves through a fluid (liquid or gas) it has to push the particlesof fluid out of the way. When the fluid is air this is known as air resistance. Air resistanceopposesthe motion of a car. Streamlining,i.e. sloping the shapeof the car, so that air flows over it smoothly, greatlyreducesair resistance.Air resistanceincludesthe movementof a car through still air as well as the movementof air againstthemotion of the vehicle (wind).

Question 2: Outline the forces involved in causing a change in the velocity of a vehicle when: - coastingwith no pressure on the accelerator - pressing on the accelerator - pressing on the brakes - passingover an icy patch on the road - climbing and descendinghills - following a curve in the road Note that becauseyou are only askedto outline the forces,your answersshould be very brief. You need maybe a sentenceor two and an appropriatediagram. I have supplied more of a description& explanationof the aboveforces in order to help your understanding.

Inthe diagramsthat follow:.Ep: force of engine,fe: air resistance,Jr: force due to friction, jr : force due to gravityJ. : centripetal force and y - velocity. (a) Coasting with no pressure on the accelerator: When there is no pressureon the acceleratorthere are no forward forces. If there were no backward forces then the car would keep moving forever at the samespeed.However there is rolling friction, air resistanceand friction betweenthe moving parts of the car acting to opposethe motion of the car. Consequentlythe car will gradually slow down and stop.

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(b) Pressing on the accelerator: Pressingon the acceleratorincreasesthe rate at which fuel is fed to the cylinders of the car. This in turn increasesthe rate of rotation of the wheels and increasesstatic friction. The reaction force to this increasesthe forward force on the car allowing it to overcomethe forces that retard the motion. If the acceleratoris held in a position where it balancesthe forces opposing motion, the car will maintain constantspeed. If the acceleratoris presseda little harderthe car will increaseits speed.

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(c) Pressing on the brakes: The hydraulic systemtransferspressureto the pads that grip the discs or drums. The pads exert a frictional force on the discs or drums that is in the opposite direction to the motion of the wheel. This slows the rate at which the wheels are rotating. This causesa forward force betweenthe wheels and the road and the reaction force to this forward force causesthe car to slow down and stop. If too much pressureis applied to the brakesthey completely stop the rotation of the wheels.This causesthe wheelsto slide (skid) over the road and since sliding (kinetic) friction is less than static friction the car travels a much greater distancebefore stopping. --v

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(d) Passing over an icy patch on the road: Ice reducesfriction to a very low value so pressingon the acceleratorwould speedup the rate of rotation of the driving wheels but they would not be able to grip the road. The wheelswould spin on the ice but the car would have no traction and would not increaseits speed. The loss of friction would be disastrousfor braking and steering.The brakeswould stop the wheels from rotating but accordingto Newton's first law) a car in motion continuesin uniform motion unlessactedon by a force. Hencethe car would skid with liule changein speeduntil it was clear of the icy patch or until it met an opposingforce such as the back of the car in front. Also becauseof the lack of friction, turning the wheelswould not be able to producea centripetalforce. Consequentlythe driver would not be able to steerand the car would continue in a straightline even if the road didn't.

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Climbing and descendinghills: All objects on Earth have a gravitational force on them pulling them towards the centre of the Earth. This is true whetherthe object is on level ground or on a slope such as a hill. A car on a hill has a gravitationalforce acting vertically down. This applieswhetherthe car is climbing (ascending),descendingor parked on the hill. The gravitationalforce mg, can be divided into componentsperpendicularto the plane and parallelto the plane. The parallel componentappliesa force of mg sinOdownhill.

The parallel componentappliesa force mg sinOdownhill. (e) Climbing a hill:

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When a caris climbing a hill the driver has to pressharderon the acceleratorto overcomethe gravitationalforce downhill.

(f) Descendinga hill:

f, When the car is descendingthe hill the driver doesnot have to pressthe acceleratoras hard since someof the downhill force is suppliedby gravity. On steephills the engine may have to supply no force at all and the car will coastdown the hill. In thesecases the car has to be slowed by the brakes.The problem is that constanthard braking can causethe brakesto overheatand becomelesseffective. An alternativeto constant braking is to choosea lower gearto descendthe hill (eg "Steep Descent- Trucks Use Low Gear" signs on the road). Using a lower gearensuresthat the wheelsturn more slowly and are subjectto less static friction.

(g) Following a curve in the road: A body will travel with uniform velocity unlessacted on by a force (Newton's first law). Thereforea force is requiredto changethe direction of a car. When following a curve in the road, the necessaryforce is a "centripetalforce". This force always actstowards the centreof the motion i.e. towards the centreof the road's curve. The force is suppliedby the friction between the tyres and the road and has a value of: F, : mu'lr,where Fr: centripetalforce, m: massof car"v : linear velocitv of car. r : radius of curve.

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Question3: Interpret NewtonosSecondLaw of Motion and relate it to the equation XF = ma Newton's secondlaw statesthat the net force on an object is equalto the product of its mass and its accelerationand that the accelerationis in the direction of the force. Thus, if a force of a given size is appliedto severaldifferent masseswe will find that the largerthe massthe smallerthe accelerationof the object. The term "net force" refersto the sum of all the forces acting on the object. Hencethe X (capital sigma) in front of the F in the formula. E standsfor "the summation of'. Examples:(i) At the school athleticscarnival, athletesprefer to use a light shot put rather than a heavy one becausethey are able to give the light shot put a larger acceleration.This meansthat it will attain a larger velocity as it leavesthe hand and so travel further before it hits the ground. (ii) In cars, if the sameengine is installed in a heavy and a light car, the light car will attain the higher accelerationfor the sameapplied force from the engine.

Question4: Identify the net force in a wide variety of situations involving modes of transport and explain the consequencesof the application of that net force in terms of Newtonts SecondLaw of Motion Note the words "identifytt and "explain" Considerthe forces acting in planes,trains and cars. Planes: The physics of flight is extremely complex. Let us considera planejust at take-off. There are two componentsof the net force that we have to consider. First there are the horizontal componentsof the motion that provide the planes forward motion and secondly there are the vertical forces acting that causethe plane to lift from the ground. The vertical motion of the plane is causedby dynamic lift (as opposedto static lift such as a balloon where the object rises in a more densefluid). The dynamic lift of an aircraftis caused by two factors, both of which rely on the plane moving forward through the air.

The first is causedby the wing sloping upward towards the direction of forward motion so that the air is deflecteddown. The secondis due to the shapeof the wing. The wing is curved

so that air travelling over the top of the wing travels a greaterdistancethan air travelling underneaththe bottom of the wing. This resultsin the air travelling over the top occupying a greatervolume in the sametime and so being less dense.While the differencein density would createvery little lift for a stationaryobject, there is substantiallift for a moving object. This is due to the Bernoulli principle that is beyondthe scopeof the current HSC physics course. It usedto be done in a Fluid Dynamics Half Elective someyearsago. The forward thrust of a jet plane is causedby the reactionforce to the exhaustgases (Newton's third law). A bigger engineor more enginesgives a greaterforward force. There is also the force of air resistanceopposingthe motion of the airqaft. The net force is forward and the accelerationis given by a: Fn.1/m. Note that as a plane takes off, the net force acting on the plane at any point in time is the sum of the vertical &horizontal forces acting on the plane atthatpoint in time. This would require a vector diagramto determinethe net force on the plane at any point in time. Trains: There are severaldifferent types (steam,diesel,electric) but all rely on the principle of a force causing the wheels to turn and the static friction betweenthe wheels and the rail providing the forward (reaction)force to causethe train to move. There is friction between the moving parts of the train as well as air resistancebut the overall result is a net force forward which results in the forward accelerationof the train. The train will attain a constant velocity when the forward force is equal to the sum of the backwardforces. Cars: Theseexperiencemuch the sameforces as trains exceptthat there is friction between the tyres and the road rather than betweenthe wheels and rail. Tyres have atread pattern,so the friction betweenthe tyres and the road is usually greaterthan the correspondingfriction betweentrain wheels and the rails. There is friction betweenthe moving parts of the car as well as air resistancebut the overall result is a net force forward which results in the forward accelerationof the car. The car will attain a constantvelocitv when the forward force is equal to the sum of the backwardforces.

A Note on Friction for the Teacher Two types of friction can occur between a car tyre and the ground, a) static friction, and b) kinetic friction. Static friction is when the tyre maintains grip or traction on the road surface,whereaskinetic friction (as the name implies) is when the tyre is moving relative to the ground. To illustrate static friction, considerfor a moment a dot on the tyre's surface.Your vehicle is moving forward (let's say it's moving very slowly), and your tyre rotatesso that the dot comesinto contactwith the ground at a certainpoint. Since a cartyre compressesa bit on the road's surface,there'sapproximately lOcm of tyre flat againstthe road at any given time. As your car moves forward, the tyre rotates,and oncethe dot touchesthe ground at a given point, the tyre and the ground move at the samerate relative to the car. That is, the dot on the tyre and the point on the ground remain in contactuntil the tyre reachesthe end of that 10cm strip of contact, when it is pulled upward from the ground to rotate around top and back to the ground.

An example of kinetic friction from the illustration above would be that the dot on the tyre reachesa point on the ground, but the dot and point move away from one another.In real life this would be if you hit the brakes and skid, or if you hit the acceleratorand burn out or spin your tires (e.g. in the snow or mud). The problem with kinetic friction is that it is weaker than static friction. Thus, when you hit the brakes, if your tyres lock up (you will hear the squealingtyres againstthe road) you are now in kinetic friction and your car will slow down less quickly comparedto when your tyres were in static friction with the ground. That is why you pump your brakes...also why anti-lock braking systems(ABS) were developed. Read more: http://wiki.answers.com/Q/Flow_does_friction act on_a_car#ixzzlyl iQAOKu

Question 5: The mass of an object is a measureof the amount of matter contained in the object. Mass is a scalarquantity. The weight of an object is the force due to gravity acting on the object. Weightis avectorquantity. W-mg, whereW-weightforce, m:masS, g: acceleration due to gravity.

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