2 force and acceleration

8/18/2019 2 Force and Acceleration

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Types of Forces

A force is a push or pull acting upon an object as a result of its interaction withanother object.

Force is a quantity that is measured using the standard metric unit known as theNewton. A Newton is abbreviated by an "N." To say "1. N" means 1. Newton of force. !ne Newton is the amount of force required to give a 1kgmass an acceleration of 1 m#s#s. Thus$ the following unit equivalency can bestated%

There are a variety of types of forces.

Contact Forces Action-at-a-Distance Forces

&rictional &orce 'ravitational &orceTension &orce (lectrical &orce Normal &orce )agnetic &orce

Air *esistance &orceApplied &orce+pring &orce

Applied Force - An applied force is a force that is applied to an

object by a person or another object. If a person is pushing a

desk across the room, then there is an applied force acting

upon the object. The applied force is the force exerted on the

desk by the person.

Gravity Force((also known as Weight- The force of gravity is the force with

which the earth$ moon$ or other massively large object attracts another objecttowards itself. ,y definition$ this is the weight of the object. All objects uponearth e-perience a force of gravity that is directed "downward" towards thecenter of the earth. The force of gravity on earth is always equal to the weight of the object as found by the equation%

Fgrav ! " # g

where g /.0 N#kg on (arth2 and m mass in kg2Nor"al Force - The normal force is the support force exerted

upon an object that is in contact with another stable object. For


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example, if a book is resting upon a surface, then the surface is

exerting an upward force upon the book in order to support the

weight of the book. n occasions, a normal force is exerted

hori!ontally between two objects that are in contact with each

other. For instance, if a person leans against a wall, the wall

pushes hori!ontally on the person.

Frictional Force The friction force is the force e-erted by a surface as anobject moves across it or makes an effort to move across it. There are at leasttwo types of friction force sliding and static friction. Thought it is not alwaysthe case$ the friction force often opposes the motion of an object. &or e-ample$

if a book slides across the surface of a desk$ then the desk e-erts a friction forcein the opposite direction of its motion. &riction results from the two surfaces being pressed together closely$ causing intermolecular attractive forces betweenmolecules of different surfaces. As such$ friction depends upon the nature of thetwo surfaces and upon the degree to which they are pressed together. Thema-imum amount of friction force that a surface can e-ert upon an object can be calculated using the formula below%

&frict 3 4 &norm

Air $esistance Force - The air resistance is a special type of

frictional force that acts upon objects as they tra"el through the

air. The force of air resistance is often obser"ed to oppose the

motion of an object. This force will fre#uently be neglected due

to its negligible magnitude $and due to the fact that it is

mathematically di%cult to predict its "alue&. It is most

noticeable for objects that tra"el at high speeds $e.g., a

skydi"er or a downhill skier& or for objects with large surfaceareas.

Tension Force - The tension force is the force that is transmitted

through a string, rope, cable or wire when it is pulled tight by

forces acting from opposite ends. The tension force is directed

along the length of the wire and pulls e#ually on the objects on

the opposite ends of the wire.


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%pring Force - The spring force is the force exerted by a

compressed or stretched spring upon any object that is

attached to it. An object that compresses or stretches a spring

is always acted upon by a force that restores the object to its

rest or e#uilibrium position.


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)ass and 5eight

QUESTION' (hen a person diets, is their goal to lose mass orto lose weight) *xplain.

ANSWER' +enerally, people diet because they wish to reduce

the amount of matter on their body - they wish to remo"e the

blubber . o people diet to lose mass. If one wishes to lose

weight, they could get a six fold reduction by mo"ing to the

moon.

The mass of an object refers to the amount of matter that is

contained by the object the weight of an object is the force of

gra"ity acting upon that object. ass is related to how much

stuf is there and weight is related to the pull of the *arth $or

any other planet& upon that stuf . The mass of an object

$measured in kg& will be the same no matter where in the

uni"erse that object is located. ass is ne"er altered bylocation, the pull of gra"ity, speed or e"en the existence of

other forces. For example, a /-kg object will ha"e a mass of /

kg whether it is located on *arth, the moon, or 0upiter its mass

will be / kg whether it is mo"ing or not $at least for purposes of

our study& and its mass will be / kg whether it is being pushed

upon or not.

The weight of an object $measured in 1ewton& will "ary

according to where in the uni"erse the object is. (eight

depends upon which planet is exerting the force and the

distance the object is from the planet. (eight, being e#ui"alent

to the force of gra"ity, is dependent upon the "alue of g - the

gra"itational 2eld strength. n earth3s surface g is 4.5 16kg

$often approximated as 78 16kg&. n the moon3s surface, g is

7.9 16kg. +o to another planet, and there will be another g

"alue.


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FORCE and ACCELERATION

Newton6s second law of motion can be formally stated as follows%

The acceleration of an o&'ect as produced &y a net force is directlyproportional to the "agnitude of the net force in the sa"e direction as the

net force and inversely proportional to the "ass of the o&'ect)

This verbal statement can be e-pressed in equation form as follows%

a ! Fnet * "

The above equation is often rearranged to a more familiar form as shown below.The net force is equated to the product of the mass times the acceleration.

Fnet ! " # a

Newton6s second law of motion pertains to the behavior of objects for which alle-isting forces are not balanced. The second law states that the acceleration ofan object is dependent upon two variables the net force acting upon the objectand the mass of the object. The acceleration of an object depends directly uponthe net force acting upon the object$ and inversely upon the mass of the object.As the force acting upon an object is increased$ the acceleration of the object isincreased. As the mass of an object is increased$ the acceleration of the object isdecreased.

http://www.physicsclassroom.com/Class/newtlaws/u2l2d.cfmhttp://www.physicsclassroom.com/Class/newtlaws/u2l2d.cfm


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Net Force

The net force is the "ector sum of all the forces that act upon

an object. That is to say, the net force is the sum of all theforces, taking into account the fact that a force is a "ector and

two forces of e#ual magnitude and opposite direction will

cancel each other out.

!bserve the following e-amples of summing two forces%


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*:A;?@ ?IA+=A

8 component of force gives acceleration to the bo-.

F+!F)cos,.!/.).0!12N

F+!")a

12N!/kg)a

a!0"*s/


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3+A4563

9icture given below shows the motion of two bo-es under the effect of applied force. &rictionconstant between the surfaces is 7!.)8. &ind the acceleration of the bo-es and tension on therope. (g!1."*s/ sin,.!.2 cos,.!.0

A1(*=

&ree body diagram of these bo-es given below.

:omponents of force$

F+!F)cos,.!,.).0!/8N

F9!F)sin,.!,.).2!10N

N1!"1)g-Fy!,.-10!1/N

N/!1.N

&f1 and &f7 are the friction forces acting on bo-es.

Ff1!7)N1!.8)1/!80N and Ff/!7)N/!.8)1.!8N

5e apply Newton6s second law on two bo-es.

"1: Fnet!")a

/.-T-Ff1!,)a /.-T-80!,)a


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"/: T-Ff/!1)a T-8!a

a!/0"*s/

T!20N

*:A;

+ince force acting on 8 is double of force acting on


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*:A;


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"/: ,g-T!,)a


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Fnet!f s

f s!1/

k)"g!1/

k),)1.!1/

k!.8

*:A;


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A1(*=

&ree body diagrams of the system are given below.

Acceleration of the 1 kg bo- is 7m#s7. Thus$ net force acting on this bo- is>

Fnet!")a

Fnet!1.)/!/.N

Nor"al force of the &o? is>

N!1..;8.-2.!0.N

Fnet!0.-8.-Ffriction


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/.!0.-8.-k)0.

k)0.!/.

k!1*8


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+ystem in the given picture below$ bo- moves under the effect of applied forceand gravity with 1m#s7 acceleration. &ind the friction constant between the bo-and surface.

AN+w(r

&ree body diagram of the system is given below>


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&orces acting on the bo- perpendicularly>

,.;0.!11.N

,o- moves downward with 1m#s7 acceleration.

Fnet!")a

2.-8.-Ffriction!1.)1

/.-k)11.!1.

1.!11.k therefore k!1*11


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UNIFORM CIRCULAR MOTION!I"!WA# CUR$E

An o%&ect that mo'es in a circle at constant s(eed ' issaid to e)(erience *ni+orm circ*lar motion,

The magnit*de o+ the 'elocit- remains constant. %*t the

direction contin*o*sl- changes as the o%&ect mo'es

aro*nd the circle,


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/eca*se the acceleration is de0ned as the rate o+change o+ 'elocit-. a change in direction o+ 'elocit-

constit*tes an acceleration. &*st as a change in

magnit*de o+ 'elocit- does,

1An o%&ect mo'ing in a circle o+ radi*s r at a constant

s(eed ' has an acceleration whose direction is toward

the centre o+ the circle and whose magnit*de is aR 2 '3r

1This is called centripetal acceleration or radial

acceleration,

For circ*lar motion.

FR 2 mar 2 m'3r

E4AM5LE

A 7888 kg car rounds a cur"e on a at road of radius B8 m at a

speed of BC km6hr$7B m6s&. (ill the car follow the cur"e, or will

it skid) Assume


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$a& the pa"ement is dry and the coefficient of static friction is Ds

E 8..

$b& the pa"ement is icy and Ds E 8./B

A1(*=

$a&

F1 E mg E 7888 x 4.58 E 4588 1

F= E ma= E m "/6r E 7888 x 7B/6B8 E CB88 1

Ffr E Ds F1 E 8. x 4588 E B588 1

ince Ffr G F= therefore the car will not skid and follow

the cur"e.

$b&

Ffr E Ds F1 E 8./B x 4588 E /CB8 1

ince Ffr H F= therefore the car will skid


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*:A;


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g tanJ E "/6r

or tan J E "/6gr

$c&for r E 58 m, " E 58 km6hr E 58 x78886K88 E //./ m6s

tan J E //.//64.5 x 58 E 8.K

J E K/8

QUI6

The banking cur"e for a design speed " is J7. (hat banking

angle J/ is needed for a design speed of /".

Ans ' $a& J/ E C J7

$b& J/ E / J7

$c& tan J/ E C tan J7

$d& tan J/ E / tan J7

2 force and acceleration

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