1969-12-17 — Page 26

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and

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and

are the final ties of them.

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170英文中學會考試題預習專欄

堅道英文書院主編

物理科

(1) For bodies which collide and travel independently

there-after-

22

(2) For bodies which.

thereafter.

lide and travel together

where v is the common velocity aftar collision

(七)

FRICTION

PHYSICS (7)

500(1

500 x 17

531 (3 sig. figures)

Ans. The tension of the cable is 531 10,4

Example 2

A 16 lb. body is dragged along a norizontal surface by a horizontal force of 10 lb.wt, The codfficient of friction between the body and the surface is 0.4. Starting from rest how far does the hody move in 3 seconds?

Planning the solution

FORCE" ( continue)

The dyne (dyn), poundal (pal) and newton ()

called absolute units of force and are defined by the above relationships •

The absolute unit in c.g.. system is one dyne which will cause a mass of one gram to accelerate at oner cm/sec/seo.

The absolute thit in f.p.s. system is one poundal. which will cause a mass of one pound to accelerate at one ft/sec/sec.

The absolute unit in m.k.. system is cne newton which will cause a mass of one kilogram to accelerate at one-metre per sec per seo.

MASS AND WEIGHT

Different bodies exhibit different resistances to a change in their motion. Each body is said to possess a different inertia.

The numerical measure of inertia is called the nass of a body is the quantity of inertia of body. It ja constant. It does not vary wherever it is placed.

asses of different bodies are compared by beam balance.

The pull of the Earth on a body is called the weight of that body. Weight of a body is a kind of force. It is a vector quantity. The weight of a body: varies according to where the body is placed to the -latitude and altitude. Weight is measured by spring

balance.

Since Fa mấy

therefore, W =\mg

where W is the weight of the body

m is the mass of the body

a is the acceleration due gravity of the

local place...

As the value of g varies according to places Bo is the weight W. To save the trouble of thia variation of the multiple g, another unit is commonly used. This is the gravitational unit of force.

One grat-wt or gram-force is a force equal in aize to the pull of the Earth on a mass of one gram

One lb-wt or lb-force (lb-f) is a force equal in size to the pull of the

on a mass of one pound.

One kg-t or kgf is a foros equal in size to the pull of the Earth on a mass of one kilogram.

If the value of g is known, the relationship or gravitational and absolute units of force are related

m-wg cynes

1 Ab-wt

g pål

8 newtona

Gravitation Unita

|pound-weight

Absolute Unite.

poundal

f.p.s. The attraction of the The force which gives a

earth one-pound:

mass on a

gram-weight

The attraction, of the earth on a one- gram mana

m.k.. Kilogram-weight

The attraction of

the earth on a one- kilogram mags

one-pound mass an

acceleration of one Toot per seo per sec.

dyne

The force which gives

a one-gram mase an.

acceleration of one om per sec per sec

newton

The force which givès. a one-kilogram mess an acceleration of one metre per ssc per s860.;

NEWTON'S UNIVERSAL LAW OF GRAVITATION.

This law states that any two bodies attract each other with a force which is

(1) directly proportional to the masses of the two

bodies, and

(2) inversely proportional to the square of the

distance between these bodies.

A body resting on a smooth horizontal surface is acted on by two vertical foros t

of the body

N-normal reaction WN

Suppose à force exerts horizontally on the body and it moves an a rough surface. As a result an additional force arises. This force, known as the friction, is always aote so as to oppose the motion.

it

As the force 7 is gradually increased from zero, the friotion force, f, increases also, being always equal bat oppose to F. There is a limit to the size of the frictional force. This maximum value depends

on

(1) the material and state of the surfaces in

contact,

(2) the normal contact force which each, body

exerts on the other

I KN

where is the coefficient of friction; for that. pair of surfaces, and is the normal contact force or normal reuotion.

Motion occurs when has been made just greater van this maximum possible value. The latter force is known as the limiting friction.

The following table tefers to the conditions the body when acted by a horizontal force. Fi.

Applied Force F

Friction

Less than N

arjuls to N greater than N

PROBLEM PROCEDURE

Step 1 Draw a diagram.

Step 2 Isolate body and indicate all forces acting

on it

Step 3 Tabulate x- and y-components of all forces

acting on the body and equations of

Solution

Force X-c

y-component

F

10.

(10

8(10

Forces to the right and upwards are positivel

Forods to the left and downwards are negative

(at equilibrium is obviously

2 x 3.6

16·

State.

at rest

[10

0.43

16/32 x

same as the applied ford

Fat rest.

· 7,2

at rest

acceleration

Step 1. Draw a diagram to represent the problem

situation, labelling all quantities involved and specifying the unknown as well as the known forces,

Step 2. Isolate the body under consideration and

indicate all forces acting on the body. Disregard the forces exerted by the body on other things else...

Step 3. Tabulate the x- and y- components of all the

forces acting on the body.

Step 4. Utilize Newton's second law, to x- and y-

components separately:

Stop 5. Attempt to solve the two equations, If more

than two unknowns are there.

Step 6. Consider another relations as

Jixample 1

Wm mg

and

A life is accelerated upward at 2 ft/seo. If it weighs 500 lb, what is the tension in the supporting cable?

Planning the golution

Step 1. Diagram. Step 2.

Isolate the body and indicate forces on it, Step 3: Set F=ma Step 4. Solve equations

SOLUTION

As there is no vertical component of acceleration. the acceleration is 7.2 ft/sec/seo in horizontal direction towards the right.

The body is dragged along be a constant force, the acceleration is constant, for which the equation of motion

Sutat is applicable

distance moved. initial velocity 0

t is the time taken

0+ £ 7.2 x 32

32.4 Ita

The distance moved in three seconds is 32.4 It..

Example 3

A 32 1b body is dragged along a practically frictionless, horizontal surface by a 2 lhe weight hanging from a cord which passes over a frictionless: pulley so mounted that the cord pulls the body parallel to the surface. What acceleration is experienced by the body and its attached weight? What is the tension in the cord?

Mg

w=mq

The force that causes motion is the 21b.wt.

F

IMPULSE AND CONSERVATION OF MOMENTUM

Impulse of a force is the change or momentum of

a body:

Ft-mv - mu

The principal of Conservation of Momentum states that if two or more bodies collide, the sum of momenta before collision is equal to the sum of momenta after the collision provided there is no external forces aot on the system.

Bum of momenta before collision sum or momenta after collision

The resultant force (18

-T) Ibut.

Therefore

(1-7)g - na

T-W

500 x 2

Se

ft/sec2

2 x 32

1.94

+2

ft/sec/seo

To finɑ une tension, we 18olate any one or they

two blocks. In this case, the 2-lb mase is isolatedi.

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