1969-12-03 — Page 23

REFERENCE LIBRARY.

30EC1969

HALL

育教俄華 頁三第張六第 日四廿月十年西己曆夏 WAH KIU YAT PO

郭日僑華

三期星日三月二十年九六九一届公年八十五國民華中

罗僑榮

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170英文中學會考試題預習專欄

经道英文書院主編號

物理科 (五)

STABLE EQUILIBRIUM

If a body is slightly tilted, its centre of gravity is raised and the body will return to its original position, it is said to be in stable equilibrium, When such a body is displaced, the weight of the body, acting downward at its centre of gravity, will cause it to fall back to ita original position.

UNSTABLE EQUILIBRIUM

If a body is slightly displaced, its centre of gravity is. lowered and tends to topple over, it is said to be in unstable equilibrium, When such a body is disturbed, its weight acting downward at its centre of gravity will cause it to fall over

NEUTRAL SQUILIBRIUM

If a body is displaced, it neither raise nor lower its centre of gravity, the body is said to be in neutral equilibrium. When such a body is displaced, it takes up a new position readily.

Join G

The resultant weight of the L-shape wire acts at Q

16x

0000

(10-0,0)

63)

30-30,0

20,0 - 30

-42

Centre of gravity is 44 on from G, on the line joining &12*

Example 2

A circular uniform flat disc has a radius of 4 in, and a hole A cut in it has a radius of 1 cm. Find the distance of the centre of gravi remaining portion from 0.

of the

PHYSICS (5)

THE MOMENT OF FORCE AND CENTRE OF GRAVITY

THE MOMENT OF A FORCE,

When a force acts on a body, it may have a rotary motion. That is, it may turn or tends to turn, The turning effect of a force about a particular axis is known as the moment of the force about tha axis. It is measured by the product of the applied force and the perpendicular distance from the pivoting point to the line of action of the force.

Homent force I distance:

Units dyne-ompenz

pdl-ft, 1b.wt.-ft;

newton-m, kg.wt.-n.

There are no special names for the units of moment.

For the syllabus of Forn 5 we concern about coplanar forces, that is the forces whose lines of action are all in the same plane, The moments are about a point rather than about an axis.

The moment of a force has a sense clockwise or anti-clockwise, and if we give one of these senses a positive sign and the other a negatively. Usually the anti-clockwise moments are positive. Moments can be added algebraically.

THE PRINCIPLE OF MOMENTS-

If a body is in equilibrium, the sum of the moments of the forces on the body about any point (axes) is zero.

Experiments to verify the Principle or Moments,

the Parallelogram of forces, the Triangle of forces th are important. Candidates moy read any text-book for their reference.

COUPLES

If two equal and parallel force, but with. different lines of action and different senses, act on a body, the body tends to turn, Suma of the resolved parts of the forces are zero, the forces do not produce equilibrium. The body turns with a moment which is the product of one of the forces and the perpendicular distance between them.

CENTRE OF GRAVITI

P

The moment of forces about X = P(1+0) - PL

Pa

A body is composed by particles, each of which is pulled by the Earth. These pulls on different parts of a body have a resultant which passes through a point called the centre of gravity of the body. This resultant force is called the weight of the body. Thus, the centre of gravity of a body is efined as the point of application of the weight

body.

METHODS OF FINDING THE CENTRE OF GRAVITY

PLUMBING LINE METHOD

The body, usually a plane body, is hung freely from two different positions together with a plumb line. Pencil marks are made along the lines, The point of intersection of these two lines is the centr of gravity of the body. Hanging it from a third point) will check the correct point has been found,

KNIFE-EDGE METHOD

The body is balanced on a thin edge and line is drawn along the edge. The centre of gravity of the body must lie along this, line. The body is balanced again on another position and another streight line. is drawn. The intersection of these lines is the centre of gravity.

CENTRE OF GRAVITY AND STATES OF EQUILIBRIUM

body is in equilibrium if the resultant of the forces acting upon it ie zero, he ease. with which the equilibrium of a body may be upset depends upon the position of its centre of gravity. In general, there are three types of equilibrium:-) stable, unstable and neutral,

STABLE EQUILIBRIUM

UNSTABLE EQUILIBRIUM

PROBLEM PROCEDURE

NEUTRAL UILIBRIUM

When forces are not acting at a point, the equilibrium conditions for such a system will only be maintained if

1. FO 2. M-0

In solving problems, the suggusted steps 126.1=

Stan 1. Draw the sketch diagram to illustrate the

points of application of all the foose concerned,

Step 2. Set up an equation of P- O Step 3. Reactiong of the supports are essential Step 4. Set up another equation on M-0 Step 5. Solve the simultaneous equations for all

the required forces, or unknowns. When dealing with problems cono

concerning Centre of Gravity of combined body, the weights of all regulaï areas are aoting individually on their own centres of gravuty. The resultant weight acts at the centre. of gravity of the combined body. The centre or gravity is calculated by moments with two arbitrari! chosen axes.

Example 1

Find the centre of gravity.

of a piece of wire 28 cm long, bent into an L-shape with the upright part 16 cm

long.

AB and BC are chosen as turning axes

G and G2 are the centre

2

of gravity of parts. AB, BQ respectively G. and

G, are the mid-po

of AB, BC.

If w gm.wt. ≈ weight per unit length of the wire, then the weight acting at

16w and at

12W gm.wt.

The total weight W × (16 + 12)w gmont. W acts at G

low acte at q

12w aota at 2

With AB as turning axis,

Wx

12W BG,

12w.x

12 6 28

24

With BC as turning axÍS

Ny 28wy

16w x

... 16 x 8

16 x 8 28

ins, C.G. of the L-shape is

AB and 30 respectively.

24

and

44

om.

the centre of gravity of the removed part.

ɑ be the centre of gravity of the disc,

be the centre of gravity of the remaining part wgn, wt. be the weight per unit area of the diso. of removed part- 7(1)

Wt, of the whole disc -7(4) w gm.wt

Wt. of the removed part (42 – 1) 7 w garwt.

Moments of the weights of parts about a point" moment of the result about the same: point,

π w × 0, 0 + (42 - 1] 7 × × Q1Q - 4° 77 w × GO

1 + 15 x 0 0

GO

16 x 4. 64-1

Ans. the C.G. of the remaining portion is

from O Exercise (5)

4.2

*DIO.

1. A thin uniform metal plate ABCD is 2 ft. square.

It is folded so that the side AB lies along the line joining the mid-points of AD and BC, and " the folded part is pressed flat. Find the position of the centre of gravity of the folded plate.

A single force is applied to the bar in Fig. to maintain it in equilibrium as shown. The weight of the bar is neglected. What is the magnitude of the force? Where should it ha applied?

2 b

10 ft.

Weights of 3, 6, 9, and 12 1b.wt, are fastened to the corners of a light wire frame 2 ft. square, Find the position of the centre of gravity of a the system.

Fig. 2 represents a double-decker bus under tast for stability. The distance between the outside.. edges of its wheel is 2.45 metres and the angle of tilt when it begins do topple is 30 degrees from the vertical. Find (1) the height of C.G. of the bus, (ii) the horizontal force which, applied through G.d. will just hold the bus in position when leaning at an angle of 45 degree. Weight of the hus is 8000 kg.wt.

Fig. 2