manhattan press (h.k.) ltd. © 2001 hkasl physics examination format and allocation of marks...
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Manhattan Press (H.K.) Ltd. © 2001
HKASL Physics
Examination format and allocation of marks
Paper Format Weighting
1 (1 hour 10 min.)Structured-type
questions (4)33%
2 (1 hour 50 min.)MC (25) 30%
Essays (2 out of 4) 22%
3 (2 years) TAS 15%
Manhattan Press (H.K.) Ltd. © 2001
What is statics?What is statics?• Statics is the branch of physics concerned with the analysis of loads (force, torque/moment) on physical systems in equilibrium.
•When in equilibrium, the forces in the system will have zero resultant and zero turning effect which will not cause any change in the motion of the object.
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Zero resultant
•If the block is in equilibrium, the resultant force acting on it is zero.
•Resolve horizontally,
F1 cos = F2
•Resolve vertically,
F1 sin = F3
F1
F2
F3
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Vector approach
•If an equilibrium system consists of n forces,
F1
F2
F3
0321 FFF
0..021 in FeiFFF
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Vector Addition
Triangular law Parallelogram law
A
C
B
ACBCAB
A
B D
C
ADACAB
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Turning effect of a force ─ rotate about axes
Pivot (or fulcrum) ─ position of axes
12.1 Turning effect of a force (SB p.170)
axis
axis
axis
axis
pivot
pivot
pivot
pivot
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Moment ─ the turning effect of a force
Moment arm ─ perpendicular distance between the force and the pivot
Unit of moment: N m
Moment
= Force Moment arm
= F d
moment arm
door hinge
Moment12.1 Turning effect of a force (SB p.170)
door hinge (pivot)
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Note: the longer d, the smaller will be the force required.
MomentMoment of F1 = F1 d1
Moment of F2 = F2 d2
Same turning effect
F1 d1 = F2 d2
As d1 > d2,
F1 < F2
Moment12.1 Turning effect of a force (SB p.171)
door hinge
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Which requires a smaller force ? (d2 > d1)
case 1 case 2
Moment12.1 Turning effect of a force (SB p.172)
force
pivot
force
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Moment ─ clockwise or anticlockwise
Moment12.1 Turning effect of a force (SB p.172)
an anticlockwise moment a clockwise moment
pivot
pivot
anticlockwise
clockwise
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Principle of moments
Two moments :same in magnitude, but in
opposite direction
cannot turn
Moment of F1
= 10 0.4
= 4 N m (anticlockwise)
Moment of F2
= 5 0.8 = 4 N m (clockwise)
12.2 Principle of moments (SB p.174)
pivotpivot
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pivot
Take the mid-point of the ruler as the pivot
= 1.6 10 0.1 + 1 10 0.4
= 5.6 N m
12.2 Principle of moments (SB p.175)
Total clockwise moment
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pivot
Take the mid-point of the ruler as the pivot
= 0.4 10 0.2 + 1.2 10 0.4
= 5.6 N m
12.2 Principle of moments (SB p.175)
Total anticlockwise moment
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Principle of momentsclockwise moment
anticlockwise moment
When a body is in balance,
Total clockwise moment
= Total anticlockwise moment
12.2 Principle of moments (SB p.175)
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Answer
Class Practice 1Class Practice 1 :: Edmond, Jessie and Tracy are sitting on a seesaw at the positions shown in the figures. Given that their masses are 65 kg, 40 kg and 50 kg respectively, and the mass of the seesaw is negligible. Find the distance of Jessie from the pivot (d) when the seesaw is balanced.
400 N 500 N 650 Npivot
d
1 m
1.7 m
12.2 Principle of moments (SB p.176)
Apply the principle of moment,
Clockwise moment = Anticlockwise moment
650 x 1.7 = 500 x 1 + 400 x d
d = 1.51 m
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•Find the reaction from the pivot.
400 N 500 N 650 Npivot
d
1 m
1.7 m
R
Since the system is in equilibrium, the resultant is zero.
R = 400 + 500 + 650
= 1550 N
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Pivot O20 N 10 N
0.5m 0.2m 0.2m
30 N
R = 60 N
XX Y
•Take moment about XX Clockwise moment
Take moment about other points
= 30 x 0.7 + 10 x 0.9 = 30 Nm
Anti-clockwise moment = 60 x 0.5 = 30 Nm
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Pivot O20 N 10 N
0.5m 0.2m 0.2m
30 N
R = 60 N
XX Y
•Take moment about YY Clockwise moment
Take moment about other points
= 60 x 0.5 = 30 Nm
Anti-clockwise moment = 10 x 0.1 + 30 x 0.3 + 20 x 1 = 1 + 9 + 20 = 30 Nm
0.1m
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Conclusion
•When an object is in equilibrium, the sum of clockwise moments about any point is equal to the sum of anticlockwise moments about that point.
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•Two blocks are placed on a light metre ruler as shown. Find the reactions at X and Y.
2 kg3 kg
0.75 m
0.25 m
X Y
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•Step 1: Draw all forces acting on the metre ruler (in equilibrium).
2 kg3 kg
0.75 m
0.25 m
X Y
30 N20 N
RX RY
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•Step 2: Apply the principle of moment for objects in equilibrium.
2 kg3 kg
0.75 m
0.25 m
X Y
30 N20 N
RX RY
Take moment about X (any point),
20 x 0.25 + 30 x 0.75 = RY x 1
RY = 27.5 N
Resolve vertically,
RX + RY = 20 + 30
RX = 50 – 27.5 = 22.5 N
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More on moment of force
Pivot O
dF
Find the moment of F about O.
d sin F
Moment of F about O
= Force x perpendicular distance from O
= F x d sin = Fd sin
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More on moment of force
Pivot O
dF
Find the moment of F about O. (Alternative method)
Moment of F about O
= Force x perpendicular distance from O
= F sin x d = Fd sin
F cos
F sin
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Example 2 A sign of mass 5 kg is hung from the end B of a uniform bar AB of mass 2 kg. The bar is hinged to a wall at A and held horizontal by a wire joining B to a point C which is on the wall vertically above A. If angle ABC = 30o, find the tension in the wire and the reaction exerted from the hinge.
Take moment about A,
(Tsin 30o)(2d) = (20)(d) + (50)(2d)
T = 120 N
Resolve vertically,
Ry + Tsin 30o = 20 + 50
Ry = 10 N
Resolve horizontally,
Rx = T cos 30o
Rx = 103.9 N
R = sqrt(Rx2 + Ry
2) = 104.4 N
= tan -1(Ry/Rx) = 5.50o
hinge
30o
C
A
20 N
50 N
T T sin 30o
T cos 30o
Rx
Ry
d d
R
Tension is 120 N and the reaction from the hinge is 104.4 N at an angle of 5.50o to the horizontal.
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Moment and couple
•Couple ─ consists of 2 equal and opposite parallel forces whose lines of action do not coincide (重疊 ).
torque of couple = F x d/2 + F x d/2 = Fd
F
Fd/2 d/2
F
F
dd
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Short test after each chapter
•Homework (SQ 2, 5, LQ 1)
•Next day 1
•Short test : Moment
•Next day 1