Download Data-Based Question

(c) Figure 5.12 shows the same force F being
applied to a metal rod at positions A, B and
C on separate occasions to lift a large stone.
metal
rod
large
stone
State the position, A, B or C, in which force F
exerts the largest moment about the small
stone. Give a reason for your answer.
(position B)
F
F (position C)
small stone
F
(position A)
▲ Figure 5.12
Position B. At position B, the perpendicular distance of the line of action of the force to the pivot
(small stone) is the longest, resulting in the largest moment about the pivot.
(d) Figure 5.13 shows an angler holding a stiff
fishing rod (of negligible mass) in a horizontal
position to support a fish of mass 3 kg.
Calculate the force F needed to keep
the rod in the horizontal position.
(Take g = 10 N kg−1)
30 cm
90 cm
F
supporting
hand
lifting
hand
3 kg
Taking moments about the supporting hand,
F × 0.3 = (3 × 10) × (0.3 + 0.9)
F = 120 N
▲ Figure 5.13
Data-Based Question
2.
Cranes such as the one in Figure 5.14 are used
to move heavy loads across large distances.
The maximum load a crane can carry depends
on its working radius, i.e. the maximum length
of the jib at a specific angle. A crane operator
can refer to the data in Table 5.1 to find out the
maximum load a crane can lift for a particular
working radius at an angle of 30°.
working
radius
load
jib
30°
▲ Figure 5.14
▼ Table 5.1
Working radius/m
14
20
28
36
Maximum load/N
900
630
450
350
(a) Using the data in Table 5.1, deduce the maximum moment provided by the crane.
Maximum moment = F × d
= 630 × 20 × cos 30° = 10 910 N m
[Note: Each working radius and corresponding maximum load in Table 5.1 should give the same
maximum moment.]
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