EQUILIBRIUM
1.
In figure below shows a
uniform bar of woo of weight and length 80 cm pivoted as shown. A force of 20 N
keeps the bar in equilibrium.
2.
The following figure shows
a light bar pivoted at a point and acted on various forces such that it remains
in equilibrium.
i)
Total clockwise moments
ii) Total anticlockwise moments
iii) Magnitude of force F
(Hint: Turning point at Pivot)
3.
A uniform bar of negligible
weight is balanced under action of several forces as shown in the figure below.
i)
The value of x.
ii) The length of the bar.
4.
The diagram below shows a
uniform bar, 1 m long. In equilibrium under the action of the forces shown,
Determine the;
i)
Total clockwise moments.
ii) Total anticlockwise moments.
iii) Weight W, of the bar.
5.
The following diagram shows
a uniform bar of length 1.0 m in equilibrium. The bar is pivoted at point P and
is under the action of a single force of 10 N.
6.
The diagram below shows a
bar of length 1.0 and negligible weight, pivoted at its centre.
7.
The uniform bar shown in
the diagram below has a weight of 3 N and a length of 1.0 m.
8.
The following diagram shows
a horizontal uniform beam resting on a rigid support on one end while the other
end is supported by a vertical rope. The beam is 10 m long and mass of 40 Kg. A
girl of mass 50 Kg walk along the beam from the point A towards point B.
i)
Maximum tension of the rope
ii) Distance moved by the girl from point A
9.
A 20 m uniform plank AB of
mass 20 Kg is put on a wedge such that it does not balances horizontally. Three
pupils of mass 50 Kg, 35 Kg and 30 Kg sit on the plank at a distance of 3 m, 7 m and
18.5 m respectively from A. How far must the wedge placed from A for the
arrangement to balance horizontally.
10.
The diagram below shows a
uniform metre rule in equilibrium under the forces shown.
Determine the weight of the
metre rule
- The line of action of a force 48 N is
at perpendicular distance of 1.5 m from the point. Find the moment of the
force about the point.
- The moment of a force about a point is 1120 Nm. If
the magnitude of a force is 5600 N, find the perpendicular distance between
the point and the line of action of the force.
- The moment of a force is 1000 Nm. If
the line of the force is at perpendicular distance of 100 m, find the
magnitude of a force.
- 100 g weight is suspended 45 cm from
the pivot A of a light rot;
i)
If a weight W suspended
20.5 cm from the pivot is used to balance the 100 g weight, determine the W.
ii) If a 300 g weight is used to balance the 100 g weight, determine
the distance of the 300 g from the pivot.
- A lever of negligible weight is 2.0 m
long. If a 0.80 N weight at one end balances a 0.20 N weight at the other
end, how far is the fulcrum from the 0.80 N weight?
16.
A metre rule is pivoted at
its mid-point and a 50 g mass is suspended from 20 cm mark. What mass balances
the rule when suspended from the 65 cm mark?
17.
A metre rule is pivoted at
its mid-point. A 1.0 N weight is suspended from the 30 cm mark and a 2.0 N weight
from the 90 cm mark. Where an upward force of 3.0 N must be applied to balance
the ruler?
- A uniform rod AB, 2.0 m long, weighs
0.40 N. If weights of 0.80 N and 0.40 N are suspended from A and B
respectively, at what point will it balance?
- A metre rule is pivoted at its
mid-point. A 0.60 N weight is suspended from one end. How far from the
other end must a 1.00 N weight be suspended for the rule to balance?
- A heavy uniform metal beam AB weighs
500 kg is supported at its ends by two supports. The beam carries a weight
of 3000 kg at distance of 1.5 m from the end A. If the beam is 4 m long,
determine the thrusts on the supports A and B.
- A uniform half-metre rule, AB is
balanced horizontally on a knife edge placed 5 cm from B with a mass of 80 g
at B. Find the mass of the ruler.
- A uniform bar AB of height 5 m weighs
60 N. The bar is supported at a horizontal position by two vertical string
X and Y. If string X is 0.6 m from A and string Y is 1.8 m from B. Find the
tension in the strings.
- A metre rule is suspended from two
balances calibrated in Newton. One balance is attached at the 5 cm mark,
the other at the 80 cm mark. If the rule weighs 1 N and downward forces of
2 N are applied at the 10 cm and 60 cm mark, find the readings on the
balance.
- A taped rod of mass 200 g is 160 cm
long. It balances at its mid-point when a 150 g mass hangs from the narrow
end. How far is the centre of gravity from the thick end?
- A uniform half-metre rule is freely
pivoted at the 15 cm mark and it balances horizontally when a body of mass
40 g is hung from the 2 cm mark;
i)
Draw a clear diagram for this arrangement
ii) Calculate the mass of the rule.
- A steel uniform beam has a weight of
25,000 N. If it is 8 m long, what force must be applied to lift one end?
- A metre rule is pivoted at its
mid-point. Vertically downward forces of 2 N and 6 N are applied at the 10 cm
and 80 cm marks respectively. What vertical upward force must be applied at
the 90 cm mark if the rule is to balance horizontally?
- A uniform scaffold plank 4 m long
weighs 100 N and rests on trestles at each end. A man of weight 700 N stands
1 m from one end. What forces do the trestles exert on the plank?
29.
A uniform bridge AB, 30 m
long and weighing 200,000 N rests on supports at each end. Find the forces on
the supports when a car of weight 10,000 N is 4 m from A and a lorry of weight
100,000 N is 10 m from B.
30.
A heavy metal beam AB
weighs 250 N is supported at its ends by two supports. The beam carries a weight
of 1500 N at a distance of 0.75 m from end A. If the beam is 2m long, determine
the thrusts at supports A and B
31.
From the figure below,
calculate the reactions R1 and R2
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