Moments of Force

1
16-Nov-09
Moments of Force
2
If the see saw is 4 metres long. Dad has a mass
of 90 kg. His daughter has a mass of 35 kg and
is sitting on the end of the see saw. Where must
dad sit to make the see saw balance?
d
2 metre
35g
90g
ACW Moments CW Moments 2 x 35g (d)
x 90g 70 90d
d 0.78 metres
3
A seesaw in a playground consists of a beam AB of
length 4 m which is supported by a smooth pivot
at its centre C. Jill has mass 25 kg and sits on
the end A. David has mass 40 kg and sits at a
distance x metres from C, as shown in Figure 1.
The beam is initially modelled as a uniform rod.
Using this model, (a) find the value of x for
which the seesaw can rest in equilibrium in a
horizontal position. (b) State what is implied
by the modelling assumption that the beam is
uniform. David realises that the beam is not
uniform as he finds he must sit at a distance 1.4
m from C for the seesaw to rest horizontally in
equilibrium. The beam is now modelled as a
non-uniform rod of mass 15 kg. Using this
model, (c) find the distance of the centre of
mass of the beam from C.
4
d
2 metre
25g
40g
ACW Moments CW Moments 2 x 25g (d)
x 40g 50 40d
d 1.25 metres
The modelling assumption assumes that the mass of
the beam acts at the centre because it is a
uniform beam
5
2 metre
1.4
x
25g
40g
15g
ACW Moments CW Moments 2 x
25g 15gx 1.4 x 40g 50
15x 56 15x 6
x 0.4 m
6
3 m
5 m
4 m
2 m
3N
5N
6N
R1
R2
Calculate R2 Taking moments about R1
ACWM CWM (3 x 3) (9 x R2) (5 x 6) (11
x 5) 9 9R2 30 55
9R2 76 R2
8.44 N
7
1N
Y
2.5m
0.5 m
X
Take moments about Y CW ACW 0.5X 1 x 3 X
6N X 1 Y Y 5
8
4N
2N
3m
dm
X
Rod is in equilibrium so X 4 2 ? X 6 Take
moments about the 4N end of the rod CW ACW 6d
2(3 d) 6d 6 2d 4d 6 D 1.5
9
4m
4m
A
B
C
60g
90g
Reaction at A and B must equal 60g 90g if there
is equilibrium and we are told the reaction at A
is twice the reaction at B A B is in the ratio
2 1 this is equal to 150 N Hence A 100N and B
50N
10
4 - d
d
4m
A
B
C
60g
90g
Taking moments at A CW ACW 60gd
4 x 90g 8 x 50g 60d 360 400 60d
40 d 0.67m
11
A
B
C
A plank AB has mass 40 kg and length 3 m. A load
of mass 20 kg is attached to the plank at B. The
loaded plank is held in equilibrium, with AB
horizontal, by two vertical ropes attached at A
and C, as shown in Figure 1. The plank is
modelled as a uniform rod and the load as a
particle. Given that the tension in the rope at C
is three times the tension in the rope at A,
calculate (a) the tension in the rope at
C (b) the distance CB.