This page will help you answer questions
such as: What is a moment? What is a mechanical advantage? How do you
calculate the turning effect of a force? Why are the turning effects of a
force so important? Where do we apply the advantages of the turning effect
of a force?
Forces can cause an object to rotate and the
turning effect of the force is called a
moment.
If a resultant force acts on an object
about a fixed turning point (the pivot) it will cause the object to
rotate e.g. turning a nut with a spanner, applying a screwdriver, opening a door
fixed on hinges. The pivot might also be called the
fulcrum.
The rotational or turning effect, the moment,
has a magnitude easily
calculated from the formula:
M = F x d, where M
= the moment of a force (Nm), F = force applied (N)
and d (m) is the
perpendicular distance from the pivot point to the line of action of the
force.
You
get the maximum moment by pushing/pulling the spanner at a right angle
(at 90o)
to the line (d) between the pivot point and the line of action where the
force is applied.
Screwing or unscrewing a nut on a bolt
This is illustrated by the simple diagram
of a spanner above. The turning
force is F x d.
The pivot point is the central axis of
the bolt on which the nut is being turned by the spanner.
To tighten or loosen the nut you apply a
force, to the best mechanical advantage, at 90o to the spanner
arm itself.
Applying the force at any other angle
less than 90o reduces d and so reduces the effective moment of
the force.
You determine the force F by how hard you
push/pull the end of the spanner, but d is a fixed distance for a given
spanner.
This is one of many situations where you
are applying a force to increase the effect of your hand muscles.
The size of the moment increases with
increase in distance d or applied force F.
The longer the spanner, the greater is d,
hence the greater the
turning force generated - the greater the mechanical advantage of the
lever system.
All sorts of machines use turning forces to increase a
force (or pressure) effect to gain a mechanical advantage from a
printer's press to a bicycle.
Relative comments on the three 'moment' situations A to C
Situation A
With the longer spanner, and applying
the force perpendicular (at 90o) to the line from the point
of applying the force (end of 'handle') to the pivot point (centre of the nut or bolt),
you generate the maximum moment (F x d).
The perpendicular distance d, is the shortest distance between the pivot
and the line of action of the force
Situation
B
If you apply the force at any other
angle than at 90o to the perpendicular distance line (d), d
will always be shorter and hence a smaller moment is generated by
applying the same force as in situation A.
Note that when the line of action of
the force is down the 'spine' of the spanner, d is zero and the moment
is zero.
This is shown by the blue force
arrow at situation D.
Situation
C
With the shorter spanner, despite
applying the force at 90o (perpendicular), d is smaller and
you cannot generate as large a moment as in situation A.
So, for the same applied force,
the moment is smaller for the smaller length spanner.
Situations A and B and riding
a bicycle
You get situation B (from above) pedalling a
bicycle when your foot and pedal are near the top or bottom of the
crank's cycle - the pivot point is the crank axle. If you press
downwards, you are creating the minimum moment - the minimum driving force forward.
At the top of the 'pedal cycle', if the direction of force is
downwards through the crank, the turning force, the moment, is very small.
BUT, at the top of the 'pedal
cycle', you soon learn to push
forwards to utilise the maximum moment and generate the maximum
force so that you mimic situation A where you are generating a force
at 90o to the pivoting axle and the line of action of the
force -
maximum moment = F x d on the above diagram.
You get the maximum force
transferred when the crank and pedal are parallel to the ground and
you exerting your maximum downward force at 90o to the
pivot point (axle) and the line of action of the force.
The centre of mass
and the stability of a free standing object
The centre of mass is a single point
in the object through which the whole weight of an object is considered to
act.
Its quite easy to envisage where it
is for a regular shape e.g. a rectangular block - shown in profile in
the diagram below. It is coincident with what is termed the 'centre
of gravity' of an object.
A standing object becomes unstable
when the vertical line through its centre of mass falls outside its
base, which effectively acts as a base - this happens if it is
tilted over on one edge, thereby creating a moment - a turning force.
Under these conditions, the weight of the object causes a
turning effect about the pivotal base.
The idea is illustrated by the
diagram below of a regular shaped block, shown in profile, and tilted at various angles (but it could be a
bus going round a corner!).
1. The vertical line from the centre
of mass passes right through the centre of the block's base.
The object
is completely stable - no moment (turning force) is generated.
2. The vertical line from the centre
of mass still passes through the base, but not its centre, and the block is unstable, so it
will wobble a bit from side to side, and eventually settle down in an
stable upright position as in 1.
The edge of the block touching the
surface acts as a pivot point.
The weight of the block creates an
anticlockwise moment (turning force) that makes the block fall back in
an anticlockwise direction, but not sufficient to topple the block over
on its longer side.
3. The vertical line from the centre
of mass passes outside of the block's base. The block won't even
wobble, it is highly unstable and will just topple over on its longer side (to
become stable!).
Again, the edge of the block
touching the surface acts as a pivot point.
Again, the weight of the block
creates a clockwise moment (turning force) that makes the block fall
over in a clockwise direction, and sufficient to topple the block
over on to its longer side.
Tests on stability in terms of the
centre of mass are important e.g. road vehicles like buses are safety
tested to see the maximum angle allowed when tilted over without
toppling over in an accident.
