Force
diagrams
Forces are vectors, that is they are described by a magnitude and
a direction. For example, if a marble was pushed across a table with a
force of 20 newton applied, due North would describe the force used to
move the marble. One way of showing forces in direction and magnitude
is by using force diagrams. In this system, an arrow is drawn in the direction
of the force, the length of the line being proportional to the magnitude
of the force.
By using force diagrams it is possible to estimate the resultant force
- that is the net force exerted on an object.
Adding
and subtracting forces in a straight line
If an object is being pushed in one direction by a force of 20 newton,
and another force of 20 newton is applied in exactly the opposite direction,
then the resultant force is 20 - 20, or zero newton. With no resultant
force, the motion of the object will not change. If it is stationary,
it will stay that way, if it is moving, it will keep moving in the same
direction and speed.
Increasing the first force by 5 newton means that the object will
accelerate in the direction of action of this new force, and the resultant
force is 25 - 20, or 5 newton.
When forces are in a straight line the resultant force is simply the
arithmetical sum of, or difference between, the two forces.
Forces at an angle
Once forces are applied at an angle to each other the calculation becomes
more complex. The simplest way of finding the resultant force, when two
forces are applied, is by a technique called a parallelogram of forces,
where the force can be estimated from the diagram.
Parallelogram of forces
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A parallelogram is a four
sided figure where both opposite sides are of the same length, and
parallel to each other. To estimate a resultant force it is first
necessary to draw the direction and magnitude of each force. The parallelogram
is completed by drawing in the two other sides parallel to the two
forces and the diagonal measured. This diagonal represents the resultant
force. |
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Uses of force diagrams
Tugs are often used to tow large ships. Two tugs pulling at an angle
produce a resultant force that can be calculated. Two people pulling on
a tree trunk to drag it out of the ground can calculate their resultant
force - and can be out of the way of the trunk when it falls!
The resultant of any two forces can be calculated using the parallelogram
of forces.
Vector diagrams
Three or more forces can also be estimated, using vector diagrams. In
fact, the force diagrams used above are based on vector diagrams. In vector
diagrams, each force is represented by its vector arrow and added in turn.
The resultant force is measured from the tail of the first force to the
head of the last.
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