A couple is where 2 forces equal in size but opposite in direction cause a body to turn.
Any force can be turned into a force and a couple, any force and couple can be turned into a singular force ..
To Deal with Statics questions
In these questions the idea is that the
Sum of the moments = the moment of the Sum
the sum being the Resultant of all the forces. Pick a point and about that point find the moments of each of the forces and add them together, they will equal the moment of the resultant forces.
In physics it can be said that the sum of the anti-clockwise moments = sum of the clockwise moments, this is the same thing, but usually involves selecting a point inbetween the various forces, this is not necessary.
The key is determining what point to use as the reference when calculating moments.
Golden Rule for picking a point for moments,
ask yourself which point will rule out the greatest number of variables,
which point will leave you with an equation involving only those variables which will prove helpful
(i.e. variables which you already have from another equation).
This usually will be where a number of forces (or lines of these forces) go through through the point you are using as your anchor point
This may not always be the shortest equation. Look for trigonometry to help you find the perpendicular distance from the line of action.
Remember that when calculating the moment of the force it is the perpendicular distance between the line of action of the force and the fulcrum. It may help to visualise the line of action by extending the force vector on both sides.
When dealing with forces and couples remember that you calulate the moment of the forces and then add (or subtract) the couple (depends on its direction of spin)
Find the resultant of the forces in x and y and using Pythagoras theorem this will give you the magnitude of the resultant force but the location can only be found by resolving the following
the sum of the various moment = the moments of the sum
this means that if you find the moments for each of the forces and combine them (adding & subtracting) this will be equal to the moment of the resultant about the same point as the point about which the moments of the forces was discovered
For objects hinged/leaning to a wall remember to put in two perpendicular forces.
One of these forces goes into the wall (resultant) and one up along the wall (friction)
If it’s a standard question involving a ladder leaning against a wall then it’s a good idea to make the length of the ladder 2L.
Remember that the centre of gravity of a triangular lamina is two-thirds of the way from the vertex to the midpoint of the opposite side.
An Applet to show the forces on a rod suspended from a wall
Go through the page with the applet, look at the (combined) reaction at the wall and the tension. At this stage it is key to understand where these forces are going and why they are going there.
If you think you understand the forces at play you can try to locate the Resultant at the wall vector and the
examine the 2 different scenarios with the beam being massless and with it having a mass
change the position of the weighted ball, in the middle, left, far left .....
change the mass of the weighted ball
drag the suspension wire up and then right down
when the wire goes up what happens the mag of the vectors ? why ? it has to do with the angle and the components of the force
work at this to note scenarios and rules ....
Take a meter stick place one end on a bench, support the other end in your hand, keeping the stick level.
Put a small pile of coins on the end of the stick that is in your hand.
Let the stick go, but then catch it in a bit.
What happened? Do all things fall at the same rate?
Try putting the coins at the 50cm mark and try again.