5. Centre of gravity of simple bodies and systems of particles Moments and couples. Equilibrium of a rigid body or bodies.
Introduction to the concept
How many nails can you balance on 1 nail?
hammer a nail into a block standing up right how many nails can you balance on the nail
the balancing tight rope walker
What does the word Static mean? http://dictionary.cambridge.org/
Statics means something that is not moving.
How can objects be static?
Why would something not be moving ?
How do objects move?
Objects can go up/down left/right.
Cast your mind back to your childhood, did you ever have a 'spinning top', a toy that spins on the spot?
A gyroscope that spins internally but does not move across the table.
Not all movements are up/down left/right, forces can also cause things to rotate.
If there are always forces on objects,
there must be a force on the other side that prevents the movement of the object
Some of these restoring forces are less than obvious because they dont make us move, they stop us moving
like friction only works against motion between two bodies always slowing you down
Forces are vectors, so we can find a resultant force on an object, no matter how many forces are acting on it. If the resultant force is zero, the forces must be balanced.
Balanced forces cause no acceleration (This means that the object will remain stationary or carry on moving at a constant speed.)
Wait a moment !!!
What's a moment?
A moment of a force is the turning power of a force.
what turns ....
a door ... where do you open a door from .....
You would be correct in saying that a more powerful force has a greater turning effect, BUT ....
the position the force is applied to the object is also important.
the law of the lever
the key to understanding is that the distance is actually the perpendicular distance between the line of action of the force and the fulcrum, the point about which the object rotates
A moment of a force is the turning effect of that force.
This is calculated by the Force x Distance the line of the force is applied from the fulcrum
The Fulcrum center Lever
The Load center Lever
The Effort center Lever
What about gravity?
The 3rd law?
So something remains Static if there is NO NET FORCE acting on it
i.e. Forces Up = Forces Down
Forces Left = Forces Right
& Forces Clockwise = Forces Anti-Clockwise
If something is static, well then it doesn't move.
The forces acting on it are balanced
It doesn't move up or down, Force Up = Force Down
It doesn't move left or right. Force Left = Force Right
It doesn't spin, Clockwise moments = Anti-clockwise moments.
So we want to be able to balance forces in order to have static objects!
The Basic Lever by wally
Using the details of the crane explain how it is able to lift such masses
caluculate the load on the left if it was to be perfectly balanced at
max mass at the max radius for the standard and long setup.
the Level crossing demonstration pg 190.
Where would you open it from ???
Where does the weight act from?
Does this have moments ? When does the barrier turn (open) ?
What are the units of moments?
Some basics / explanations / survival tactics
- Anti-Clockwise moments get a positive sign by convention, therefore, clockwise moments are negative
- Moments are often called torque
- If the effort of the force passes thru the fulcrum / hinge, there is no perpendicular distance therefore the moments of that force = 0 Nm
- A force has 3 properties, (i) Magnitude (ii) Direction (iii) Line of Action
- The hinge is not just a point! It is a line that operates perpendicular to the plane of rotation. Forces that cause rotation must be measured perpendicular to this line
Net forces are the balancing of different forces. Those that are going in the same direction should be added together and those that go in opposite directions should be subtracted from each other.
combine & resolve forces going
- up / down
- left / right
- anticlockwise / clockwise
When we have different forces going up/down we find the net force and call this the resultant.
Now we can calculate the some of the moments about any point