CSEC Physics: Types of Levers, Reactionary Forces and Center of Gravity
There are three types of levers:
First Class Levers
Second Class Levers
Third Class Levers
The difference between all of these classes of levers is what component of the lever is in the center. As you know, a lever has 3 parts, the load (what is being lifted), the fulcrum (the turning point), and the effort (where force is applied to lift the load).
For first class levers, the fulcrum is in the center.
For second class levers, the load is in the center.
For third class levers, the effort is in the center.
You can remember this with the FLE acronym:
Before we start discussing types of levers in more detail, you must first understand reaction forces.
Say for example, we have a book on the table (maybe Breath, Eyes, Memory if you haven't picked it up in a while). This book has the force of gravity acting on it constantly. This force would continue to push the book down all the way to the center of the earth if it had nothing to counteract of challenge it.
The book, however does not plunge down to its destruction in the Earth's core because the table is pushing against it. It is pushing it upwards with a force known as a reaction force.
This pair of forces is an action-reaction pair: equal and opposite forces acting on two different objects in contact. This may sound familiar, as it aligns with Newton's Third Law, that every action has an equal and opposite reaction. The reaction force from the table is called the normal force because this force is oriented normal (perpendicular) to the surface of the table.
The force of gravity acts through a specific point known as the center of gravity. This is the average location of all the weight in an object. In regular shaped objects, it is found it the geometric center of the object- so the center of gravity of a sphere would be directly at the center.
But how do you find the center of gravity of an irregular object?
Say, for example, we must find the center of gravity of a piece of cardboard.
First, you make a plumb line by tying a nut at one end of a string and a nail at the other. Punch three holes (a bit larger than the nail) at different points near the edges of the cardboard. Insert the nail into one of the holes and hold the setup by the nail. Once the setup becomes steady, mark a line along the thread on the cardboard. Hold the setup by the nail in other holes and draw lines along the plumb line. You will notice that all the lines intersect at the same point. This point is the center of gravity of the cardboard.
This brings us nicely into the concept of equilibrium and stability.
Equilibrium/Stability
The center of gravity helps us to understand why things topple over. After all, if gravity only pulls things downwards, why would it cause something to fall over? That happens because gravity is concentrated at a certain point (which we know is the center of gravity. When the center of gravity is not over the pivot or base of an object, the object will fall over.
Look at this pencil, for example:
The pencil will obviously topple over. This is because the center of gravity is not directly over the pivot, and a perpendicular distance is created between the force of gravity and the pivot. Sounds familiar right? That's because this is the formula for a moment. So, a turning effect is created and the pencil 'turns' and topples over.
The clockwise moment and anticlockwise moments are unequal, so the pencil is not in equilibrium. The clockwise moment is greater than the anticlockwise moment, so it turns clockwise.
If the center of gravity of an object is over the pivot meaning that the total moments acting on the object are zero, then the object is in equilibrium. There are 3 types of equilibrium:
Stable Equilibrium
An object is in stable equilibrium if, when it is moved, the moment it experiences is opposite to the direction of the movement.
The pencil is in stable equilibrium because when it was shifted in a clockwise direction, it experienced an anti-clockwise moment.
Unstable Equilibrium
An object is in unstable equilibrium if, when it is shifted, it experiences a moment in the direction it was shifted.
The pencil is in unstable equilibrium because when it was shifted in a clockwise direction, it experienced a clockwise moment (in the same direction, trying to return it to a more stable position).
Neutral Equilibrium
An object is in neutral equilibrium if a shift in any direction causes no moment to be experienced.
First Class Levers
This class of levers has the fulcrum in the center.
These include see-saws, scissors and pliers.
As we discussed before, forces come in pairs. This pair of forces is an action-reaction pair: equal and opposite forces acting on two different objects in contact.
The first class lever has both the load and effort acting in the same direction (downwards), so, we can calculate the total force acting through the center of gravity,and therefore the reactionary force being applied by the fulcrum:
Reaction Force of Fulcrum = Effort + Load
R = E + L
Second Class Levers
In this class of levers, the load is in the center. These levers include wheelbarrows and nutcrackers.
This is better illustrated with a wheelbarrow:
In a second class lever, the effort acts upwards while the load acts downwards. So, we can calculate the total force acting through the center of gravity,and therefore the reactionary force being applied by the fulcrum:
R = L - E
Third Class Levers
In this lever class, the effort is in the center. This includes things such as tweezers, brooms and staplers.
The effort and load act in the same direction, so the reactionary force of the fulcrum is calculated thus:
R = E + L