The inclined plane is one of the six classic simple machines that allows improving or redirecting a system of forces to facilitate mechanical work.
If you think about it, you've probably seen or even used an inclined plane without realizing it.
A typical example is a ramp. Imagine you are carrying a heavy suitcase and you have to carry it up a flight of stairs. It would be much easier to carry it up if there was a ramp instead of lifting it directly up the stairs, right? Well, this is one of the basic principles of the inclined plane: it makes it easier to move heavy objects compared to doing it vertically.
What is an inclined plane?
An inclined plane is a surface that is tilted relative to the ground, without being completely vertical or completely horizontal. It is somewhere in between, like the ramp we were talking about.
In simple terms, when we talk about an inclined plane in physics, we are referring to how this inclination affects the force required to move an object.
When you climb a ramp, for example, you use less force than if you tried to lift the object straight up. This is because the inclined plane distributes the force over a greater distance.
The important thing is that even though you are using less force at a given time, you need to apply it over a greater distance. So even though the force decreases, the work you do remains the same.
How does the inclined plane work?
To better understand how this simple machine works, we need to talk about forces.
In physics, forces are anything that can make an object move, change direction, or stop. In the case of the inclined plane, there are several forces at play when you try to move an object along it.
The main ones are:
- The force of gravity: This is the force that attracts objects to the Earth. It always acts vertically, that is, downwards.
- Normal force: It is the force exerted by the surface of the inclined plane on the object, and is perpendicular to that surface.
- The force of friction: Also called the force of friction, is the force that opposes the movement between two surfaces that are in contact, such as the object and the inclined plane.
- Applied Force: This is the force that you or anyone applies to move the object along the inclined plane.
The decomposition of forces
Gravity is the ever-present force that affects everything that has mass. On an inclined plane, gravity breaks down into two components or parts:
- A component perpendicular to the inclined plane: This is the part of the force of gravity that presses the object against the inclined plane.
- A component parallel to the inclined plane: This is the part of gravity that "pushes" the object down the slope. If there were no friction and we did not apply any other force, this component would be what would make the object slide down.
When we have an inclined plane, as I mentioned, the force of gravity can be divided into two directions: one that acts parallel to the inclined plane (trying to slide the object down) and another that is perpendicular to the plane (pressing the object against the surface).
To visualize this better, imagine that you place a block on an inclined plane and stop applying any force.
The block, due to gravity, will try to slide down the ramp. Why? Because the parallel component of gravity is acting in that direction.
If the angle of the inclined plane is small enough and there is enough friction, the block will not move, but if the angle increases, the block will start to slide.
Formulas and mathematical calculations
Once we understand how forces are broken down, we can use some basic formulas to analyze what happens on an inclined plane.
Gravity, in mathematical terms, is equal to the mass of the object (m) multiplied by the acceleration due to gravity (g), that is:
F gravity = m⋅g
Now, this force of gravity can be broken down into the two components we mentioned earlier using some basic trigonometry:
- The component perpendicular to the inclined plane:
F\perpendicular =m⋅g⋅cos(θ)
- The component parallel to the inclined plane:
F \parallel =m⋅g⋅sin(θ)
Where θ is the angle of inclination of the plane.
These equations allow us to understand how the force of gravity is distributed when an object is on an inclined plane.
The interesting thing is that the force you must apply to move an object up a ramp directly depends on this parallel component.
Advantages of the inclined plane
One of the most important benefits of the inclined plane is that it reduces the amount of force needed to lift an object. Instead of lifting a heavy object straight up, which would require a great deal of force, you can use an inclined plane to reduce this force.
For example, if you had to lift a 100 kg object vertically, you would need to apply a force equal to the gravity acting on the object, i.e. 100 kg multiplied by 9.8 m/s², resulting in 980 N (newtons).
However, if you use an inclined plane, the force required would be less because the plane distributes the work over a greater distance. The longer the inclined plane and the smaller its angle, the less force you need to apply.
Friction on the inclined plane
We cannot talk about inclined planes without mentioning friction. Friction is the force that opposes motion between two surfaces in contact.
In the case of an inclined plane, friction acts in the opposite direction to the movement of the object.
There are two types of friction that we could consider on an inclined plane:
- Static friction: This is the force that prevents an object from moving when it is at rest. If you place a block on an inclined plane, it is static friction that keeps it in place.
- Kinetic friction: It is the force that acts on an object that is already in motion. Once the object begins to slide, kinetic friction is what opposes its motion.
Friction depends on two main factors: the type of surface and the normal force.
On an inclined plane, the normal force is less than if the object were on a flat surface, because the normal force is perpendicular to the inclined plane, not downward. This means that on an inclined plane, the friction is less than if you were trying to move the same object on a horizontal surface.