If we apply a force to an object, this force can be represented with an arrow.
The strength of the force is represented by the length of the arrow.
If an object experiences several forces at the same time,
then the result is the same as if the object experienced just a single force
that is represented by all the arrows added together.
If an object experiences several forces at the same time,
then the result is the same as if the object experienced just a single force
that is represented by all the arrows added together.
No matter what order we add the arrows in, the result is the same.
The resultant total force can also be represented as
the sum of three arrows pointing in each of the three dimensions.
The effect of the forces in each of the dimensions can be analyzed separately.
For example, suppose we have a ball bouncing around in a box with no gravity present.
The ball’s path in each dimension is the same as it would be
if it was just bouncing around in a one dimensional box.
The ball’s path in all three dimensions is just the combination of these three paths.
Now let us consider the path of a ball with gravity present.
The ball’s path in the Y direction due to gravity is as follows.
The ball does not experience any forces in the X dimension,
so the path in the X direction is just a straight line.
The combination of the paths in these two dimensions
ends up being the actual path of the ball.
According to Einstein’s Theory of Relativity,
gravity is not actually a force but a curvature in space time.
But, we can think of gravity as a force
when analyzing the path of objects such as this ball.
When the ball is sitting on top of a rectangle,
the apparent force of gravity is still present.
But, the rectangle’s surface will exert a force
that exactly cancels out the force of gravity.
We call this force generated by the rectangle’s surface the surface’s “normal force.”
As the rectangle changes direction,
this “normal force” stays at 90 degrees to the rectangle’s surface.
But, the apparent force of gravity is still always downward.
The apparent force of gravity can be thought of as the combination of
an arrow that is parallel to the rectangle’s surface,
and an arrow that is 90 degrees to the rectangle’s surface.
The portion of gravity that is at 90 degrees to the surface
is always exactly cancelled out by the force that is generated by the rectangle.
This leaves just the portion of gravity that is parallel to the rectangle’s surface.
The larger the angle of inclination of the rectangle,
the larger the portion of gravity that is parallel to the rectangle’s surface.
This is why balls roll down a steep ramp faster than they do down a shallow ramp.
Much more information about the laws of motion and the
effects of forces on objects is available in the other videos on this channel.