Elastic Force, Drag, Buoyancy

What is Elastic Force?

Elastic objects, such as springs, can be manipulated but they always try to return to their original form.
This force that allows them to restore their form is called elastic restoring force.
If the spring is pulled it will retract in order reach its natural length. Similarly, if pushed back, then the spring will expand to reach its natural length once again.
Elastic restoring force is proportional to the amount the spring has been stretched by.
The image below shows the direction the elastic restoring force will act in order to achieve the natural length.

The spring constant is the stiffness of the spring. A higher spring constant means that the spring is stiffer, and a lower spring constant means that it is more flexible.

When moving, we constantly collide with particles that slow us down. This is the reason for example, of why you feel the wind against your face when running.
In this scenario liquids and gasses both function very similarly, thus viscous drag force can be applied to both of them.
Imagine viscous drag force as how it would feel to try and run through a ball pit. The balls would collide with you and slow you down. In this scenario balls represent atoms, except much, much larger.
Viscous drag force scales with velocity. The faster you go, the more drag you encounter.
Drag is always applied to the direction opposite to the movement.

Keep in mind that calculations are much more difficult for more complicated forms.
Bullets and airplanes for example can take advantage of different forms, as a more rounded and narrow form causes less drag force.
The formula for viscous drag force is shown below.

Buoyancy is the force experienced by a body when it is partly or fully immersed in a fluid.
Buoyancy is what makes bodies, such as container ship, float on the surface of a fluid, such as water.
This is due to the movement of water particles pushing against an object.
Some bodies float and other bodies do not float. In both cases, the bodies experience buoyancy.
Bouncy is caused by a difference in pressure at the top and bottom of an object. As water has higher pressure than air, the object floats on the surface of water.
The same still applies to fully submerged objects.

The buoyancy experienced by a body immersed in a fluid is equal to the weight of the fluid displaced.
Thus incredibly heavy cargo ships can still float, due to them displacing a lot of water, and thus experiencing a lot of buoyancy.
The volume of liquid displaced is equal to the volume of the submerged object.
It is independent of mass or weight and is affected by the space taken up by the object.
The equation for buoyancy is shown below.