Calculus/Pressure and force

Force
Force is a fundamental concept in physics. It is defined as a push or pull on a point mass. The magnitude of this physical quantity is given algebraically as a linear equation by the newton's second law of motion.

$$\ F=\ ma$$, where $$\ m$$ is the mass of the point particle in kilograms and $$\ a$$ is the rate of change of velocity with respect to time (acceleration) in ms-2 (the force obtained will be in newtons).

Derivative definition of Force(Instantaneous Force)
Force (F) is also defined as the rate of change of linear momentum (p) with respect to time (t):

$$\ F=\frac{dp}{dt}$$

Effects of Force
Force plays an important role in the motion of objects as it can cause these effects on the object:


 * It can make an object at rest acquire motion.
 * It can make an object in motion come to rest.
 * It can change the state of motion of an object.
 * It can change the shape and size of an object.
 * It can change physical and chemical properties of an object.
 * It can change the direction of motion of an object.

Pressure
Pressure (P) is defined as force acting normally on an object per unit area of its surface. It always acts parallel to the surface of an object.

$$\ P = \frac{F}{A}$$, where $$\ F$$ is the force acting in newtons and $$\ A$$ is the area on which the force is acting on the body in m2 (the pressure obtained will be in pascals).

$$\ P=\frac{dF}{dA}$$ gives the instantaneous pressure.