# Calculus/Pressure and force

## Contents

##### 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.

${\displaystyle \ F=\ ma}$ , where ${\displaystyle \ m}$ is the mass of the point particle in kilograms and ${\displaystyle \ a}$ 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):

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

##### 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.

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

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