Tips by Dr. Abhijit Kar Gupta, e‐mail: kg.abhi@gmail.com

Recipe for Solving Physics problems

Mechanics:

• This begins and ends with Newton’s 2nd law of motion: Force = mass x acceleration. In fact, this is the only formula in this chapter that is used in many disguises.

So whenever there is force think of acceleration or vice versa.

• Velocity can be calculated from the acceleration or acceleration from velocity – just a matter of integration or differentiation. Similarly position also can be calculated from velocity or the other way round. If you know the position of a particle at any time, you know its trajectory. Example: particle in a projectile motion

But be mindful of the initial conditions – the initial values of velocity or position or acceleration. Example: If a particle is thrown upwards, the initial velocity is given some value whereas if it falls from a height, the initial velocity is equal to zero.

• Energy conservation: Total energy should always remain constant (unless in a case where dissipation or energy loss is taken into account). If velocity is known, Kinetic energy is also known. Think of the potential energy and how it can be found out in different situations or calculated from the force when the force is conservative. Sometimes, the expression for potential energy is provided and you have to differentiate it to get the expression for force.

• When there is static equilibrium, the vector sum of all the forces to and by the system must be

constant. While solving a problem, each force is resolved into two perpendicular components (scalars): one along X‐axis and other along Y‐axis. Now the sum of the components of all the forces along X‐axis should be zero and similarly, the sum along the Y‐axis will be equal to zero.

• If there is no equilibrium, there must be some motion involved. So the net force on the particle/ system in a certain direction will be non‐zero. This net force is calculated or its components along X‐axis and Y‐axis are calculated separately first and then resultant is taken. At the end, again Newton’s law is applied to get the acceleration.

Note that any problem, however complicated, cannot escape the above framework. Just have patience and have confidence on you, think for a longer time to dig out the relevant forces in all directions, resolve them in two perpendicular directions, equate them with the product of mass and acceleration, think of the initial conditions and so on……move on…

Watch out the next recipes to follow…