Question

Write down Newton's second law in terms of momentum and acceleration. Write down this law in the form of differential equation (DE).

Answer 1

Newton's second law, in terms of momentum, states that the net external force is equal to the rate of change of momentum, mathematically expressed as Fnet = dp/dt. When mass is constant, it simplifies to Fnet = ma.

Step-by-step explanation:

Newton's second law in terms of momentum states that the net external force acting on an object is equal to the rate of change of its momentum (p). This can be mathematically expressed in the form of a differential equation as Fnet = dp/dt, where p is the momentum (p = mv), m is the mass, v is the velocity, and t is time.

If mass is constant, the equation can be simplified using the definition of acceleration (a = dv/dt) to obtain Fnet = m dv/dt, which is the classic form of Newton's second law expressed as Fnet = ma.

Answer 2

Step-by-step explanation:

According to Newton's second law of motion, the rate of change of momentum is directly proportional to the applied unbalanced force. The mathematical expression is given by:

`F=(d(mv))/(dt)`

Where

F is the applied force

m is the mass of the object

v is the velocity with which it is moving

`F=m(dv)/(dt)`

Momentum of a particle is given by the product of mass and velocity as :

`p=mv`

Hence, this is the required solution.