mathematical formula for rate of change of momentum when mass remains constant.
Answers
I’m assuming that by rate, you mean with respect to time.
Well, first of all, momentum is equal to product of mass and velocity of the object.
P = m*v
Now, rate of change of momentum means change in momentum with respect to time is defined as force.
F = dP/dt = d(mv)/dt
Now, momentum can be changed in a number of ways.
Mass remains constant and velocity changes.
In this case formula will become
F = d(mv)/dt = m*dv/dt = ma (I’m explaining this a later on.)
Example: You are driving a car with varying speed. So, speed changes but mass of the car is still nearly the same (why nearly?…think.)
2. Velocity remains the same and mass changes.
F = d(mv)/dt = v*dm/dt
Example a conveyor belt is empty and moving at a constant speed. Now you start putting some stuff onto the moving belt. So, here velocity of the belt is maintained constant and mass is changing.
When I say the change in momentum with respect to time is force. It means that is the amount of force acted on that object which result in change in momentum.
In point one i said i’ll explain that ‘a’ later.
Well, here it is. It’s the answer to your second question that rate of change in velocity. It is termed as acceleration.
a = dv/dt
Now this part is just for some extended information. When i said mass of the car remains nearly the same, I was thinking about the concept of relative mass. As your speed increases your mass also increase. In fact at speed of light, your mass will become infinite!!!
Formula : m (v-u) /t
Where m=mass, v=final velocity,u=initial velocity , t=time