Q. newton's second law of motion states that the time rate of change of momentum of the body is equal to the resultant force acting on it. using this law formulate a mathematical model to determine the terminal velocity of a free falling body near the earth's surface. I don't know how to solve it.
Hello Vennapusa charan kumar reddy,
Well, at the terminal velocity, its velocity will not change, hence its momentum will also not change and therefore rate of change of momentum is 0 or the accelaration will be 0 (since accelaration = rate of change of momentum ), so: At the terminal velocity,
Fnet=mg−FD=ma=0.(where FD is the drift force due to air resistance, say FD = 1/2CρAv^2 )(where C is constant, ρ is the density of air, A is the surface area of the body, V is the velocity of body and in this case V = Vt or terminal velocity )
Thus,
mg=FD.mg=FD.
Using the equation for drag force, we have
mg=1/2CρAv^2
Solving for the velocity, we obtain
vt=√2mgρCA.
for more details you can refer to ( Terminal Velocity (https://courses.lumenlearning.com/suny-osuniversityphysics/chapter/6-4-drag-force-and-terminal-speed/) )
Hope this helps, and feel free to ask any further query...
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