Question

A small ball has a mass of 2.3 g and a terminal speed of 9.0 m/s. The drag force is of the formbv2 a) How much is the acceleration when the terminal speed is reached? b) Calculate the magnitude of the drag force when the terminal speed is 5. reached c) What is the value of b? g = 9.8 m/s2

Answer 1

a) As given, small ball attain the terminal velocity, i.e highest velocity during falling

Therefore,Sum of drag force and buoyancy =downward force of gravity F_g

Hence the net force=0,

Acceleration, a=0

b) The net force acting on the object falling near the surface of earth

$F_{net}=ma=mg-bv^{2}$ ;----------------(i)

As terminal velocity is attained ,Hence put a=0 in above eq(i) we get:

$0=mg-F_{drag}$ ;--------------(ii)

$F_{drag}=mg$ ; neglecting buoyancy Force

$F_{drag}=2.3\times 9.8N$

$F_{drag}=22.54N$

c) Again from eq (ii)

$0=mg-bv^{2}$ ;

$b=\frac{mg}{v^{2}}$ ; v=terminal velocity

$b=\frac{2.3\times 9.8}{9^{2}}$ ;

$b=0.28$