Question

Question #cc79c

Answer 1

A falling object experiences two forces

1. Force due to gravity.
   A downward force directed towards center of earth on the mass `m`.
   `F_g=mg` .....(1)
   where `g` is acceleration due to gravity.
2. Drag force due to air resistance.
   A force acting opposite to the direction of motion of the falling object. As such it is an upwards force slowing down the falling body.
   Drag force `F_{D}` depends on the the size, shape, and speed of the object. It also depends on physical properties of air and is given by the expression
   `F_{D}=\frac {1}{2}\rho \v^{2}C_{D}\A` .....(2)
   where `rho` is the density of air, `v` is velocity of the object relative to air, `A` is the area of cross section and `C_{D}` is the drag coefficient which is a dimensionless number.

Therefore, net force `F_"net"` acting on the falling body is
`F_"net"=F_g-F_{D}`
Using (1) and (2) we get
`F_"net"=mg-\frac {1}{2}\rho \v^{2}C_{D}\A`

Using equation for Newton's second law of motion we obtain
`a_"net"=F_"net"/m`
`=>a_"net"=(mg-\frac {1}{2}\rho \v^{2}C_{D}\A)/m`
`=>a_"net"=g-\frac {1}{2m}\rho \v^{2}C_{D}\A" ms"^-2`