Answer to Question #306278 in Mechanical Engineering for Kamal

Question

A rain drop of mass 3gm starts to fall from rest under the effect of gravity from a height of

100m. There is an air drag acting on the rain drop, the drag force is given by the equation,

F = bv.

Here, b = 2 × 10−3kgs−1 s

(a) Determine the governing differential of the system.

(b) Build a SIMULINK model of the system using transfer functions.

(c) Show velocity vs time graph with and without the effect of air drag on the same

plot.

(d) Show height vs time graph with and without the effect of air drag on the same

plot.

(e) From your graphs, determine the approximate time required for the rain drop to

reach the ground.

Answer 1

The work done on the raindrop by the gravitational force is given by 

$W=mgh=(3.35×10−5 kg)(9.80m/s2)(100m)=3.28×10−2 J$   

(b) Since the raindrop is falling at a constant velocity, all forces acting on the drop must be in balance, and R=mg, so      

$Wair−resistance ​=−3.28×10−2 J$