Kinematics-12

A small sphere of mass m is released from rest in a large vessel filled with oil where it experiences a resistive force proportional to its speed i.e., F=-kv, where k is a constant and v is the velocity.

(a) Find the speed of the ball with which it varies.
(b) After a certain time the sphere reaches a terminal speed, find it.

3 Answers

1133
Sourish Ghosh ·

a) v = e-ktm

b) v = mgk(1 - ρlρs)

1133
Sourish Ghosh ·

Alright here's what I have done. Where am i going wrong?

When body attains terminal vel (vt), net force is zero.

F = -kv
=> mdvdt = -kv
on solving,
v = e-kt/m
a = -kme-kt/m

mg = Fb + kvt
=> Fb = mg - kvt

At any general point before terminal velocity,

mg + ma = Fb + kv
=> ma = k(v - vt)

on substituting values,
vt = 2e-kt/m

1161
Akash Anand ·

Here is the solution

Your Answer

Close [X]