Question 161: Work, Energy and Power & Circular Motion

Question

A body of mass m = 10
–2
kg is moving in a medium and experiences a frictional force F = –kv
2
. Its initial speed is v
0
= 10 ms
–1
. If, after 10 s, its energy is $${1 \over 8}mv_0^2$$, the value of k will be:

Accepted Answer

According to the question, final kinetic energy  = $${1 \over 8}mv_0^2$$
Let final speed of the body = V
f
So final kinetic energy = $${1 \over 2}mv_f^2$$
According to question,
$${1 \over 2}mv_f^2$$ = $${1 \over 8}mv_0^2$$
$$ \Rightarrow {v_f} = {{{v_0}} \over 2}$$ = $${{10} \over 2}$$ = 5 m/s
Given that, F = Ã¢ÂÂkv
2
$$ \Rightarrow $$ $$m\left( {{{dv} \over {dt}}} ight)$$$$ =  - k{v^2}$$
$$ \Rightarrow {10^{ - 2}}\left( {{{dv} \over {dt}}} ight) =  - k{v^2}$$
$$ \Rightarrow \int\limits_{10}^5 {{{dv} \over {{v^2}}}}  =  - 100k\int\limits_0^{10} {dt} $$
$$ \Rightarrow {1 \over 5} - {1 \over {10}} = 100k 	imes 10$$
$$ \Rightarrow k = {10^{ - 4}}kg\,{m^{ - 1}}$$

Answer

10
-1
kg m
-1
s
-1

Answer

10
-3
kg m
-1

Answer

10
-3
kg s
-1

Answer

10
-4
kg m
-1

Work, Energy and Power & Circular Motion

A body of mass m = 10 –2 kg is moving in a medium and experiences a frictional force F = –kv 2 . Its initial speed is v 0 = 10 ms –1 . If, after 10 s, its energy is ${1 \over 8}mv_0^2$, the value of k will be:

Choose the correct answer: