An engine pumps water continuously through a hose. Water leaves the hose with velocity v and m is mass per unit length of the water jet. If this jet hits a surface and came to rest instantaneously, the force on the surface is

Question

An engine pumps water continuously through a hose. Water leaves the hose with velocity v and m is mass per unit length of the water jet. If this jet hits a surface and came to rest instantaneously, the force on the surface is (A) mv3 (B) mv2 (C) (1/2)mv2 (D) (1/2)mv3

Tardigrade Admin · Accepted Answer

Rate of kinetic energy KE =( d / dt ) (1/2) Mv 2 text But M = mL KE =(1/2) ( dm / dt ) Lv 2=(1/2) mv 3

Q. An engine pumps water continuously through a hose. Water leaves the hose with velocity $v$ and $m$ is mass per unit length of the water jet. If this jet hits a surface and came to rest instantaneously, the force on the surface is

$m v^{3}$

$m v^{2}$

$\frac{1}{2} m v^{2}$

$\frac{1}{2} m v^{3}$

Rate of kinetic energy
$K E = \frac{d}{d t} \frac{1}{2} M v^{2}$
$But M = m L$
$K E = \frac{1}{2} \frac{d m}{d t} L v^{2} = \frac{1}{2} m v^{3}$

Q. An engine pumps water continuously through a hose. Water leaves the hose with velocity v and m is mass per unit length of the water jet. If this jet hits a surface and came to rest instantaneously, the force on the surface is

mv3

mv2

21​mv2

21​mv3