A Tanker

Classical Mechanics Level 4

A Cubical tanker completely filled with water ( combined weight = 20000 N 20000 \text{ N} ) is moving with a constant velocity v = 20 m/sec v = 20 \text{ m/sec} . A Hole develops at the bottom in its horizontal surface through which water comes out at the rate of 200 gm 200\text{ gm} per second. If the velocity of tanker becomes x x times its initial velocity after 30 seconds since the flow start. Then find x x .

Neglect friction.

This is a part of my set Aniket's Mechanics Challenges .


The answer is 1.

Aniket Sanghi by Aniket Sanghi , 21, India

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2 solutions

Aniket Sanghi
Mar 19, 2016

If you see carefully you see that the water separates out with its linear momentum (dm *v) in the horizontal direction. Hence their is no change in velocity of container.

3 Helpful 0 Interesting 0 Brilliant 0 Confused

Can we say like this.. that as the hole is made at the bottom, then, if we see the mass dependence upon time, we can see that

m ( t ) = m o − μ t m(t)=m_{o}-\mu t where μ \mu is mass its loosing per second.

Now if we see carefully, we can see that, the water is going in the vertically downward direction... not changing the horizontal motion anyway?

Md Zuhair - 3 years, 3 months ago

but the tanker is getting lighter so its velocity should increase on applying conservation of momentum in horizontal direction in absence of any external horizontal force???

Aryan Bansal - 1 year, 9 months ago
Istiak Reza
May 31, 2016

We probably can use the law of conservation of momentum, since the mass is decreasing..anyway we the decrease in mass in 30 seconds is comparably too small.. If we go mathematically, Mv=m (xv) which gives x=M/m Now m=(20000-((200 30/1000) 9.8))N=19941.2N Which simply gives the ratio x=20000÷19941.2=1.002948

0 Helpful 0 Interesting 0 Brilliant 0 Confused

You got it right for the wrong reason. When the water is released from the bottom of the tank, it keeps it's velocity in the x-direction. Thus the momentum of the tanker will decrease linearly with the mass and velocity of the tanker is constant.

William G. - 3 years, 11 months ago

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