Question on Archimedes principle.

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  • #1
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Homework Statement



A solid sphere of mass m=2 kilogram and specific gravity s=0.5 is held stationary to a tank as shown in figure. The tank is accelerating upward with a=2ms-2. calculate the tension in the string? If suddenly string break then the acceleration of the ball in frame of tank.

Homework Equations



Archimedes principle

The Attempt at a Solution


see in attachment.
for second question. My answer is
net force =B-mg=20 so acceleration in frame of ground is 10. In frame it should 10-2=8.
 

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Answers and Replies

  • #2
ehild
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Homework Statement



A solid sphere of mass m=2 kilogram and specific gravity s=0.5 is held stationary to a tank as shown in figure. The tank is accelerating upward with a=2ms-2. calculate the tension in the string.

Homework Equations



Archimedes principle

The Attempt at a Solution


see in attachment.

Hi Vkash,
What is your question?

ehild
 
  • #3
318
1
Hi Vkash,
What is your question?

ehild
A solid sphere of mass m=2 kilogram and specific gravity s=0.5 is held stationary to a tank as shown in figure. The tank is accelerating upward with a=2ms-2.
(1) calculate the tension in the string?
(2) If suddenly string break then the acceleration of the ball in frame of tank?
I have tried to answer these questions. Where am i wrong.
 
  • #4
ehild
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The problem is easiest to solve if you use the accelerating frame of reference, fixed to the tank. Have you learnt about accelerating frames of reference? You feel heavier in a lift which accelerates upward as if the gravitational acceleration g would be bigger. And you feel lighter in a frame of reference accelerating downward. In a falling lift you are weightless.

Buoyant force arises because of the weight of the liquid. In a falling tank, there would be no buoyant force. You could immerse any object into the liquid, it would stay at the same place.
This tank accelerates upward with a=2 m/s^2. Everything feels heavier, as if the gravitational constant would be g'=g+2 instead of 10 m/s^2. Even the buoyant force will be larger than in the tank in rest.

Can you proceed?


ehild
 
  • #5
318
1
The problem is easiest to solve if you use the accelerating frame of reference, fixed to the tank. Have you learnt about accelerating frames of reference? You feel heavier in a lift which accelerates upward as if the gravitational acceleration g would be bigger. And you feel lighter in a frame of reference accelerating downward. In a falling lift you are weightless.

Buoyant force arises because of the weight of the liquid. In a falling tank, there would be no buoyant force. You could immerse any object into the liquid, it would stay at the same place.
This tank accelerates upward with a=2 m/s^2. Everything feels heavier, as if the gravitational constant would be g'=g+2 instead of 10 m/s^2. Even the buoyant force will be larger than in the tank in rest.

Can you proceed?


ehild

yes i have read this in starting mechanics.(working with non inertial frame of reference)
In your way.
B=M(g+a)+T
Is it correct?

if string is snapped.
B-m(g+a)=ma'
answer of second question.
 
  • #6
ehild
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I hope It will be OK if you calculate the buoyant force correctly.

ehild
 
  • #7
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I hope It will be OK if you calculate the buoyant force correctly.

ehild

volume of ball is 2/500=4*10-3
B=(4*10-3)*(10)*(1000)
here i did it wrong.
It should B=(4*10-3)*(10+2)*(1000)
thanks ehild. I got the mistake.
 
  • #8
ehild
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Well done!

ehild
 

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