# Question on Archimedes principle.

## 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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ehild
Homework Helper

## 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

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.

ehild
Homework Helper
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

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)
B=M(g+a)+T
Is it correct?

if string is snapped.
B-m(g+a)=ma'
answer of second question.

ehild
Homework Helper
I hope It will be OK if you calculate the buoyant force correctly.

ehild

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.

ehild
Homework Helper
Well done!

ehild