Question on Archimedes principle.

[vkash]

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.

 

[ehild]

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

 

[vkash]

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]

The problem is easiest to solve if you use the accelerating frame of reference, fixed to the tank. Have you learned 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

 

[vkash]

The problem is easiest to solve if you use the accelerating frame of reference, fixed to the tank. Have you learned 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.

 

[ehild]

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

ehild

 

[vkash]

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]

Well done!

ehild