Tension of strings in an elevator

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To determine the tension in the strings of two masses hanging in an elevator, one must analyze the forces acting on each mass in different scenarios. The tension can be calculated using the formula F=ma, considering the gravitational force and the acceleration of the elevator. When the elevator is stationary, the tension equals the weight of the masses. For upward or downward movement, the net force changes based on the acceleration, affecting the tension in each string. Understanding these principles allows for accurate calculations of tension in various elevator conditions.
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Two masses are connected by a string and are hanging from the ceiling of an elevator like this:

[string 1]
|
[4kg mass]
|
[string 2]
|
[6kg mass]

Show the tension of each string in the following situations:
i) Stationary
ii) Moving up at 3m/s
iii) Moving down at 3m/s
iv) Moving up at 3m/s/s
v) Moving down at 3m/s/s

Ok, I am kinda stumped. Where do I start? Is there a formula for tension? Is it F=ma? Or F=m(9.8-a) or something?

I'm just so horrible at physics, I'll be so grateful if someone could explain how this works..

Thanks! :)
 
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You just need to look at the net force on each string. For example, you have two forces on the first string (weights of the hanging bodies). Other one is even easier. Remember the 1st Newton's law. That's when the elevator is stationary.

The formula F=ma can be used in part (iv) and (v). It's the inertial force. Just be aware of its direction.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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