Finding the weight of an object submerged in water

[haha0p1]

Homework Statement

A piece of wax is attached to a Newton metre. In air, the reading on the Newton metre is 0.27 Newton and when submerged in water of density 1000 kg per metre³ the reading is 0.16 Newton. Calculate: the reading on the newton-meter when the wax is submerged in a liquid of density's 800kg/m³

Relevant Equations

Density=Mass/volume

I have solved the question in the following way:
The downward force is equal to the upward force. the upward force is equal to the weight of water displaced. If we find the weight of the water displaced then we will know the upward force. And since upward force is equal to downward force, we will automatically know the value on the Newton-meter.
Volume of water displaced= 1.1×10-5 (we found this in the previous part of the question)
Weight=Mass×Gravitational field strength= Density×Volume×Gravitational field strength= 800 × 1.1×10-5×9.81 = 0.086N
My answer is coming 0.086N, but I checked the answer sheet and 0.086 is not the right answer. Kindly tell where am I going wrong.

 

[BvU]

My neck hurts from trying to read your picture sideways !

And I cannot for the life of me understand how you can find something for the reading that is not between 0.16 and 0.27 Newton...

Check out what it is that you did calculate !

 

[haha0p1]

My neck hurts from trying to read your picture sideways !

And I cannot for the life of me understand how you can find something for the reading that is not between 0.16 and 0.27 Newton...

Check out what it is that you did calculate !

I have changed the picture to vertical form

 

[BvU]

Do you understand why I "insist" on a result in the range between 0.16 and 0.27 N ?

$\$

 

[haruspex]

Weight=Mass×Gravitational field strength= Density×Volume×Gravitational field strength= 800 × 1.1×10-5×9.81 = 0.086N

Weight of what?

 

[haha0p1]

Do you understand why I "insist" on a result in the range between 0.16 and 0.27 N ?

$\$

TBH no...

 

[haha0p1]

Weight of what?

Weight of the water that has been displaced by the wax

 

[BvU]

TBH no...

Because the 800 density is between that of the water and the air !

you have calculated the upward thrust. The exercise asks for something else !

$\$

 

[MatinSAR]

Weight of the water that has been displaced by the wax

This is right ...
But does the newton meter show the weight of the displaced fluid?
No!
It shows the net force ...

I think you should calculate: mg - weight of displaced liquid with ρ=800 kg/m³

 

[haha0p1]

This is right ...
But does the newton meter show the weight of the displaced fluid?
No!
It shows the net force ...

I think you should calculate: mg - weight of displaced liquid with ρ=800 kg/m³

See this is the logic i used:
The newton meter shows the downward force of the wax. Since the wax is in equilibrium, downward force=upward force.
Now I have to find the upward force on the wax. According to Archimedes'principle, upward force is equal to the weight of the water displaced.So,
Downward weight=Upward force=Weight of water displaced
So. Downward force=Weight of water displaced
And therefore I found the weight of the water using 800Kg/m³ density. I know I am going wrong somewhere but don't know where. Kindly tell if I am missing out any concept.

 

[MatinSAR]

The newton meter shows the downward force of the wax.

I think this is wrong.
As far as I know newton meter measures the net force acting against object.

Look here : (Source : homework.study.com)

 

[nasu]

See this is the logic i used:
The newton meter shows the downward force of the wax. Since the wax is in equilibrium, downward force=upward force.
Now I have to find the upward force on the wax. According to Archimedes'principle, upward force is equal to the weight of the water displaced.So,
Downward weight=Upward force=Weight of water displaced
So. Downward force=Weight of water displaced
And therefore I found the weight of the water using 800Kg/m³ density. I know I am going wrong somewhere but don't know where. Kindly tell if I am missing out any concept.

There are three forces acting on the object:
1. weight (downwards) - W
2. buoyant force (upwards) - Fb
3. the (tension) force from the meter on the object (upwards) - T

The equilibrium means that
T+Fb=W or

T= W-Fb.

The force meter shows the value of T.

 

[MatinSAR]

As far as I know newton meter measures the net force acting against object.

I should have said that this is true if you ignore spring force.@nasu
Can you please tell if I am wrong or not?

 

[haruspex]

Weight of the water that has been displaced by the wax

Which is not what the question asks for.

 

[nasu]

I should have said that this is true if you ignore spring force.@nasu
Can you please tell if I am wrong or not?

The meter has no idea of what acts on the other object. It measures the (net) a force acting on itself. The one I called "T". You have to figure out how this relates to other forces acting on other objects

 

[haruspex]

It measures the (net) force acting on itself.

Not quite what you meant, I'm sure. Unless the meter is accelerating, there is no net force on it. I would say it measures the tension exerted on it.
Please excuse the pedantry.

 

[nasu]

Not quite what you meant, I'm sure. Unless the meter is accelerating, there is no net force on it. I would say it measures the tension exerted on it.
Please excuse the pedantry.

Yes, you are right of course.

 

[kuruman]

See this is the logic i used:
The newton meter shows the downward force of the wax. Since the wax is in equilibrium, downward force=upward force.
Now I have to find the upward force on the wax. According to Archimedes'principle, upward force is equal to the weight of the water displaced.So,
Downward weight=Upward force=Weight of water displaced
So. Downward force=Weight of water displaced
And therefore I found the weight of the water using 800Kg/m³ density. I know I am going wrong somewhere but don't know where. Kindly tell if I am missing out any concept.

I have highlighted in red where you went wrong. When the wax is in equilibrium, the sum of the downward forces is equal to the sum of the upward forces. As @nasu pointed out in #12, there are three forces acting on the wax: Tension and buoyant force upward and gravity downward.