Fluids Archimedes principle apparent weight question

In summary, the conversation discusses the weight readings on a physical balance when a solid is suspended in water. The first case involves the weight of the vessel with water and the solid, while the second case involves the weight of the vessel with water only. The difference between the two cases is that in the first case, the weight reading includes the weight of the solid, while in the second case, the weight reading only includes the weight of the water displaced by the solid. The second part of the conversation discusses the importance of understanding the force needed to balance the torque of the balance arm, and how the weight reading may change if the thread is tied to the other end.
  • #1
sachin123
121
0
Homework Statement

Vessel contains water.It is placed on the pan of a physical balance.A solid(specific gravity=1) is suspended from an thread(from an independent support),such that it is immersed completely in the water.
What the weight it reads?

If the thread was tied to the arm of the balance,what would the weight have been?

The attempt at a solution
First Part:
Water exerts a buoyant force on the solid.This results in a reaction force (equal and opposite).
Thus the weight read is that of vessel with water+solid.

Correct?
Second Part:
My book says it is equal to the weight of the vessel with water only.How it is so?How is it different from the first case?
 
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  • #2
Although the answer is correct you shouldn't say the weight on the balance would be the weight of water plus that of the solid. Rather it is better to say that the reading shows the weight of water plus the weight of water that would have been enclosed in the solid had it been made of water. Here the density of solid is equal to that of water (a coincidence).
 
  • #3
Okay.But what about the 2nd part.That is more important.Please read that too.
 
  • #4
The weight reading is actually the force needed to balance the torque of the other arm. Since distances are equal from both sides this aspect is not important. But how do you suppose the force on the vessel changes if the thread were tied to the other end?
 

1. What is Archimedes' principle?

Archimedes' principle states that the buoyant force on an object submerged in a fluid is equal to the weight of the fluid that the object displaces.

2. How does Archimedes' principle relate to apparent weight?

According to Archimedes' principle, the apparent weight of an object submerged in a fluid is reduced by the weight of the fluid it displaces. This is because the buoyant force acts in the opposite direction of gravity, making the object feel lighter.

3. How can I calculate the buoyant force using Archimedes' principle?

The buoyant force can be calculated by multiplying the density of the fluid by the volume of the fluid displaced by the object. This is represented by the equation FB = ρVg, where ρ is the density of the fluid, V is the volume of the displaced fluid, and g is the acceleration due to gravity.

4. Does the shape of an object affect the buoyant force according to Archimedes' principle?

Yes, the shape of an object does affect the buoyant force. Objects with a larger surface area will displace more fluid, resulting in a greater buoyant force. This is why objects with a larger surface area, such as a boat, can float on water even though they are heavier than the water they displace.

5. Can Archimedes' principle be applied to gases?

Yes, Archimedes' principle can be applied to gases as well. For example, a hot air balloon rises because the hot air inside the balloon is less dense than the surrounding cool air, resulting in a greater buoyant force according to Archimedes' principle.

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