Archimedes Principle, Buoyant Force

In summary: Overall, the density of the crown can be determined by finding the mass of the crown, the buoyant force, and using the buoyant force equation. The density of the crown is approximately 16g/cm^3.
  • #1
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Homework Statement


Your local king has asked you to determine the density of a crown. If you suspend
it from a spring scale, the scale reads 8.33 N. If you then lower the statue into a tub of
water, so that it is completely submerged, the scale reads 7.81 N. What is the density
of the material from which the crown is made?


Homework Equations


buoyant force=pVg


The Attempt at a Solution


1.since the spring scale read 8.33N, i just used mg to find the mass of the crown, which is 0.85kg
2.since the scale read 7.81N when the crown was in the water, then the buoyant force is just the difference between its weight and the new scale reading,8.33N-7.81N right?
3. then i used Fb=pVg, where p is the density of the water and where V=mass of the crown/ density of the crown, then i just solved for the density of the crown. I got 16g/cm^3

is that right?
 
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  • #2
roman15 said:

Homework Statement


Your local king has asked you to determine the density of a crown. If you suspend
it from a spring scale, the scale reads 8.33 N. If you then lower the statue into a tub of
water, so that it is completely submerged, the scale reads 7.81 N. What is the density
of the material from which the crown is made?

I don't know, but the statue is clean!

Homework Equations


buoyant force=pVg


The Attempt at a Solution


1.since the spring scale read 8.33N, i just used mg to find the mass of the crown, which is 0.85kg
2.since the scale read 7.81N when the crown was in the water, then the buoyant force is just the difference between its weight and the new scale reading,8.33N-7.81N right?
3. then i used Fb=pVg, where p is the density of the water and where V=mass of the crown/ density of the crown, then i just solved for the density of the crown. I got 16g/cm^3

is that right?

Looks good.
 

1. What is Archimedes' Principle?

Archimedes' Principle states that the buoyant force acting on an object in a fluid is equal to the weight of the fluid displaced by the object.

2. How does buoyant force affect floating objects?

Buoyant force is responsible for keeping objects afloat in a fluid. If the buoyant force is greater than the weight of the object, it will float. If the buoyant force is less than the weight of the object, it will sink.

3. Does the shape or size of an object affect the buoyant force?

Yes, the shape and size of an object can affect the buoyant force. Objects with a larger volume will displace more fluid and experience a greater buoyant force. The shape of an object also plays a role in the distribution of the buoyant force.

4. Can an object sink in a fluid even if it is less dense than the fluid?

Yes, an object can still sink in a fluid if it is less dense than the fluid. This is because the weight of the object may still be greater than the buoyant force acting on it, causing it to sink.

5. How is the buoyant force calculated?

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

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