Volume of Stone submerged in Water

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SUMMARY

The discussion centers on calculating the volume of a submerged stone using the principles of buoyancy and Archimedes' principle. The stone weighs 254N when submerged and 1235N when out of water, indicating a weight difference of 981N, which corresponds to the weight of the water displaced. The correct conversion factor for weight from Newtons to kilograms is 9.81 m/s², leading to the conclusion that the volume of the stone is 0.1 cubic meters.

PREREQUISITES
  • Understanding of buoyancy and Archimedes' principle
  • Knowledge of weight conversion from Newtons to kilograms using gravitational acceleration
  • Basic familiarity with density calculations
  • Ability to perform unit conversions and basic arithmetic operations
NEXT STEPS
  • Study Archimedes' principle in detail
  • Learn about density calculations and their applications in fluid mechanics
  • Explore the concept of buoyancy and its effects on submerged objects
  • Practice weight conversion using gravitational acceleration in various contexts
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Students in physics, engineers working with fluid dynamics, and anyone interested in understanding the principles of buoyancy and volume displacement in liquids.

scbeturner
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A submerged stone weighs 254N, but out of the water it weighs 1235N. The density of the water is 1000 kg per cubic meter. What is the volume of the stone?



I understand that density=mass/volume but I don't know which numbers to plug in and I can't find help anywhere!
 
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scbeturner said:
A submerged stone weighs 254N, but out of the water it weighs 1235N. The density of the water is 1000 kg per cubic meter. What is the volume of the stone?



I understand that density=mass/volume but I don't know which numbers to plug in and I can't find help anywhere!

Why does the stone weigh less when it's submerged in water? What does the weight difference represent?
 
Because of the buoyancy force??

i took the difference between the weights which is 981N, divided it by 98.1 and got 10, then divided it by 1000 and got .01 is that right?
 
scbeturner said:
Because of the buoyancy force??
Yes, that's correct.
i took the difference between the weights which is 981N, divided it by 98.1 and got 10, then divided it by 1000 and got .01 is that right?

Why 98.1? What is 98.1?
 
The force of gravity to convert it from Newtons to kilogram
 
scbeturner said:
The force of gravity to convert it from Newtons to kilogram

The acceleration due to gravity is 9.81 m/s2.
 
So should I not have used it as the conversion factor?
 
scbeturner said:
So should I not have used it as the conversion factor?

Yes, you want to use the acceleration due to gravity in the conversion. But the value you employed was 10x to large. You used 98.1 rather than 9.81.
 
Sorry that's what I meant
So I on the right track?
 
  • #10
scbeturner said:
Sorry that's what I meant
So I on the right track?

Yes, you're on the right track.

Once you realized that the weight difference represents weight of the water displaced by the stone, you were on the right track to find the volume of the stone by finding the volume of that displaced water.
 
  • #11
so how do i use the volume of the displaced water to find the volume of the stone?
 
  • #12
scbeturner said:
so how do i use the volume of the displaced water to find the volume of the stone?

Archimedes' principle of displacement -- the volume of water displaced by a submerged object is equal to the volume of the object...
 
  • #13
oh ok so .01 cubic meters is the answer?
 
  • #14
scbeturner said:
oh ok so .01 cubic meters is the answer?

No, that's still off by a factor of 10. Did you fix your value of g?
 
  • #15
with that fixed the answer comes out to .1 cubic meters correct?
 
  • #16
scbeturner said:
with that fixed the answer comes out to .1 cubic meters correct?

That looks better :wink:
 
  • #17
haha ok thanks!
 

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