What is the ratio of an objects weight in water as opposed to it's weight in air?

Answer 1

Its called specific gravity and its different for each object.

(check related link)

I feel like this answer is not entirely correct. I am a Mechanical Engineer at the University of Notre Dame and from what I have learned in my classes I would say the following. The weight of an object can be found by multiplying our mass times the acceleration of gravity. Take for example a 10 kilogram weight. This is the mass. Now we know that here on earth, the acceleration is about 9.8 m/s^2. So weight = 10*9.8 which is equal to 98Newtons which is about 22 lbs. Sorry if this is technical and seems kinda pointless, but my point is that the weight is mass times the acceleration due to gravity.

The weight in water is a bit different. This is so because not only do you still have gravity acting on the 10 kilogram weight, but you also have a bouyant force from the water pushing the weight up. The force that the water pushes on the object depends on how much water the object has displaced. Which is why the link discusses p (rho). p is the density of the object, a mass per unit volume. So the force from the water on the object is pVa (rho which is the density of the water*volume of object*acceleration due to gravity)

So long story short is as follows:

apparent weight = weight - bouyant force

weight = mg-pVg

weight = mass * gravity - density of water*volume of object*gravity

So if you wanna find this for something in particular here is what you should do:

I have simplified the equation into a form that is easy to use and will have units that we can understand. W is weight in pounds and V (volume is in cubic ft). If you prefer to use SI units an equation is below this one and the force, will be in Newtons. Here on earth we say that the force we feel is the weight, but this is a different topic.

final simplified form

weight = w(lb) - V(ft^c)*64.43

force= m(kg)*9.81 - 1*V(m^3)*9.81

So I guess the actual answer to your question is that there is no exact ratio, the above equation is what you should expect to get for your weight. One final note on this equation, you may see that if you have a large volume and a small weight, then you will end up with a negative weight. What this means is that you will have something that floats, like a rubber duck or a peice of wood for example.

Sorry for the long winded explanation, but I hope this helps.