# buoyancy-Gravity: object completly submerged in water

• October 21st, 2013, 11:50 AM
GulledOsman
buoyancy-Gravity: object completly submerged in water
I am working on a projekt and have stumbled upon a problem. Lets say you have a "cat" that is completly submerged in water and is swimming downwards.

You are given the buoyancy on the cat.
You are given the gravity on the cat.
You are given the volume of the cat, like for instance 35cm^3
You are given the weight of the cat, like for instance 80g=0.080kg

How can i calculate the minimum force the cat has to provide to swim downwards in constant speed?
Also if the cat has to reach a depth of 400cm, how i can calculate the force needed for that?
• October 21st, 2013, 01:45 PM
Arcane_Mathematician
Buoyancy works by displacement. For example, lets say I have an object with a density of that I put into a body of water. Let's assume, for the sake of the example, that the density of the water is exactly 1, and is uniform throughout the body of water, regardless of depth. What that means is that force exerted upward by the water on the object will by the downward force of gravity on the object.

If we assume that gravity acts with exactly , for the purpose of the example, and knowing the mass of the object, in the case it will be 5kg, lets us solve the problem. the 5kg object will experience a downward force of 50N by Gravity, and an upward force of 62.5N from the buoyancy of the water. So, If I want the object to sink, I need to exert more than 12.5N of force downward, to overcome the buoyancy of the water. Now, obviously this example can't be dragged and dropped directly into your problem, but it does give you a general base work to use to solve the problem.
• October 21st, 2013, 02:30 PM
GulledOsman
I understood how to find the force to make it swim down with constant speed, but not completly on how to calculate the work/force needed by the object to get down; lets say 400cm.
• October 21st, 2013, 04:10 PM
merumario
Quote:

Originally Posted by GulledOsman
I understood how to find the force to make it swim down with constant speed, but not completly on how to calculate the work/force needed by the object to get down; lets say 400cm.

I think you would have to assume that if you apply the 12.5N in other to immense the entire cat,the cat will be immense only few cm into the water and once you double the force the depth of the cat in the water increases. You would have to repeat this till it gets to 400cm and then note the force that has immense it that deep#
• October 21st, 2013, 05:42 PM
MagiMaster
@merumario, Three Incorrect Laws of Motion - YouTube

@GulledOsman, There's a significant difference between force and work. Which one are you trying to solve for here?
• October 21st, 2013, 07:08 PM
Arcane_Mathematician
Well, not to do you're homework for you, but ignoring fluid dynamics, the friction caused by moving through a fluid medium, and the fact that the density of water increases with depth, all the force you need to reach 400cm depth, hell, with my example, 10km depth, is just enough force to make the cat accelerate even an iota in the fluid. Immediately after it accelerates even a little, maintaining a force that, combined with gravity, equalizes the force from the buoyancy of the object in the water, will leave it to move at a constant velocity until the desired depth is reached, at which point a slight lack in force until the cat accelerates to a rest and then immediate re-application of the neutralizing force would cause the cat to rest at whatever depth you wanted. Sorry, but when it comes to the work done, I'll leave you to figure that one out on your own.

In real-world systems, this obviously won't work, because water is a compressible fluid and as such has different densities at different depths. Knowing those densities, however, you can determine the ideal force necessary to sink to, and the rest at, a desired depth. Sorry, but the OP was stated too much like a homework problem for me to give you answers beyond my hypothetical perfect-world scenario
• October 21st, 2013, 07:15 PM
Arcane_Mathematician
Quote:

Originally Posted by merumario
Quote:

Originally Posted by GulledOsman
I understood how to find the force to make it swim down with constant speed, but not completly on how to calculate the work/force needed by the object to get down; lets say 400cm.

I think you would have to assume that if you apply the 12.5N in other to immense the entire cat,the cat will be immense only few cm into the water and once you double the force the depth of the cat in the water increases. You would have to repeat this till it gets to 400cm and then note the force that has immense it that deep#

This is inherently false, as it completely ignores Newton's Laws of Motion. Any force, no matter how small, that upsets the balance of forces that an object at rest has will cause the object to accelerate. The only way that acceleration will stop, or change in any way, is if the force that caused the acceleration disappears, or another force acts on the object counteracting the force causing the acceleration.
• October 21st, 2013, 08:55 PM
Harold14370
The buoyant force on the cat is equal to the weight of the water displaced (in newtons, mass times the acceleration due to gravity). That's his volume multiplied by the density of water multiplied by g. The net force the cat exerts to swim down is the buoyant force minus its weight in Newtons. The work done is defined as force multiplied by distance, so it's the net force multiplied by the depth to which it swims. This neglects any force due to drag, but that will be negligible if it swims very slowly.