Fluids- Sphere dropped in ocean

[allykat]

Homework Statement

A solid sphere of aluminum (density 2.7 g/cm^3) is gently dropped into a deep ocean. (The density of ocean water is approximately 1.03 g/cm^3.) Calculate the sphere's acceleration at the point where it is completely submerged into the ocean. As the sphere drops deeper, does the acceleration increase or decrease compared to the acceleration beneath the surface?

Homework Equations

Knowing that density = ρfVfg and that mg is greater that this, the Fnet equation becomes
Fnet= mg-ρfVfg where the volume is also the volume displaced by the sphere

The Attempt at a Solution

Okay so I attempted to find the ratio of Wapp/Wactual which is Vsphere(ρsphere-ρwater)g/Vsphere(ρsphere)g so I could find a relation between the two such that I could find m in the Fnet equation, but I couldn't get really far with this approach. I know the acceleration changes though.

 

[SteamKing]

Although your attempt at solution was apparently unsuccessful, it would still be helpful to post your calculations. There may be some error in calculation or logic which has escaped your attention, but which might be readily apparent to fresh eyes.

 

[allykat]

So I did Wapp/ Wactual= Vsphere(ρsphere-ρfluid)g/ (Vsphereρsphereg)= V(2.7-1.03)g/2.7Vg=
0.6185, but I do not know what to do with this result.

 

[haruspex]

So I did Wapp/ Wactual= Vsphere(ρsphere-ρfluid)g/ (Vsphereρsphereg)= V(2.7-1.03)g/2.7Vg=0.6185, but I do not know what to do with this result.

You have an object of known mass. In air, its weight would lead to a certain well-known acceleration. You have found the weight to have been reduced by a certain fraction. What will that do to the acceleration?

I know the acceleration changes though.

Because?

 

[allykat]

Well, I'm not given the weight, only the densities, but I tried to calculate a relation by canceling out the volumes and g. The acceleration should change because the pressure changes with depth.

 

[haruspex]

Well, I'm not given the weight, only the densities, but I tried to calculate a relation by canceling out the volumes and g.

I should have written Suppose you have an object of known mass...
If the mass stays the same but the weight is reduced by a factor, what will that do to the acceleration?

The acceleration should change because the pressure changes with depth.

Pressure is equal all around the sphere, so cancels out. You are to assume the density of the water is constant. Yet there is a reason the acceleration will change.