Sinking Object

[Orpington3]

An object weighing 16 lb is dropped from rest on the surface of a calm lake and thereafter starts to sink. While its weight tends to force it downward, the buoyancy of the object tends to force it back upward. If this buoyancy force is one of 6 lb and the resistance of the water (in pounds) is numerically equal to twice the square of the velocity (in feet per second), find the formula for the velocity of the sinking object as a function of time.

I honestly don't even know how to start this problem, but I do know that the answer is
v=(((5)^(1/2))(1-e^(-8t((5)^(1/2)))/(1+e^(-8t((5)^(1/2))
which might be easier to understand as:
v equals radical 5 ( 1 - e to the -8 radical 5 times t ) all divided by one plus e to the -8 radical 5 times t

all help will be greatly appreciated!

 

[tutor_joel]

If this buoyancy force is one of 6 lb

Can you clarify this? The devil is in the details and grammar is important here.

 

[Orpington3]

I wish I could, that is exactly what the book says. I was assuming that ment 1/6, but your guess is as good as mine

 

[JuicyBurger]

I wish I could, that is exactly what the book says. I was assuming that ment 1/6, but your guess is as good as mine

"buoyancy force is one of 6 lb " = "the buoyancy force is 6 lb". IT is just a different way of saying it.

Draw a free body diagram. What forces are pulling the object down? Which ones are pulling it up?

Then we know that...

\(\displaystyle \sum{}{}F = ma\)

Hope this helps!

 

[tutor_joel]

So, to set this up as a differential equation, you need to be able to relate the velocity of the system to time.

given
\(\displaystyle \sum{}{}F = ma = mg - buoyant\; force - water\; resistance\)

(Using the convention that down is positive.) Any acceleration is dV/dt, gravity is a constant here as usual.

The buoyant force is traditionally specific gravity times the volume, but they give you that. Water resistance is twice the velocity squared, or 2V^2

 

[Deleted member 4993]

Remember

\(\displaystyle a = \frac{dv}{dt}\)

You'll need to set-up a differential equation. Give it a try and show us how far you can go with hints above.

 

[mmm4444bot]

"buoyancy force is one of 6 lb" For scientific writing, this seems like an awkward use of the pronoun 'one'. To me, it reads more like a typographical error. I mean, it looks like something is missing. Where's the editor?