# B Rate of sinking objects

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1. Oct 13, 2016

### jrwints

Hi All,

I have a problem (with 3 separate instances) to which I believe I have the answers, but would like check with those more knowledgeable than myself. They revolve around 3 blocks sinking through water and which falls quicker. I am ignoring friction.

Instance 1:
All blocks are exactly the same shape and size. They have different masses however. Which falls quicker?

Instance 2:
All blocks are of different sizes (short/medium/long), but have the same mass. Which falls quicker?

Instance 3:
All blocks are made of the same material but are different sizes (short/medium/long). Which falls quicker?

My understanding of the answers is based upon Newton's second law, buoyancy and free body force diagrams:
W(obj) - W(wat) = mass of object x acceleration (where Weight of water is equal to its density x volume of object x gravity):

a- ( m(o) - m(w) ) g = m(o) a
b- ( p(o) - p(w) ) vg = p(o) v a (mass = density x volume)

1. Using eqn a: Although m(o) increases, m(w) remains constant, therefore acceleration increases and heavier mass falls quicker

2. Using eqn a: As they have the same mass, m(o) remains constant, but m(w) increases as the size of the object increases. Therefore, the smaller object falls quicker

3. Using eqn b: All densities are equal, but as the volume on both sides of the equation cancel each other out, they fall at the same rate

Is this the correct understanding? I believe it is, but it does do your head in!!!

2. Oct 13, 2016

### BvU

Hello jr,

If you want to ignore friction, you are back to Galileo Galilei's experiments.
You equations are hard to read and understand. are the a and the b enumerators or variables ?

 all right, enumerators.

Instance 1 and 2: I agree. Some can even move upwards...
Instance 3: agree also.

In all cases it's pretty straightforward to write an expression for the acceleration.

3. Oct 13, 2016

### jrwints

Thanks BvU,
It basically comes down to density. Those with greater densities sink faster than those with smaller densities.
It's basic physics but something I haven't needed to think about or do for ages - when they come up in aptitude tests you forget the equations and logic behind the reasoning!

4. Oct 13, 2016

### BvU

Same here: Galilei had to do with non-vacuum and was genius enough to reason through that limitation. For a fish such luck isn't there