# Can you help me solve this?(Not homework)

This is not homework,is just a problem which is the subject of an argument I have with my professor.Can you please help?

A cube is thrown under the water with the speed of 1m/s.After 0.4 s the cube has traveled 1m.Knowing the density of water find the density of the cube.

I say that this is solved using notions of acceleration which are over what is learned in my grade and my professor say it’s a very easy problem solved using only mechanics of fluids and energy variation laws but she didn’t tell me how to actually solved it.

Can you help me please?

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## 10 Answers

There seems to be omitted data from the question, such as “what direction was the cube ‘thrown’ underwater?” ‘Upward’ and ‘downward’ will have to deal with gravity’s effects on the throw, and a lateral ‘throw’ should be specified… if that’s the case.

The size of the cube is totally relevant. You can’t figure density without knowing volume.

I can’t remember them, but there are equations etc… for dealing with air resistance. I think the same would apply for an object going through any fluid..

Analyzing for a cube is really hard because the drag coefficient is different depending on orientation relative to the direction of motion. You need a lot of pieces to solve this puzzle properly. Maybe your professor wants to do something relative to F=ma?

the cube is thrown downward and the friction with water is negligible you take into account only the Arhimedic Force.

Sorry for omitting these informations.

@Christian95 Wait… what? I’m confused.

How can the friction with the water be negligible? What role does the water play in the question? Just buoyancy?

Something seems fishy…

Can you make the problem more clear? Here is what I read so far:

A cube is traveling straight down and hits a swimming pool.

The moment it hits the water, it is traveling at 1 m/s.

After 0.4s it has traveled 1m.

Given the density of water, d_w, find the density of the cube d_c.

Is this right?

If so, here is my setup, though it might be wrong.

There is some acceleration on the cube. The acceleration is created by two factors

1) Gravity

2) Buoyancy

We know

d = v_0 * t + ½ * a * t^2

1 = 1 * 0.4 + ½ * a * .16 (leaving out units for now… its hard to read if I put them in).

0.6 = .08 * a

a = 7.5 m/s^2

Here is where I’m stuck. I’m sure there is an equation involving the buoyancy that involves the two densities and maybe some other information, but I can’t remember it.

Does this help? Or am I on a completely wrong track?

Yep, F=ma. F1 is bouyancy, F2 is gravity. Draw a diagram to show the correct directions, subtract the forces. D = ½ at^2 + vt. You have D, v, and t. Solve for a, put that back into the F=ma equation to find the bouyancy force. Subtract out the density of water => voila.

@RocketGuy

So wait..

Assuming we know the m of the cube. Say its 2 kg.

F_b = m*a_b

a_b = 2.3m/s^2

So you have

F_b = 4.6 N.

How do you “subtract out the density of water?”

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