Homework Help: I'm so lost! Volume and tension?

1. Nov 17, 2004

If a ball of styrofoam ( p=100kg/m^3) is totally submerged in water. the ball has a mass of 300g. How can i find the volume? and if it is being held by a string how do i find the tension of this string? :uhh: I don't know where to start! i've tried using the denisty equation but i still get lost. ( d=m/v)

2. Nov 17, 2004

Nylex

You've got the density, mass and the equation that relates those and volume. Surely it's not that hard to find the volume??

3. Nov 17, 2004

But ?

What is the p= 100kg/m^3 thing? what is that? How do i find the density?
I don't know what the p stands for and i can't find the density without the volume, but that is what i'm trying to find.

Last edited: Nov 17, 2004
4. Nov 17, 2004

I would be really easy if i could find the density and if i knew what the p thing was. maybe it just me ? but i'm so lost!

Last edited: Nov 17, 2004
5. Nov 18, 2004

jimbo007

you already have the density and dont need to work it out
mass of the ball = 0.3kg
density of the ball = 100kgm^(-3)
re arrange your density formula to solve for volume, v
v=m/d
insert numbers and out pops the volume
v = 0.3/100 m^3

6. Nov 18, 2004

brewnog

Shadow, 'p' is actually the greek letter 'rho'. You'll likely come across it a lot when referring to density.

7. Nov 18, 2004

Thanks! Tension?

thanks alot people but now i'm haveing trouble finding the tension of this problem , the professor never told us how to get the tension i have been trying to find it. Would it just be the weight of the ball plus gravity? I don't know she never gave us a formula if i had the formula or knew how to find it i could get it>

8. Nov 18, 2004

brewnog

Start off with the density of water, and compare it with the density of your styrofoam. Do you know why things float? Since your ball is being restrained so that it is completely under water, it will have displaced it's exact volume in water. And you know how dense water is....

9. Nov 22, 2004

What?? I'm Lost??

the density of water is 1g/cm^3, but it can change with temperature??
I still can figure out what to do! The ball floats because of its density compared to that of the waters.I kow that! But How do i find the tension in the string? Is it just The Density of the Ball + That Of the Water or am I totally Confused? :grumpy:

10. Nov 22, 2004

Staff: Mentor

The ball is not exactly "floating", since it's being held under water by a string. But it is in equilibrium, so you know that the net force on it is zero. So consider all the forces acting on the ball. There are three:
(a) weight of the ball (acting down)
(b) buoyant force (acting up)
(c) the tension in the string (acting down)​
These forces must add to zero.

Since you know the mass of the ball and its density, you can figure out its weight and volume. Using the volume you can find the buoyant force. Then use the equilibrium equation (forces add to zero) to solve for the tension.