Find density on dropping a ball

1. Jun 23, 2009

fawk3s

I remember my friend telling me once about this task in his physics competition. I had forgotten about it and remembered last night taking a shower. Started thinking but couldnt figure it out. Maybe you can help?

So you are given a small plastic ball, a ruler and a timer. Find the density of the ball. (I dont know if its full plastic or filled with air).

Finding cubage is easy. But finding the mass?

First I thougth that maybe I could find the mass with Ek=m*v(scuared)/2 or Ep=mgh, but you dont have neither of the E's (at least I dont think it was given).
So how do you get it? (Hope its not too simple cuz then I would looks really stupid again).

fawk3s

2. Jun 23, 2009

HallsofIvy

Staff Emeritus
Here's the method that is used to determine mass in orbit, in, say, the space station.

Attach the ball to one end of the ruler. Hold the other end firmly or clamp it to something and start the ball vibrating. The period of vibration will be proportional to the square root of the mass. Of course, you will need some known mass to compare to in order to be able to specify the mass of the ball.

3. Jun 23, 2009

fawk3s

what equation is that? or is it?

Last edited: Jun 23, 2009
4. Jun 23, 2009

northern expo

yes the concept described appears to be simple harmonics when you talk about the period of an oscillation. hmmm, remind me if i'm wrong but mass is not in the period of an ocsillation in simple harmonics

T = 2(pi)(sq. root)(length/g)

5. Jun 23, 2009

dave_baksh

Northern expo> You can replace the (length/g) with (mass/k) where k is the 'spring constant'

6. Jun 23, 2009

fawk3s

Ok, what equation is that? (Yes, srsly, I dont know).

7. Jun 23, 2009

dave_baksh

8. Jun 23, 2009

Andy Resnick

What about rolling it down a measured incline, timing it, and using that to calculate the moment of inertia? The moment of inertia will tell you if it is a solid sphere or a shell.

Or, let the ball rise/sink in a tub of water: if terminal velocity is reached, you can calculate the mass of the ball using Stokes flow; that plus the volume gives the density.

I'm sure there's other ways....