How much G force can I apply to a mouse that is at the bottom of a 10-gallon bucket...?

Question

...being swung as quickly as possible at arm's length in a vertical circle?

Answer 1

These calculations are approximations although the equations are correct.

I suspect you'd get about 5 revs per second maximum (and even then I suspect you might take off!).

Lets assume the bottom of the bucket to your shoulder is 1metre.

Centrifugal (although the mouse actually feels a centripetal) force is given by the equation m*r*w^2 (m=mass, r=radius in metres, w=omega=rotation in radians per second)

So, w=2*pi*5=10*pi

Therefore the centrifugal force is:
m*1*(10*pi)^2=m*100*pi^2

For approximation we can call pi^2=10 so the centrifugal force is approx m*1000N

Gravitational force is mg where g=9.81m/s^2 (again approx 10) so the gravitational force is m*10N.

Therefore dividing the centrifugal force by the weight we get 100 g. However, if we can only spin the bucket at 2revs a second, we would get not 2/5 but 4/25ths of the g force and hence only about 16g.

At the bottom of the swing you'd gain a g and at the top you'd lose a g as the gravity either adds or subtracts from the centrifugal force.

Also, you would need to be stronger to hold on to it the faster you spin it. If your bucket and mouse weighed a kilogram at rest, at 2 revs per second it'd weigh 16kg, but at 5 revs per second it would weigh 100kg. Better start pumping iron, but I think the mouse is safe.

Answer 2

For one, don't actually carry this out with a live animal. It isn't an experiment, just sadistic. Lets just use a bucket with some water in it.

Some basic assumptions: you're not superman so your arm will only be able to do ~2 cycles per second max. This is a radial velocity of w=4*pi radians/sec. We'll say the radius of curvature is r=1m to be simple, but you could measure your arm to be more accurate.

The linear velocity is v=w*r = (4*pi rad/sec)*1m

accerleration a=v^2/r, so a = r*w^2 = 158m/sec^2, or 16g.

Answer 3

That depends on how cruel you are.

Answer 4

Why would you do this?

Answer 5

Go for it.'