Maths/physics whizzes please

[Oakie]

Related to Health and Safety at my work.

A) A weedeater's cutting circle has a diameter of 30cm. The string revolves at 10000rpm. How fast does the end of the cutting string go?

Now for double points and a free set of steak knives:

B) If the end of the string were to hit a 20 gram pebble, how fast would the pebble fly initially and how far could the pebble fly?

This is all to do with people who walk behind our Maintenance guys while they do weedeating, despite the warning signs and then complain when they get hit by flying debris.

[ellipsis]

...at what height above sea level...

[mashman]

When spinning does it spin in a straight line keeping the diameter at 30cm? doesn't it spin at 10000 rpm?

How big is the pebble? and at what angle is the pebble struck at?

Are there any swallows involved?

[FJRider]

How long does it take for paint to dry. So if you put up a "wet paint" sign ... you can put on the sign ... what time it will be safe to touch it.

A few WILL try to prove it wrong though ...

[Asher]

A) Circumference of the string= Pi X 30cm = 94.25cm
The string revolves 10,000 times per minute = 94.25 x 10000= 942500cm per minute
1cm per minute= 0.0006 kmh x 942500 = 565.5kmh

[Asher]

The second part to work out you would need the mass of the string, the mass and shape of the pebble and the angle it was struck

[gatch]

I wager that there is a tiny reduction drive inside the weed eater. And that the head isn't spinning at 10,000 rpm..

I find it highly unlikely that the tip speeds could exceed mach 4..

[Asher]

I wager that there is a tiny reduction drive inside the weed eater. And that the head isn't spinning at 10,000 rpm..

I find it highly unlikely that the tip speeds could exceed mach 4..

yeah i fucked up the maths, around 500kmh doesnt sound too unreasonable, how cool would it be to have a weedeater that broke the speed of sound

[Oblivion]

Relationship between RPM and velocity is V = r*w, and to convert to W (angular velocity), you need to multiply the RPM by 2π/60.

So, 6.28....../60*10000=1047 rads/s

Times that by the radius, which is 0.153,
and you get a velocity of 157mps.

The second one is a deflection question, which needs alot more info that what you got. Angle of deflection, pebble mass, and so on.

[FJRider]

Relationship between RPM and velocity is V = r*w, and to convert to W (angular velocity), you need to multiply the RPM by 2π/60.

So, 6.28....../60*10000=1047 rads/s

Times that by the radius, which is 0.3,
and you get a velocity of 314mps.

The second one is a deflection question, which needs alot more info that what you got. Angle of deflection, pebble mass, and so on.

I thought dia was 0.3 ... ???

[Asher]

yea that would make the radius .15 = 157m/s or 565km/h

[ellipsis]

...therefore, taking into account all the facts, variables and equations, the stone if hit in the precise zone of maximum applied force, could either fuck off into the universe on its great journey quite fast or hit some bint in a short skirt and whatever force the pebble had, in its flight, would diminish rapidly...how rapidly it stops is probably more the question...probably easier to answer, anyway...i

[Oblivion]

I thought dia was 0.3 ... ???

My bad Reading is a very valuable skill apparently.

[Berries]

This is all to do with people who walk behind our Maintenance guys while they do weedeating, despite the warning signs and then complain when they get hit by flying debris.

I think you will need a pilot vehicle, and probably even a full lane closure. Might be cheaper to get sheep instead.

[Oakie]

Brilliant! I got 400kph and thought that sounded ridiculous. I thought the second part of the question would incolve all sorts of crap like drag co-efficients and that sort of stuff but thought I'd ask anyway. Cheers guys. Knew I could count on you.