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 ... :innocent:

[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 :blink: Reading is a very valuable skill apparently. :facepalm:

[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.

[jellywrestler]

speaking of weedeaters, you ain't seen colourful till you've chased a peacock round a paddock with a weedeater....

[Spuds1234]

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

You could take a rough guess though and say the pebble was 20g and the string was 5g and that all the rotational energy of the plastic string was transferred into the pebble (I doubt it would be though as the string is flexible and the impact would be elastic) which would give you a rough speed that the pebble leaves the string at 80m/s. Obviously this is way to high though as its based off perfect world estimates, but for Oakies needs its probably good enough.

[gunnyrob]

you're over thinking it. Refer to the manufacturers safety info. Most normally specify a distance of about 30 feet. You should be doing a hazard assessment and be acting in accordance with your company safety policy. (Spot the safety auditor)

[The Singing Chef]

Step one: Get weedeater.
Step two: Get 20 - 20g Pebbles of different shapes.
Step three: Play golf.

A fun way to find out? I think so!

[bogan]

Stepping back from the highlighted problem a bit, but why are you guys running a weed eater over pebbles? They do a better job if you use them on weeds!

[Oakie]

Stepping back from the highlighted problem a bit, but why are you guys running a weed eater over pebbles? They do a better job if you use them on weeds!

Used to be just weeds but earthquakes put pebbles, asphalt, crud etc in our green areas.

[Oakie]

you're over thinking it. Refer to the manufacturers safety info. Most normally specify a distance of about 30 feet. You should be doing a hazard assessment and be acting in accordance with your company safety policy. (Spot the safety auditor)

Good point. I guess I am doing a hazard assessment in a round-about way and we will finish up with a policy by default. It's just one of those annoying ones where you'd think everyone will recognise how to keep safe ... but noooo! Silly thing is that even though this is a facility for intellectually disabled adults, it was one of the staff who walked themselves into danger! Seeing the maintenance guy head to foot in PPE wasn't enough of a clue it seems.

[5150]

Is it electric or petrol powered weed eater? If petrol, is it a 4 stroke or a 2 stroke?

Also is it clockwise or anticlockwise spin?

[avgas]

The safe distance is actually a lot smaller than you think. Its to do with the fact that the nylon bends on contact absorbing most of the energy.
So don't be surprise if the actually around 10-20m/s - around a good slingshot speed.

This is why pebbles don't fly a few km's, go through legs of individuals etc after being hit by a weed eater line...............which some of the calculations here would leave you believe (fyi @ 50m/s is tornado speeds......and would blow a pebble through a thin wall).
I almost giggled at the 3-400m/s........that is nearing .22 cal speeds. And those things go for km!

[Oakie]

Is it electric or petrol powered weed eater? If petrol, is it a 4 stroke or a 2 stroke?

Also is it clockwise or anticlockwise spin?

Petrol and 2 stroke I believe. A whole 1.2hp.

[5150]

Petrol and 2 stroke I believe. A whole 1.2hp.

Shit. By my calculations using my FX-82 scientific calculator, she'd be travelling at over mach 4. :weird: Oh, hang on, I am holding the calculator up side down. :facepalm:


Ok. Further following a prctical test in my driveway using a Ryobi 2 smoke weed eater and a 10mm round(ish) stone I can confirm that it hit the neighbours shed window from aprox 25 metres away. that was at full blast 10.000 RPM with 3km head wind.

Result. Neighbour is giving me evils. :innocent:

[slofox]

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

Same answer I got...MUST be right then!

[mossy1200]

Weedeater should have guards on it to prevent peeble from being able to be shot out other than the front in which would be angled towards the uncut weeds that would slow or prevent the peeble from going anywhere. Unless you were to leave weedeater on its side running and the peebles were thrown into it. Im thinking refer the user manual for operating instructions.

[avgas]

Shit. By my calculations using my FX-82 scientific calculator, she'd be travelling at over mach 4. :weird: Oh, hang on, I am holding the calculator up side down. :facepalm:


Ok. Further following a prctical test in my driveway using a Ryobi 2 smoke weed eater and a 10mm round(ish) stone I can confirm that it hit the neighbours shed window from aprox 25 metres away. that was at full blast 10.000 RPM with 3km head wind.

Result. Neighbour is giving me evils. :innocent:
So it didn't blow a hole in the garage?
Must be less that 50kph then?.....................................NOT 500KPH!

Sometimes I wonder if calculators make people stupid, or smarter?

[5150]

So it didn't blow a hole in the garage?
Must be less that 50kph then?.....................................NOT 500KPH!

Sometimes I wonder if calculators make people stupid, or smarter?

On closer inspection of the said shed window, I can confirm 3 things.

1) The stone did not leave any damage on the glass
2) The neighbour has a fine collection of nudie posters on his garage walls
3) His garage is a fucking mass

[bogan]

Same answer I got...MUST be right then!

Sounds right to me, I mean, a bit of plastic cable aint going to cut fuck all if it is just lightly pushed against it now is it!

What you really want to do, is jam a knife handle first into some grass, then weed wacker it to see how far the plastic flys when cut. 5150 is your neighbour still watching? Might want to warn him about flying bits of plastic this time around, hopefully the knife will stay where it is though.

This distance will give the inertia of the thingumy, and a brightly colored bit of plastic is easier to find than a pebble. From there you can scale the pebble distance by the inverse of the weight. So for a 30g pebble and 1g bit of plastic that goes 90m, would give you a pebble safe distance of 3m.

[bogan]

Or better idea, hire more people to paint the pebbles high vis yellow, and put little parachutes on them to ensure they stay below mach 4.

[Ratti]

Bogan wins this round.

Have been crying with laughter right through this thread. had run-in with my neighbour today...I might just get the weedeater out and practice Pebble flinging. He'd have insurance right?

[Oakie]

Ok. Further following a prctical test in my driveway using a Ryobi 2 smoke weed eater and a 10mm round(ish) stone I can confirm that it hit the neighbours shed window from aprox 25 metres away. that was at full blast 10.000 RPM with 3km head wind. Result. Neighbour is giving me evils. :innocent:

Practical maths. Love it! I shall add the findings of your experiment to my report to the HSE Committee on Tuesday and even give you credit! You may be awarded a chocolate fish!


Weedeater should have guards on it to prevent peeble from being able to be shot out other than the front in which would be angled towards the uncut weeds that would slow or prevent the peeble from going anywhere. Unless you were to leave weedeater on its side running and the peebles were thrown into it. Im thinking refer the user manual for operating instructions.

Yeah it does have guards. The person who got hurt approached our guys from behind and walked in front of them. Blamed them of course.

[Spuds1234]

Yeah it does have guards. The person who got hurt approached our guys from behind and walked in front of them. Blamed them of course.

I thought your employees were supposed to be less special than the customers....

[Marmoot]

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..

If 560kmh is more than mach 4, then my bike actually went mach 2 or twice the speed of sound at the pukekohe back straight??? :blink:

[Oakie]

I thought your employees were supposed to be less special than the customers....
Alas, so did I. Sometimes the line is really blurry!

[Oakie]

If 560kmh is more than mach 4, then my bike actually went mach 2 or twice the speed of sound at the pukekohe back straight??? :blink:

Off the top of my head I'd say 560kph is about mach .4 that's mach point 4. Like a bit less than half the speed of sound.

[Marmoot]

Off the top of my head I'd say 560kph is about mach .4 that's mach point 4. Like a bit less than half the speed of sound.

That guy i quoted said mach 4, dude.

[Oakie]

That guy i quoted said mach 4, dude.

Yeah I know. Just clarifying for the general population.

[5150]

Practical maths. Love it! I shall add the findings of your experiment to my report to the HSE Committee on Tuesday and even give you credit! You may be awarded a chocolate fish!




No need for chocolate fish, but if they have any jobs going in RnD', then put me down.