[cc100]

here we go:

a man lies on a bed of nails, so that his whole weight is supported on their tips. his weight is 650N and the area of each nail tip is is 1 mm2(squared). the pressure on his skin from each nail can be calculated in the samne way as the stress. if a pressure of 4 N mm-2 is the maximum he can withstand without pain, calculate the smallest number of nails he must lie on in order not to be hurt.

(this may help: pressure= force divided by area, where pressure is in N mm-2, force is in N, area is in mm2(squared)


i know its a toughie but , can you help??

[Stu xxx]

2 - sorry hon that is just a guess - all too confusing for my little brain x

[BusyBee]

Sorry my head hurts just reading it, will have to go and have a lie down.



I need a calculator to add up and then I do it three times, get the same answer twice and that's the right one.

[Sticks]

OK

Suppose we have

• body of weight W N
• Maximum pressure endured Pmax Nmm^-2
• Area of each pin is a mm^2
• And X pins

The weight must be distributed evenly the X pins and given the surface area of each pin this will be an area X.a

The maximum pain threshold Pmax is defined as force / area

This gives us:


Pmax = w / (X.a)

Rearranging gives


X = W / (Pmax.a)


An examination of the units show they cancel out

Plugging in the numbers gives 162.5

Since we canot have 0.5 of a pin, we round up to give the answer of 163 pins

Pluging the nuimbers back

Pmax = 650 / (163 * 1) = 3.99

Just under tollerance

QED

[cc100]

Good man, well done!!!

a follow up question:

why does he have to be careful when getting on and off the the bed of nails??

[Sticks]

Unless he teleports onto the nails he will have to bend, thus exposing less surface area, and less nails to support him. The value of Pmax will then climb past the threshold set

[cc100]

correct!!!

would you like another?

[Sticks]

How about one for you

A crane is working on a building site, see attached diagram.

The crane bob is moved in and out along the gantry (X) and of course up and down (Y). The crane top also rotates through an angle of (č)

The crane picks an item up from the ground at one end of the site and delivers it to the top of the construction (h) after turning through an angle and moving the crane bob from near the end of the gantry to near the centre of the crane tower (As in the diagram)

Describe the curve in 3D space that the crane bob travels in algebraic terms.

(I have not yet worked this one out either )

[Mark]

A Twisted Cubic or a Horopter are the nearest I can find so far - but they aren't perfect.

I'll keep looking

- Mark

[Sticks]

This is a suggestion from a friend in the United States

I hope this helps

I don't know about algebraic terms, but you could certainly express it as an integral. The motion is a combination of polar motion (rho, your X, and theta), and linear motion in the vertical (I would have called it Z). The motion is the sum of these two, or rather the integral of the two differential motions.

I'm doubting that it can be represented as a simple algebraic formula.

[cc100]

ouch...my head hurts....erm.............