Question

I need to model a chain being wrapped around a spherical object. A chain wraps around the object perfectly forming a circle. New elements are added to the chain at a rate of 1/4πm/hour.


circumference of 40000km
the speed chains are being added 1/4πm/hour
so from the last term I guess that i know the circumference is increasing so that is the change in the circumference.

C = 2pir

so that i need to work out the rate of change of the radius
do i take the derivate of dC/dr

Answer 1

Call the length of the extra bit \(\Delta C\). Then \(\dfrac{\Delta C}{\Delta t}=\dfrac{\pi}{4}m/h\). Because \(C=2\pi r\), you get \(C+\Delta C=2\pi (r+\Delta r)\), so \(C+\Delta C=2\pi r+2\pi \Delta r\) and \(\Delta C=2\pi\Delta r\).

It seems to me that the change of the radius is equal to the change of the circumference divided by two pi.

Answer 2

Would you mind reformating your answer. I am finding it hard to follow.
I am not sure where you replace changeC/changeT = pi/4 m/h

Answer 3

Hope you can read this: (see image)

Answer 4

i am not sure where you have substituted changeC/changeT = pi/4

Answer 5

could you show me please where you insert that into the equation

Answer 6

Your information says: change of circumference is pi/4 per hour.
My calculation gives: change in radius is change of circumference divided by 2pi.

Combine the two: change in radius is pi/4 divided by 2pi, so 1/8 m/h

Answer 7

thanks I understand now.

Answer 8

YW!