How Far Can You Safely Walk on a Pole to Rescue a Cat at the Grand Canyon?

[Planckenstein]

I've a test soon, and I've been thinking about this, and not quite sure how to approach it. I think I understand the chapter, but I can't seem to get it.

A uniform 210lb telephone pole is sticking out over the Grand Canyon (32 feet of it is sticking out) with a massless cat stuck at the end of it. If you weigh 190lbs, how far out can you walk onto the pole to rescue the cat.

This seems relatively easy but, again, I just can't get it. Answer's suppost to be 14.4ft. Thanks!

 

[Andrew Mason]

A uniform 210lb telephone pole is sticking out over the Grand Canyon (32 feet of it is sticking out) with a massless cat stuck at the end of it. If you weigh 190lbs, how far out can you walk onto the pole to rescue the cat.

You will have to give us all the information. I gather the pole has a total length greater than 64 feet. How much longer than 64 feet is it?

AM

 

[Planckenstein]

Whoops! The pole is 90 feet long. That's all the information I've been given.

 

[Andrew Mason]

Whoops! The pole is 90 feet long. That's all the information I've been given.

This is a torque problem about a fulcrum at the cliff edge. Think of the 58 feet of pole on the ground as a weight of 58/90ths of the pole weight with a centre of mass located at the midpoint of that 58 foot length, or 29 feet from the fulcrum. Similarly the 32 foot section is a mass of 32/90ths of 210 with a centre of mass at 16 feet. Add the torque caused by you at a distance s from the fulcrum and that has to equal the torque of the ground section.

But why risk your life? If it is a massless cat, it is not going to fall!

AM