Plumb bob

[encipher]

I'm trying to solve the following problem with little success:

 

"A plumb bob does not hang exactly along a line directed to the center of the Earth, becaose of the earth's rotation. How much does the plumb bob deviate from a radial line at 35 degrees north latitude. Assume that the Earth is spherical"

 

Help would be greatly appreciated. I would tips on how to start the problem off.. or a run through of the problem rather than just solving the problem itself. I'd like to work it out(well.. most of it anyways) myself. Thanks alot!

[[Tycho?]]

So, whats a plum bob?

 

Just by the way the question is phrased I assume this has to do with centrifugal [centripital] force. Assuming this is true you'll need the equation F=mv^2/r. The radius will be the distance from the point on the surface to the earths axis of rotation, which you can get with the latitude. You'll end up with some "centrifugal" force which you can subtract from gravititational force which you can also find. If this plum bob thing is hanging you might have to some extra trig work to find out the appropriate angles.

 

If this isn't the question, then I dont know what to say.

[encipher]

Yeah, a plumb bob is basically a weight. So its weight hanging from a thread. So how would I go about doing the "extra calculations" you speak of?

 

Thanks again.

[[Tycho?]]

I dont really know, I'm just thinking of this off the top of my head.

 

You would get a force vector from the wieght of the plum bob, this would be pointing to the center of the earth. Then you would have a force vector pointing outward, perpendicular to the axis of rotation of the Earth. Now before other people jump on me, "centrigual" force doesn't really exist, but thinking about it in this way can help a lot.

 

So, you'll have those two force vectors. You'll need to figure out the angle between them, and then add or subtract some components. You'll be left with the component force vectors acting on the plum bob, and from there do a bit of pondering to figure out how it leans.

 

Thats the best I'm willing to do without writing anything down. If you need more help, uhh, ask I guess and hope someone else answers.

[swansont]

First step: Identify the forces on the plumb bob. (Draw a free-body diagram, and come up with the constituents of the net force)