Calculating Plumb Bob Deviation at 35 Degrees North Latitude

[evman150]

Ok, here's the one question I can't get on my assignment. I really have no idea where to start.

A plumb bob does not hang exactly along a line directed to the centre of the Earth's rotation. How much does the plumb bob deviate from a radial line at 35 degrees north latitude?

How do I even go about starting this problem?

Any hints or help?

 

[ek]

Whoops, wrong account, didn't realize I had two accounts. Oh well. Anyways, this is my question. Sorry for having two accounts, when I signed up the email wouldn't send so I just got another account.

Also, there is a "hint" that goes with this question: "You can approximate the apparent weight by the real weight."

I don't know how that helps though.

 

[Doc Al]

centripetal acceleration

Here's a hint: If the Earth weren't rotating, the plumb bob would point straight towards the Earth's center. Furthermore the bob would be in equilibrium. But, alas, the Earth rotates. Thus the bob is accelerating towards its axis of rotation. Figure out that acceleration and then apply Newton's 2nd law to find the angle that the bob must hang.

 

[ek]

Here's a hint: If the Earth weren't rotating, the plumb bob would point straight towards the Earth's center. Furthermore the bob would be in equilibrium. But, alas, the Earth rotates. Thus the bob is accelerating towards its axis of rotation. Figure out that acceleration and then apply Newton's 2nd law to find the angle that the bob must hang.

Beauty. I wouldn't have thought of it like that. I don't really have a problem with this material, but I think the abstraction in this question was just too much.

Thanks.