Posted by Cooper-Nichol on Sunday, September 30, 2007 at 10:35pm.
that should be a= gtan? (theta, not ?)
What is the physical situation that this formula is supposed to apply to? What is theta? One can't derive a formula of this type without knowing the problem
Thats my thoughts exaclty! It is this rubber stopper of mass m is in a car and then when the car accelerates it makes an angle with the veritcal which is theta. We are supposed to find a=gtantheta in terms of mass and L, which must be radius, cause the rubber stopper (which is on a string on a rear view mirror) is spinning, so something to do with centripetal motion...this is all I can gather...please try and help me with this, I know its a lot to ask, but Im drowning with this, its the only question I cant even begin to guess!
Forget about the rubber stopper spinning and that it has a radius. Just treat it as a mass at the end of a string. The string exerts a tension force T on the stopper. When the car accelerates, the string deviates from a vertical line by an agle theta. Write down the force balance on the stopper.
T cos theta = m a
T sin theta = m g
Divide the first equation by the second:
(sin theta)/(cos theta) = tan theta
= a/g
Note that the mass cancels out.
I get it, but I think it needs to be T cos theta=mg and T sin theta =ma and then when you divide you divide Tsintheta=ma/T cos theta=mg
which leaves u with Sintetha=a/Cos theta=g
so Tantheta=a/g and then rearrange to get a=gtantheta... so thanks! a lot! This makes sense now!
You are right; I got my sines and cosines mixed up, and then I mixed up the equaitons to cancel out my mistake. I was in too big a hurry. Nice work catching my error(s)!