Physics Derivation URGENT!!

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Can someone please show me how to derive this...I am going crazy I have tried everyhthing that I can think of with this equation..even the Range Equation and that doesnt work! So please! I am dying and aahaha! How does this work in terms of mass and L? I think L has to be radius though, and you use something to do with centripetal force? HELP

a= gtan?

  • Physics Derivation URGENT!! -

    that should be a= gtan? (theta, not ?)

  • Physics Derivation URGENT!! -

    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

  • Physics Derivation URGENT!! -

    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!

  • Physics Derivation URGENT!! -

    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.

  • Physics Derivation URGENT!! -

    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!

  • Physics Derivation URGENT!! -

    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)!

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