A small sphere is hung by a string from a ceiling of a van. When the van is stationary, the sphere hangs vertically. However, when the van accelerates, the sphere swings backewards so that the string makes an angle of (z) with respect to the vertical. a)Derive an expression of the magnitude "a" of the acceleration of the van in terms of the angles (z) and the magnitude of "g" of the acceleration due to gravity. b) Find teh acceleration of the van when (z) = 10 degrees.

Hi, I don't know if you still need an aswer to this question, but I was thinking about it, and here's the answer I believe.

A tension T is created when the sphere is swung backwards. That T is equal to let's say m1 (mass of the sphere) multiplied by the sin of the angle multiplied by g. T=m1(g)sin(z). Conversely, T is equal to the force required to swing the sphere back this far. T is a force in which F=ma. In this case the acceleration of the van is the cause of that force. So T=m1a1 in which a1=acceleration of the van such that yields m1(g)sin(z)=m1a1. Mass cancels so (g)sin(z)=a1... so for problem 2

9.8*sin(10)=a1

I don't have a calculator so I can't give the answer to a1, but I believe that's right..if any other physics folks can check this out to make sure my trig and formulas are correct I would appreciate. Thank you.