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.