Question

A small sphere is hung by a string from the ceiling of a van. When the van is stationary, the sphere hangs vertically. However, when the van accelerates, the sphere swings backward so that the string makes an angle of$\theta$with respect to the vertical. (a) Derive an expression for the magnitude a of the acceleration of the van in terms of the angle$\theta$and the magnitude g of the acceleration due to gravity. (b) Find the acceleration of the van when$\theta = 10.0 ^ { \circ }$(c) What is the angle$\theta$when the van moves with a constant velocity?

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The angle of the sphere when the van is moving is $\theta$. We need to: a) derive the expression of the acceleration, first by the terms of the angle, then by the terms of the gravitational acceleration b) calculate the acceleration of the van if:

$\theta= 10.0^o$

c) calculate the angle when the van is moving with a constant velocity.

We know the gravitational acceleration is:

$g=9.8\,\text{m/s}^2$

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