A block is hung by a string from the inside roof of a van. When the van goes straight ahead at a speed of , the block hangs vertically down. But when the van maintains this same speed around an unbanked curve , the block swings toward the outside of the curve. Then the string makes an angle with the vertical. Find .

θ = tan ( v²/gr)

Explanation:

This exercise we must find the angle of the string, for this we use Newton's second law

       F = m a

Let's create a reference system with one vertical axis and the other in radial direction,

vertical axis

        - W = 0

        T_{y} = W

Radial axis

        T_{r} = m a

As we are in a curve, they relate it to a switchboard

       a = v² / r

We use trigonometry to find the components of the tension

      cos θ = T_{y} / T

      sin θ = T_{r} / T

      T_{y} = T cos θ

      T_{r} = T sin θ

we substitute

    T cos θ = mg

     T = m g / cos θ

    T sin θ = m v² / r

    (mg / cos θ) sin θ = m v² / r

     tan θ = v² / g r

     θ = tan ( v²/gr)