Question

A small sphere is given a vertical velocity of magnitude \(v_0 = 5 m/s\) and it swings in a vertical plane about the end of a massless string. The angle \(\theta\) with the vertical at which the string will break, knowing that it can withstand a maximum tension equal to twice the weight of the sphere, is...

Length = 2 m.

Answer 1

@ganeshie8 i'm excellent at these questions but for some reason don't know where i'm getting it wrong!

Answer 2

1: Conservation of energy\[mg\ell (1 - \cos \theta) = \frac{1}2 m(v^2 - 25)\]2: Forces\[T - mg\cos \theta = \frac{mv^2}{\ell}\]Now put \(\ell = 2\) and \(T = T_{breaking} = 2mg\).

Answer 3

\[2mg(1 - \cos \theta)+25m/2 = \frac{1}{2}mv^2 \]\[\Rightarrow 2mg - mg \cos \theta = 2mg(1 - \cos \theta) + 25m/2\]

Answer 4

\[2mg - mg \cos \theta = 2mg - 2mg \cos \theta + 25m/2\]\[10\cos \theta = 25/2\]...oh no