All Problems

The Fundamental Equation of Dynamics

Problem 1.85

A small sphere of mass \(m\) suspended by a thread is first taken aside so that the thread forms the right angle with the vertical and then released. Find: (a) the total acceleration of the sphere and the thread tension as a function of \(\theta\), the angle of deflection of the thread from the vertical; (b) the thread tension at the moment when the vertical component of the sphere's velocity is maximum; (c) the angle \(\theta\) between the thread and the vertical at the moment when the total acceleration vector of the sphere is directed horizontally.

Reveal Answer
 (a) w=g1+3cos⁡2θ,T=3mgcos⁡θ (b) T=mg3 (c) cos⁡θ=1/3,θ=54.7∘ . \text { (a) } w=g \sqrt{1+3 \cos ^{2} \theta}, \quad T=3 m g \cos \theta \text { (b) } T=m g \sqrt{3} \text { (c) } \cos \theta=1 / \sqrt{3}, \quad \theta=54.7^{\circ} \text { . }
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