Watch out, this bob might hit you unawares!

Find the tension in the string when the bob is released from rest in the following figure.

also see my set

2 3 m g \frac{\sqrt{2}}{3}mg 3 2 m g \frac{\sqrt{3}}{2}mg N o n e None 0 0 2 3 m g \frac{2}{\sqrt{3}}mg

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3 solutions

Vaibhav Prasad
Mar 24, 2015

The component in the vertical direction :

m g × cos θ mg \times \cos \theta

= 3 2 × m g = \frac{\sqrt3}{2} \times mg

Tanishq Varshney
Mar 24, 2015

ok if u get this wrong , no problem. I was also wrong on the first attempt.

Force will be balanced along the string as there is no acceleration along the string .

So T = 3 2 m g T=\frac{\sqrt{3}}{2}mg

Do upvote

Jake Lai
Apr 4, 2015

The key thing to note is that the system is a pendulum, which has a periodic circular motion. This implies that when the ball is released, there is a force tangential to the arc (ie perpendicular to the radius).

By Newton's second law of motion, F net,rad = 0 F_{\text{net,rad}} = 0 . Since the two forces are the weight of the bob m g mg and the tension in the string T T , we then know that

T = m g cos 3 0 = 3 2 m g T = mg\cos 30^{\circ} = \boxed{\frac{\sqrt{3}}{2}mg}

after resolving the vectors.

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