Question

Suppose the bob of the previous problem has a speed of 1.4 m/s when the string makes an angle of 0.20 radian with the vertical. Find the tension at this instant. You can use $cos\theta \approx 1-{\theta }^2/2$ and $sin\theta \approx \theta$ for small $\theta .$

Answer 1

Bob has a velocity 1.4 m/sec, when the string makes an angle of 0.2 radian,

g = 0.1 kg, m = 100,

r = 1 m, v = 1.4 m/sec,

From the diagram,

$T-mgcos\theta =\frac{m{v}^2}{R}$

$\Rightarrow T=\frac{m{v}^2}{R}+mgcos\theta$

Given $cos\theta =1-\frac{{\theta }^2}{2}$

$\therefore T=\frac{0.1\times (1.4{)}^2}{1}+\left(0.1\right)\times 9.8(1-\frac{{\theta }^2}{2})$

$=0.196+0.98\times (1-\frac{2^2}{2})$

$=0.196+0.98\times \left(0.98\right)$

$=0.196+0.9604$

$=1.156N\approx 1.16N$