Question

A pendulum bob of mass 1kg is attached to a string 1m long and made to resolve in a horizontal circle of radius 80cm. What is the tension in the string?

Answer 1

Let's apply the Newton's Second Law of Motion in projections on axis $x$ and $y$:

$$Tsin\theta=\dfrac{mv^2}{r},$$ $$Tcos\theta=mg.$$

We can find the tension in the string from the second equation:

$$T=\dfrac{mg}{cos\theta}.$$

We can find angle $\theta$ from the geometry:

$$sin\theta=\dfrac{r}{L},$$ $$\theta=sin^{-1}(\dfrac{r}{L})=sin^{-1}(\dfrac{0.8\ m}{1\ m})=53^{\circ}.$$

Finally, we can calculate the tension in the string:

$$T=\dfrac{1\ kg\cdot9.8\ \dfrac{m}{s^2}}{cos53^{\circ}}=16.3\ N.$$