Question

A 0.30-kg flying pig toy is attached to the ceiling with a string. When the pig’s wings flap, it moves at a constant speed of � = 2.00 m/s in a horizontal circle of radius � = 0.25 m. Find the angle � the string makes with the vertical.

Answer 1

Answer:

58.5 deg

Explanation:

$v$ = mass of the pig toy = 0.30 kg

$v$ = speed of the toy = 2 m/s

$r$ = radius of the circle = 0.25 m

$\theta$ = Angle of the string with the vertical = ?

$T$ = Tension force in the string

Using equilibrium of force in vertical direction

$T Cos\theta = mg$                                     eq-1

Along the horizontal direction, the component of tension force provides the necessary centripetal force, hence

$T Sin\theta = \frac{mv^{2}}{r}$                                  eq-2

Dividing eq-2 by eq-1

$\frac{T Sin\theta}{T Cos\theta} = \frac{\frac{mv^{2}}{r}}{mg}$

$tan\theta= \frac{v^{2}}{rg}$

$tan\theta= \frac{(2)^{2}}{(0.25)(9.8)}$

$tan\theta = 1.63$

$\theta$ = 58.5 deg