Question

2. Consider a conical pendulum with a bob of mass m = 77.0 kg on a string of length L = 10.0 m that makes an angle of ???? 3.00° with the vertical. (Consider +î to be towards the center of the circular path and +ĵ to be upward.) a) Determine the horizontal and vertical components of the force exerted by the string on the pendulum. b) Determine the radial acceleration of the bob.

Answer 1

Explanation:

It is given that,

The mass of bob, m = 77 kg

Length of the string, L = 10 m

Angle made by the string with the vertical, $\theta=3^{\circ}$

(a) Let T is the force exerted by the string on the pendulum. At equilibrium,

$T\ cos\theta=mg$

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

$T=\dfrac{77\times 9.8}{cos(3)}$

T = 755.63 N

The horizontal component of the force is given by,

$T_H=T\ sin\theta$

$T_H=755.63\ sin(3)=39.54\ N$

The vertical component of the force is given by,

$T_V=T\ sin\theta=mg$

$T_V=754.59\ N$

(b) Let a is the radial acceleration of the bob. It can be calculated as :

$a=\dfrac{T_H}{m}$

$a=\dfrac{39.54\ N}{77\ kg}$

$a=0.51\ m/s^2$

Hence, this is the required solution.