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

Step-by-step 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=(mg)/(cos\theta)`

`T=(77* 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=(T_H)/(m)`

`a=(39.54\ N)/(77\ kg)`

`a=0.51\ m/s^2`

Hence, this is the required solution.