Question

A red ball of mass 5.57 kg is suspended between two walls on a string, as illustrated here. The weight of the ball causes the string to sag, making an angle \theta=θ= 19.4 degrees as indicated. What is the resulting tension F T ​T ​​ in the string, in Newtons?

Answer 1

164.33 N

Step-by-step explanation:

Given:

The mass of the ball, m = 5.57 kg

Angle made by the sag = 19.4°

it is required to find the tension
`F_T` in the string

Note: Refer the attached figure

The tension in the string will be caused by the weight of the wall

thus,

Weight of the ball, W = 5.57 kg × 9.8 m/s² = 54.586 N

Now the resolving the tension
`F_T` in the string into components as shown in the figure attached, the weight of the ball will be balanced by the sin component of the tension

thus,

W =
`F_T`sinΘ

or

54.586 N =
`F_T` sin 19.4°

or

`F_T` = 164.33 N

Hence, the tension in the string will be 164.33 N