Question

A massive light hangs over the table in Jeremy's dining room. The light is supported by four strong chains which make an angle of 73.9° with the horizontal. The force in each chain is 38.4 N. Determine the mass of the light in kilograms (kg). Use the approximation g ≈ 10 m/s^2.Answer: ___________ kg

Answer 1

Given:

The is supported by four strong chains which make an angle of

$\theta=73.9\degree$

The force on each chain is

$F=38.4\text{ N}$

The acceleration due to gravity is

$g=10\text{ m/s}^2$

To find:

The mass of the light

Explanation:

The horizontal force by each chain is given by,

$\begin{gathered} F_h=Fcos\theta \\ =38.4\times cos73.9\degree \\ =10.6\text{ N} \end{gathered}$

The vertical force by each chain is given by,

$\begin{gathered} F_v=Fsin\theta \\ =38.4\times sin73.9\degree \\ =36.9\text{ N} \end{gathered}$

The weight of the light is balanced by the vertical force of the chains.

The weight of the light is,

$\begin{gathered} W=4F_v \\ =4\times36.9 \\ =147.6\text{ N} \end{gathered}$

The mass of the light is,

$\begin{gathered} m=\frac{W}{g} \\ =\frac{147.6}{10} \\ =14.76\text{ kg} \end{gathered}$

Hence, the mass of the light is 14.76 kg.