Question

A person is standing on the very end of a 2 m long board that is level and balanced. The balance point is 0.20 m from the end the person is on. The board has a mass of 20 kg.a) What is the mass of the person?

Answer 1

Given data:

* The length of the board is L = 2 m.

* The distance of the person from the center of the board is d = 1 m.

* The distance of the balancing point from the person is x = 0.2 m.

* The mass of the board is m_1 = 20 kg.

Solution:

The diagrammatic representation of the given case is,

From the diagram, the beam is in a balanced state under the action of the weight of the person as well as the weight of the board.

Thus, the moment about the center of the gravity (taking anticlockwise as positive and clockwise as negative) is,

`M=m_1*(d-x)-m_2* x_{}`

where m_2 is the mass of the person,

The net moment is zero, as the board is in a balanced state,

Substituting the known values,

`\begin{gathered} 0=20*(1-0.2)-m_2*0.2 \\ 0=20*0.8-m_2*0.2 \\ 0.2m_2=16 \\ m_2=(16)/(0.2) \end{gathered}`

By simplifying,

`m_2=80\text{ kg}`

Thus, the mass of the person is 80 kg.