Question

A father and son improvise a seesaw out of a plank and a sawhorse. The plank is uniform, has a mass one-fourth that of the father, and is 6 m long, with the sawhorse placed at the center of mass of the plank. If the son sits at the end of the plank, 3 m from the sawhorse, the father finds that to achieve balance, he has to sit 2 m from his end of the plank. What is their mass ratio Mf Ms

Answer 1

Their mass ratio,
`(M_f)/(M_s) \hspace{0.09cm}is \hspace{0.09cm}3`

Step-by-step explanation:

Here we have the principle of conservation of moment

Let the mass of the father = Mf and

The mass of the son = Ms and

The mass of the plank = 1/4 Mf

With the mass of the plank being uniform, the center of mass of the plank is at the center of the plank

Taking moment about the center of the plnk we have

Sum of moment about the y axis = 0

3 m × Ms + (-1 m) × Mf = 0

∴ 3 m × Ms = (1 m) × Mf

Therefore;

`(M_f)/(M_s) = \frac{3\hspace{0.09cm} m}{1\hspace{0.09cm} m} =3`