Answer :
Answer:
it is safe to stand at the end of the table
Explanation:
For this exercise we use the rotational equilibrium condition
Στ = 0
W x₁ - w x₂ - w_table x₃ = 0
M x₁ - m x₂ - m_table x₃ = 0
where the mass of the large rock is M = 380 kg and its distance to the pivot point x₁ = 850 cm = 0.85m
the mass of the man is 62 kg and the distance
x₂ = 4.5 - 0.85
x₂ = 3.65 m
the mass of the table (m_table = 22 kg) is at its geometric center
x_{cm} = L/2 = 2.25 m
x₃ = 2.25 -0.85
x₃ = 1.4 m
let's look for the maximum mass of man
m_{maximum} = [tex]\frac{ M x_1 -m_{table} x_3}{ x_2}[/tex]
let's calculate
m_{maximum} = [tex]\frac{ 380 \ 0.85 - 22 \ 1.4}{3.65}[/tex](380 0.85 - 22 1.4) / 3.65
m_{maximum} = 80 kg
we can see that the maximum mass that the board supports without turning is greater than the mass of man
m_{maximum}> m
consequently it is safe to stand at the end of the table