Question

Static Equlibrium: The principle of static equilibrium is based on Newton's Second Law of Motion in the linear (translational) and rotational dimensions. The Second Law in these dimensions are: ∑?_?=0 ∑?_?=0 ∑?=0 where τ = rFsinθ is the torque. When all of these conditions are true, we have achieved static equilibrium. Below is a picture of a rod, suspended by a rope. On either end is an object which exerts a torque on the rod about the pivot point (the rope).

Since there are no x-component forces, we can ignore that equation. Use the conditions of static equilibrium (∑F=0 and ∑τ=0) to derive two equations for this setup, and simplify as much as possible. (Your Force equation will end up only in terms of Tension (FT), masses, and gravity (g).) (Your Torque equation will end up only in terms of distances and masses.) ∑?_?=0 ∑?=0

Answer 1

Equation of force Sigma f = 0: - (m_1 + m_2) = T --- iy equation of torque Sigma tau = 0: - T_clockwise = T_anticlockwise = > m_1gd_1 = m_2gd_2 = > m_1d_1 - m_2d_2 = 0 --- iiy From equation iy & iiy we masses, distances R forces applied.