A 2 kg block is suspended from the ceiling of an elevator using a massless spring having a spring constant k = 100 N/m . The elevator is going up with an acceleration of 2.0 m/s ^2 . Find the elongation of the spring. If an additional 1 kg is attached to the block, what would be the further elongation?

Step-by-step solution

Given m₁ = 2 kg , k = 100 N/m , elevator upward acceleration a = 2.0 m/s ^2 , and taking g = 10 m/s ^2 . Inside the accelerating elevator, the effective acceleration due to gravity is g_ eff = g + a = 10 + 2.0 = 12 m/s ^2 . At equilibrium, the restoring force balances the apparent weight of the block. k x₁ = m₁ g_ eff 100 x₁ = 2 12 x₁ = 0.24 m When an additional mass m₂ = 1 kg is attached, the additional restoring force balances the additional apparent weight. k x₂ = m₂ g_ eff 100 x₂ = 1 12 x₂ = 0.12 m The initial