The two wires depicted in the figure are constructed from the same material, which possesses a breaking stress of 8 imes 10^8 N/m ^2 . The cross-sectional area of the upper wire is 0.006 cm ^2 and that of the lower wire is 0.003 cm ^2 . Given that the mass m₁ = 10 kg , m₂ = 20 kg and the hanger is light, determine the maximum load that can be placed on the hanger without breaking a wire. Also, state which wire will b

Step-by-step solution

Let M be the mass of the load placed on the hanger. The tension in the lower wire is given by T₁ = (m₁ + M)g = (10 + M) 10 . The tension in the upper wire is given by T₂ = (m₁ + m₂ + M)g = (10 + 20 + M) 10 = (30 + M) 10 . The cross-sectional area of the lower wire is A₁ = 0.003 cm ^2 = 3 10⁻⁷ m ^2 . The cross-sectional area of the upper wire is A₂ = 0.006 cm ^2 = 6 10⁻⁷ m ^2 . The breaking stress for both wires is _ max = 8 10^8 N/m ^2 . For the lower wire not to break, the stress must be less than or equal to the