Two rods of equal length are rigidly connected in parallel. Rod A has area 2 cm² and Young's modulus 200 GPa. Rod B has area 4 cm² and Young's modulus 100 GPa. A total tensile load of 60 kN is applied to the common end plate. If rod A carries N kN, find N.
Physics · Properties of solid and fluid · Elastic Properties of Solids: Stress, Strain and Elastic Moduli
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Question

Two rods of equal length are rigidly connected in parallel. Rod A has area 2 cm² and Young's modulus 200 GPa. Rod B has area 4 cm² and Young's modulus 100 GPa. A total tensile load of 60 kN is applied to the common end plate. If rod A carries N kN, find N.

Physics · Properties of solid and fluid · Elastic Properties of Solids: Stress, Strain and Elastic Moduli

G1 Physics · Accepted Answer

Parallel rods between rigid plates undergo the same strain ε. Therefore, F = YAε. For rod A, Y(A)A(A) = 200×2 in common proportional units. For rod B, Y(B)A(B) = 100×4. Both products are equal: 200×2 = 100×4 = 400. Hence both rods carry equal force. Therefore, F(A) = 60/2 = 30 kN. Hence, N = 30.