A heavy block is supported by three lines as shown. Which of the following statements is true in its entirety? A) T₁ T₂ and T₂ T₃ B) T₂ T₁ and T₁ T₃ C) T₂ T₃ and T₃ T₁ D) T₃ T₁ and T₁ T₂ E) T₁ T₃ and T₂ T₃

Question

A heavy block is supported by three lines as shown. Which of the following statements is true in its entirety? A) T₁ > T₂ and T₂ > T₃ B) T₂ > T₁ and T₁ > T₃ C) T₂ > T₃ and T₃ > T₁ D) T₃ > T₁ and T₁ > T₂ E) T₁ > T₃ and T₂ > T₃

Quizplus · Accepted Answer

According to the principle of equilibrium, the sum of the upward forces must be equal to the sum of the downward forces. The block is in equilibrium, so the tension in each of the three ropes must be equal. Therefore, T₂ = T₃. The tension in T₁ must be equal to the weight of the block, but we cannot determine its relative value to the tension in the other two ropes. However, since the tension in T₂ is shared between the weight of the block and the other two ropes, it must be greater than both of them individually, hence T₂ > T₃. Similarly, since the tension in T₃ is shared between the weight of the block and the other two ropes, it must be greater than both of them individually, hence T₃ > T₁. Therefore, option C is the correct answer.

A Heavy Block Is Supported by Three Lines as Shown