Worked Exercise — Block Hanging from Two Ropes

Problem

A block of $80\;\text{kg}$ hangs from a vertical rope attached to a ceiling. Find the tension $t$ in the rope.

Solution

Step 1 — Forces on the block. Only two vertical forces act on the block: the weight, directed downward, and the rope tension, directed upward.

$\vec{P} = (0,\ -80\cdot 9{,}81) = (0,\ -784{,}8)\;\text{N} \qquad \vec{t} = (0,\ t)$

Step 2 — Equilibrium condition. Since the block is at rest, the vector sum of the forces is zero, $\vec{P} + \vec{t} = \vec{0}$. The $y$ component gives

$-784{,}8 + t = 0$

Step 3 — Result. The rope tension is

$\ev{t = 784{,}8\;\text{N}}$

Links

Topics: Statica ed equilibrio Concepts: Equilibrio statico · Tensione · Forza peso Objects: Blocco · Fune ideale