Question

A $2.0kg$ rope hangs from the ceiling. What is the tension at the midpoint of the rope?

Short answer

The tension in the midpoint of the rope is$9.8N$.

Step-by-step solution

Given information

Mass of the rope $m=2kg$.

Explanation

At the midpoint, the tension in the rope is supporting half the weight of the rope. For this, evaluateF and T

$F=mg\dots \dots \left(1\right)$

The tension at the midpoint localid="1649059361867" $T=\frac{F}{2}\dots \dots \left(2\right)$

Substituting the values in the equation $\left(1\right)$

localid="1649613472744" $$\begin{gathered} F=\left(2kg\right)\left(9.8m/s^2\right) \\ =19.6N \end{gathered}$$

Substituting the values in the equation $\left(2\right)$

localid="1649613456661" $$\begin{gathered} T=\frac{19.6N}{2} \\ =9.8N \end{gathered}$$

The tension in the midpoint of the rope $T=9.8N$.