Question

Two 25.0-N weights are suspended at opposite ends of a rope that passes over a light, frictionless pulley. The pulley is attached to a chain from the ceiling.

(a) What is the tension in the rope?

(b) What is the tension in the chain?

Short answer

(a) The tension in the rope is 25N.

(b) The tension in the chain is 50N.

Step-by-step solution

Tension in Rope

Given Data:

• The weight of suspended objects from the rope is $W=25\mathrm{N}$.

The tension in each rope is found by using the vertical equilibrium of each weight. The tension in each rope is the same because the attached weight on both sides is also the same. The tension in the chain is equal to the sum of tensions in both ropes.

Determine the tension in the rope by using vertical equilibrium(a)

The tension in each rope is calculated as:

$$\begin{gathered} T-W=0 \\ T=W \end{gathered}$$

Here$T$is the tension in each rope$W$is the attached weight.

Substitute all the values in the above equation, and we get,

$T=25\mathrm{N}$

Therefore, the tension in the rope is 25 N.

Determine the tension in the chain(b)

The tension in the chain is calculated as:

$$\begin{gathered} T_c-W-W=0 \\ {T}_c=2W \end{gathered}$$

Here$T_c$is the tension in the chain.

Substitute all the values in the above equation, and we get,

$$\begin{gathered} T_c=2\times \left(25\mathrm{N}\right) \\ {T}_c=50\mathrm{N} \end{gathered}$$

Therefore, the tension in the chain is 50 N.