Chapter 2, Problem 3TC

A block of iron is suspended by ropes in the positons shown below. Scales measure the tension (stretching force) in the ropes. Rank the scale reading from greatest to least.

To determine

The ranking of scale reading from greatest to least.

Answer to Problem 3TC

The ranking of scale reading from greatest to least is B = D > C > A.

Explanation of Solution

In case A, the block is suspended by three ropes, and tension in each rope is $T_A$. Assume the sum of all the tension of ropes is equal to $T$.

Write the expression for the force balance equation.

$\begin{array}{c}{T}_A+T_A+T_A=T\\ T_A=\frac{T}{3}\end{array}$

The tension force supports the weight of the block.

Write the expression for the relation of tension force and weight of block.

$T_A=\frac{W}{3}$

Here,

$W$ is the weight of the block

Thus, the tension scale will read $\frac{W}{3}$.

In case B, the block is suspended by one rope, and tension in the rope is $T_B$.

Write the expression for the relation of tension force and weight of block.

$T_B=W$

Thus, the tension scale will read $W$.

In case C, the block is suspended by two ropes, and tension in each rope is $T_C$.

Write the expression for the force balance equation.

$\begin{array}{c}T=T_C+T_C\\ T_C=\frac{T}{2}\end{array}$

Write the expression for the relation of tension force and weight of block.

$T_C=\frac{W}{2}$

Thus, the tension scale will read $\frac{W}{2}$.

The block D is suspended with one rope having two scale. The tension in the rope is $T_D$.

Write the expression for the relation of tension force and weight of block.

$T_D=W$

Thus, the tension scale will read $W$.

Conclusion:

Therefore, the ranking of scale reading from greatest to least is B = D > C > A.