Chapter 8.1, Problem 44E

To determine

To find: the pull on each part of wire.

Answer to Problem 44E

  $14lbs$

Explanation of Solution

Given information:

Weight of wire =24 pounds

Angle formed by the parts of wire with each other is $120°$ .

The figure below represents the angle formed by the parts of wire with each other.

Calculation:

The angle formed by the each wire on the painting be $x$ . The value of $x$ can be evaluated by using the angle sum property of triangle as shown below.

  $\begin{array}{c}120°+x+x=180°\\ 120°+2x=180°\\ 2x=60°\left[\text{Subtract 120}°\text{ from each side}\right]\\ x=30°\left[\text{Divide each side by 2}\right]\end{array}$

Thus the angle formed by each wire with the painting is $30°$ .

The vertical component of the vector is evaluated as follows:

  $\begin{array}{c}v=\text{magnitude}\times \sin \left(\text{direction}\right)\\ =24\sin \left(30°\right)\left[\text{Put the value of magnitude and direction}\right]\\ =14lbs\end{array}$

Thus the pull on each part of wire is 14lbs.