Q3E - University Physics with Modern Physics

Question

bio Jaw Injury. Due to a jaw injury, a patient must wear a strap (Fig. E4.3) that produces a net upward force of 5.00 N on his chin. The tension is the same throughout the strap. To what tension must the strap be adjusted to provide the necessary upward force?

Step-by-Step Solution

Answer

The tension in the strap must be adjusted to$3.15 N$   to provide 5.00 N upward forces.

Step 1: Given data

The straps make an angle $75°$  between them.

Step 2: Vector sum

The magnitude of vector sum of two vectors  $\overrightarrow{A}$ and  $\overrightarrow{B}$ with an angle   $\theta$between them is

  $R=\sqrt{A^2+B^2+2ABcos\theta } .....\left(1\right)$

Step 3: Tension in the string

Let the tension in each strap be T . Thus, from equation (1)

 $\begin{array}{rcl}5 \text{N}& =& \sqrt{T^2+T^2+2T^2\cos 75°}\\ & =& \sqrt{2}T\sqrt{1+\cos 75°}\\ & =& 1.59T\\ T& =& 3.15 \text{N}\\ & & \end{array}$ 

Thus, the tension in the strap should be  $3.15 \text{N}$.