Chapter 5, Problem 7STP

To determine

To choose: The correct option.

Answer to Problem 7STP

The correct option is (B), 15 N.

Explanation of Solution

Given:

A force of 18 N being exerted by a string on a box at an angle of $34°$ with the horizontal .

Formula used:

A given vector R can be resolved into horizontal and vertical components and it is related to the vector using angle it makes with the horizontal axis as shown below.

  

Figure 1

The horizontal and vertical component of the vector are respectively given by

  $\begin{array}{l}{R}_x=R\cos \theta \\ R_y=R\sin \theta \end{array}$

Calculation:

Now, consider the given force 18 N exerted at an angle 34^o to the horizontal as shown in the Figure 2.

  

Figure 2

From Figure 2, the horizontal component of the vector is given by,

  $\begin{array}{c}{F}_x=F\cos 34°\\ =18\cos 34°\\ =14.92\text{N}\\ \simeq \text{15 N}\end{array}$

Conclusion:

Thus, the correct option representing the horizontal component of the given force is (B).