Two forces of magnitudes 10 N and 6 N act at an angle of 60 degrees to each other. Find the magnitude of the…

Question

Two forces of magnitudes 10 N and 6 N act at an angle of 60 degrees to each other. Find the magnitude of the resultant force.

ScanSolve AI Tutor · Accepted Answer

To find the magnitude of the resultant force, we use the law of cosines for vector addition.

Identify the given values.
The first force is $F_1 = 10 \text{ N}$ .
The second force is $F_2 = 6 \text{ N}$ .
The angle between the forces is $\theta = 60^\circ$ .
Apply the formula for the magnitude of the resultant force ( $R$ ).
The formula is:
$R = \sqrt{F_1^2 + F_2^2 + 2 F_1 F_2 \cos \theta}$
Substitute the values into the formula.
$R = \sqrt{(10 \text{ N})^2 + (6 \text{ N})^2 + 2 (10 \text{ N}) (6 \text{ N}) \cos 60^\circ}$
Calculate the terms.
We know that $\cos 60^\circ = 0.5$ .
$R = \sqrt{100 \text{ N}^2 + 36 \text{ N}^2 + 2 (60 \text{ N}^2) (0.5)}$ $R = \sqrt{100 \text{ N}^2 + 36 \text{ N}^2 + 60 \text{ N}^2}$ $R = \sqrt{196 \text{ N}^2}$
Calculate the square root.
$R = 14 \text{ N}$
The magnitude of the resultant force is $14 \text{ N}$ .

Comparing this with the given options:
A. 14 N
B. 16 N
C. 8 N
D. 12 N

The correct option is A.

The final answer is $\boxed{\text{A. 14 N}}$ .

Two forces of magnitudes 10 N and 6 N act at an angle of 60 degrees to each other. Find the magnitude of the resultant force.