Question

What is the resultant force of two forces of magnitude 3 and 5 N acting at an angle of 60° ?

• A. 6 N
• B. 8 N
• C. 7 N
• D. 9 N

Hint:

This is a classic vector problem.
Remember that \( \cos 60^\circ = 0.5 \), which simplifies the calculation under the square root to \( \sqrt{F_1^2 + F_2^2 + F_1 F_2} \).

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
The resultant of two forces acting at a single point can be calculated using the law of cosines for vector addition.
Key Formula or Approach:
The magnitude of the resultant force \( R \) is given by:
\[ R = \sqrt{F_1^2 + F_2^2 + 2 F_1 F_2 \cos\theta} \]

Step 2: Detailed Explanation:
Let the two forces be:
\( F_1 = 3\text{ N} \)
\( F_2 = 5\text{ N} \)
The angle between them is \( \theta = 60^\circ \).
Substitute these values into the formula:
\[ R = \sqrt{3^2 + 5^2 + 2 \times 3 \times 5 \times \cos 60^\circ} \]
Since \( \cos 60^\circ = 0.5 \):
\[ R = \sqrt{9 + 25 + 30 \times 0.5} \]
\[ R = \sqrt{34 + 15} = \sqrt{49} \]
\[ R = 7\text{ N} \]
Therefore, the magnitude of the resultant force is exactly \( 7\text{ N} \).

Step 3: Final Answer:
The resultant force is \( 7\text{ N} \).