Question

a block is pulled by two forces. the first force is \\(78.5\text{ n}\\) at an angle of \\(83.3^{\circ}\\) and the second is \\(96.5\text{ n}\\) at an angle of \\(273^{\circ}\\).

what is the x-component of the total force acting on the block?

\\\vec{f}_x = \text{ ? }\text{ n}\\
\\\vec{f}_x = |\vec{f}_1|\cos\theta_1 + |\vec{f}_2|\cos\theta_2\\

Explanation:

⚡ Using what you learned: Vectors in Plane and Space (components, magnitude, direction)

Step 1: Identify given values

$$ |\vec{F_1}| = 78.5\text{ N}, \quad \theta_1 = 83.3^\circ $$

$$ |\vec{F_2}| = 96.5\text{ N}, \quad \theta_2 = 273^\circ $$

Step 2: Calculate individual x-components

$$ F_{1x} = 78.5 \cdot \cos(83.3^\circ) \approx 78.5 \cdot 0.11667 = 9.1587\text{ N} $$

$$ F_{2x} = 96.5 \cdot \cos(273^\circ) \approx 96.5 \cdot 0.05234 = 5.0504\text{ N} $$

Step 3: Sum the components

$$ F_x = F_{1x} + F_{2x} \approx 9.1587 + 5.0504 = 14.2091\text{ N} $$

Answer:

14.2