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 \\(y\\)-component of the total force acting on the block?

\\ \vec{f}_y = \\ ?\\ \text{ n} \\
\\ \vec{f}_y = |\vec{f}_1|\sin\theta_1 + |\vec{f}_2|\sin\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 y-components

$$ F_{1y} = 78.5 \cdot \sin(83.3^\circ) \approx 78.5 \cdot 0.99317 \approx 77.964\text{ N} $$

$$ F_{2y} = 96.5 \cdot \sin(273^\circ) \approx 96.5 \cdot (-0.99863) \approx -96.368\text{ N} $$

Step 3: Sum the components

$$ F_y = F_{1y} + F_{2y} $$

$$ F_y = 77.964 + (-96.368) \approx -18.4\text{ N} $$

Answer:

-18.4