Question

a block is pulled by two forces. the first force is \\(45.0\text{ n}\\) at an angle of \\(49.0^{\circ}\\) and the second is \\(55.0\text{ n}\\) at an angle of \\(56.3^{\circ}\\).

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

\\\vec{f}_x = ? \text{ n}\\

Explanation:

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

Step 1: Find the x-component of the first force

$$ F_{1x} = 45.0 \cdot \cos(49.0^\circ) \approx 29.523\text{ N} $$

Step 2: Find the x-component of the second force

$$ F_{2x} = 55.0 \cdot \cos(56.3^\circ) \approx 30.517\text{ N} $$

Step 3: Sum the x-components

$$ F_x = F_{1x} + F_{2x} = 29.523 + 30.517 = 60.04\text{ N} $$

Rounding to three significant figures:

$$ F_x \approx 60.0\text{ N} $$

Answer:

60.0