Question

a block is pulled by two horizontal forces. the first force is 500 n at an angle of 65.0^{\circ} and the second is 415 n at an angle of 270^{\circ}.

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

\vec{f}_x = ? n

Explanation:

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

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

$$ F_{1x} = 500 \cos(65.0^\circ) \approx 500 \times 0.422618 = 211.31\text{ N} $$

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

$$ F_{2x} = 415 \cos(270^\circ) = 415 \times 0 = 0\text{ N} $$

Step 3: Calculate the total x-component

$$ F_x = F_{1x} + F_{2x} = 211.31 + 0 = 211.31\text{ N} $$

Rounding to three significant figures:

$$ F_x \approx 211\text{ N} $$

Answer:

211