Question

a block is pulled by two forces. the first force is \\(25.5\text{ n}\\) at an angle of \\(80.0^{\circ}\\) and the second is \\(16.0\text{ n}\\) at an angle of \\(66.7^{\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: Calculate the x-component of the first force

$$ F_{1x} = F_1 \cos(\theta_1) $$

$$ F_{1x} = 25.5 \cos(80.0^\circ) \approx 4.428 \text{ N} $$

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

$$ F_{2x} = F_2 \cos(\theta_2) $$

$$ F_{2x} = 16.0 \cos(66.7^\circ) \approx 6.329 \text{ N} $$

Step 3: Sum the x-components to find the total x-component

$$ F_x = F_{1x} + F_{2x} $$

$$ F_x = 4.428 + 6.329 \approx 10.8 \text{ N} $$

Answer:

10.8