QuestionApril 29, 2025

Add the three forces at the joint. What is the X component of the threeforces combined? Show the minus if the value is negative.

Add the three forces at the joint. What is the X component of the threeforces combined? Show the minus if the value is negative.
Add the three forces at the joint. What is the X component of the threeforces combined? Show the minus if the value is negative.

Solution
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Answer

F_{total\_x} (with sign) Explanation 1. Identify Forces Assume forces are given as vectors with magnitudes and angles. For example, F_1, F_2, and F_3 with angles \theta_1, \theta_2, and \theta_3 from the positive X-axis. 2. Calculate X Components Use the formula for the X component of a force: **F_x = F \cdot \cos(\theta)**. - F_{1x} = F_1 \cdot \cos(\theta_1) - F_{2x} = F_2 \cdot \cos(\theta_2) - F_{3x} = F_3 \cdot \cos(\theta_3) 3. Sum X Components Add the X components: F_{total\_x} = F_{1x} + F_{2x} + F_{3x}.

Explanation

1. Identify Forces<br /> Assume forces are given as vectors with magnitudes and angles. For example, $F_1$, $F_2$, and $F_3$ with angles $\theta_1$, $\theta_2$, and $\theta_3$ from the positive X-axis.<br /><br />2. Calculate X Components<br /> Use the formula for the X component of a force: **$F_x = F \cdot \cos(\theta)$**.<br />- $F_{1x} = F_1 \cdot \cos(\theta_1)$<br />- $F_{2x} = F_2 \cdot \cos(\theta_2)$<br />- $F_{3x} = F_3 \cdot \cos(\theta_3)$<br /><br />3. Sum X Components<br /> Add the X components: $F_{total\_x} = F_{1x} + F_{2x} + F_{3x}$.
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