Question

Given the following concurrent forces; 150 lbs at 30o above the OX axis, 100 lbs at 315o from OX, and 50 lbs at -45o from OX. Find the magnitude and direction of the resultant.

Answer 1

Answer on Question #63910 – Physics – Mechanics | Relativity

Question:

Given the following concurrent forces; 150 lbs at 30° above the OX axis, 100 lbs at 315° from OX, and 50 lbs at -45° from OX. Find the magnitude and direction of the resultant.

Answer:

$$\begin{array}{l} \overrightarrow{F_1} = 150 \cos(30{}^\circ) \vec{i} + 150 \sin(30{}^\circ) \vec{j} = (75\sqrt{3}; 75); \\ \overrightarrow{F_2} = 100 \cos(315{}^\circ) \vec{i} + 100 \sin(315{}^\circ) \vec{j} = (50\sqrt{2}; -50\sqrt{2}); \\ \overrightarrow{F_3} = 50 \cos(-45{}^\circ) \vec{i} + 50 \sin(-45{}^\circ) \vec{j} = (25\sqrt{2}; -25\sqrt{2}); \\ \overrightarrow{F_{res}} = \overrightarrow{F_1} + \overrightarrow{F_2} + \overrightarrow{F_3} = 75(\sqrt{3} + \sqrt{2})\vec{i} + 75(1 - \sqrt{2})\vec{j} = (50\sqrt{2}; -50\sqrt{2}); \\ \left|\overrightarrow{F_{res}}\right| \approx 238 \text{ lbs}. \end{array}$$

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