Questions: Resultants of Coplanar Force Systems 3.1 through 3.3 Determine the magnitude, direction, and sense of the resultant for the coplanar concurrent force systems shown. Use the parallelogram law. Also sketch the force triangle.

Resultants of Coplanar Force Systems
3.1 through 3.3 Determine the magnitude, direction, and sense of the resultant for the coplanar concurrent force systems shown. Use the parallelogram law. Also sketch the force triangle.

Transcript text: Resultants of Coplanar Force Systems 3.1 through 3.3 Determine the magnitude, direction, and sense of the resultant for the coplanar concurrent force systems shown. Use the parallelogram law. Also sketch the force triangle.

Solution

Solution Steps

Step 1: Resolve Forces into Components

Resolve the 25 lb force into its x and y components.
- \( F_{1x} = 25 \cos(60^\circ) = 25 \times 0.5 = 12.5 \) lb
- \( F_{1y} = 25 \sin(60^\circ) = 25 \times 0.866 = 21.65 \) lb
Resolve the 45 lb force into its x and y components.
- \( F_{2x} = 45 \cos(10^\circ) = 45 \times 0.9848 = 44.316 \) lb
- \( F_{2y} = 45 \sin(10^\circ) = 45 \times 0.1736 = 7.812 \) lb

Step 2: Sum the Components

Sum the x-components of the forces.
- \( F_{x} = F_{1x} + F_{2x} = 12.5 + 44.316 = 56.816 \) lb
Sum the y-components of the forces.
- \( F_{y} = F_{1y} + F_{2y} = 21.65 + 7.812 = 29.462 \) lb

Step 3: Calculate the Resultant Force

Use the Pythagorean theorem to find the magnitude of the resultant force.
- \( R = \sqrt{F_{x}^2 + F_{y}^2} = \sqrt{56.816^2 + 29.462^2} = \sqrt{3227.5 + 867.9} = \sqrt{4095.4} \approx 63.99 \) lb

Final Answer

The magnitude of the resultant force is approximately 63.99 lb.
The direction can be found using the tangent function:
- \( \theta = \tan^{-1}\left(\frac{F_{y}}{F_{x}}\right) = \tan^{-1}\left(\frac{29.462}{56.816}\right) \approx 27.5^\circ \) from the x-axis.

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!