Find the resultant of 3 concurrent coplanar forces: 60 N acting 20 degrees east of north, 30 N east, and 150 N acting 40 degrees east of south.

Find the resultant of 3 concurrent coplanar forces: 60 N acting 20 degrees east of north, 30 N east, and 150 N acting 40 degrees east of south.

• A. 240 N east
• B. 160 N 68 degrees east of south
• C. 60 N 40 degrees east of south
• D. 140 N 100 degrees east of south

Answer: (B)

To find the resultant of the three concurrent coplanar forces, it is necessary to resolve each force into its x (horizontal) and y (vertical) components using trigonometry, and then sum those components. Starting with the first force, which is 60 N at 20 degrees east of north, we can resolve it as follows: - The y-component (vertical) is 60 N * cos(20°) = 56.34 N. - The x-component (horizontal) is 60 N * sin(20°) = 20.79 N. The second force, 30 N acting directly east, has components: - The y-component is 0 N (since it acts purely in the x direction). - The x-component is 30 N. The third force, 150 N acting at 40 degrees east of south, requires careful resolution: - Since it is east of south, we can consider it as 180° - 40° = 140° from the positive x-axis (east). The components will be: - The y-component is 150 N * cos(40°) = 114.59 N (now negative since it's directed south). - The x-component is 150

To find the resultant of the three concurrent coplanar forces, it is necessary to resolve each force into its x (horizontal) and y (vertical) components using trigonometry, and then sum those components.

Starting with the first force, which is 60 N at 20 degrees east of north, we can resolve it as follows:

• The y-component (vertical) is 60 N * cos(20°) = 56.34 N.

• The x-component (horizontal) is 60 N * sin(20°) = 20.79 N.

The second force, 30 N acting directly east, has components:

• The y-component is 0 N (since it acts purely in the x direction).

• The x-component is 30 N.

The third force, 150 N acting at 40 degrees east of south, requires careful resolution:

• Since it is east of south, we can consider it as 180° - 40° = 140° from the positive x-axis (east). The components will be:

• The y-component is 150 N * cos(40°) = 114.59 N (now negative since it's directed south).

• The x-component is 150