What is the magnitude and direction of the resultant of four concurrent forces of 10 N at 32 degrees east of north, 35 N at 50 degrees east of north, 25 N at 72 degrees east of north, and 85 N at 40 degrees east of south?

What is the magnitude and direction of the resultant of four concurrent forces of 10 N at 32 degrees east of north, 35 N at 50 degrees east of north, 25 N at 72 degrees east of north, and 85 N at 40 degrees east of south?

• A. 70 N 56 degrees east of north
• B. 45 N 44 degrees east of north
• C. 196 N 87 degrees east of south
• D. 114 N 77 degrees east of south

Answer: (D)

To determine the magnitude and direction of the resultant of the four concurrent forces, it's essential to break down each force into its components (i.e., x and y components) and then sum these components. 1. **Force breakdown:** - The first force of 10 N at 32 degrees east of north can be expressed as: - \( F_{1x} = 10 \sin(32^\circ) \) - \( F_{1y} = 10 \cos(32^\circ) \) - The second force of 35 N at 50 degrees east of north: - \( F_{2x} = 35 \sin(50^\circ) \) - \( F_{2y} = 35 \cos(50^\circ) \) - The third force of 25 N at 72 degrees east of north: - \( F_{3x} = 25 \sin(72^\circ) \) - \( F_{3y} = 25 \cos(72^\circ) \) - The fourth force of 85 N at 40 degrees east of south (which is equivalent to 180 degrees - 40 degrees

To determine the magnitude and direction of the resultant of the four concurrent forces, it's essential to break down each force into its components (i.e., x and y components) and then sum these components.

1. Force breakdown:

• The first force of 10 N at 32 degrees east of north can be expressed as:

• ( F_{1x} = 10 \sin(32^\circ) )

• ( F_{1y} = 10 \cos(32^\circ) )

• The second force of 35 N at 50 degrees east of north:

• ( F_{2x} = 35 \sin(50^\circ) )

• ( F_{2y} = 35 \cos(50^\circ) )

• The third force of 25 N at 72 degrees east of north:

• ( F_{3x} = 25 \sin(72^\circ) )

• ( F_{3y} = 25 \cos(72^\circ) )

• The fourth force of 85 N at 40 degrees east of south (which is equivalent to 180 degrees - 40 degrees