Understanding the Forces
* Man's Force: 100N east. This means the man is pulling directly to the east with a force of 100 Newtons.
* Boy's Force: 80N, 60 degrees west-south. This means the boy is pulling with a force of 80 Newtons in a direction that's 60 degrees from both west and south.
Visualizing the Forces
Imagine a compass. The man is pulling directly east (towards the right). The boy is pulling in a direction that's:
* 60 degrees to the west (towards the left)
* 60 degrees to the south (towards the bottom)
Finding the Net Force
To find the net force, we need to consider both the magnitude and direction of the forces:
1. Break the Boy's Force into Components: We can break the boy's force into two components: one acting westward and one acting southward. We use trigonometry for this:
* Westward Component: 80N * cos(60°) = 40N
* Southward Component: 80N * sin(60°) = 69.28N (approximately)
2. Combine the Forces:
* East-West: The man pulls 100N east, and the boy pulls 40N west. The net force in the east-west direction is 100N - 40N = 60N east.
* North-South: The man doesn't exert a force in the north-south direction, while the boy pulls 69.28N south. The net force in the north-south direction is 69.28N south.
3. Resultant Force: The net force is the combination of these two components. We can represent it as a vector pointing 60N east and 69.28N south.
Finding the Magnitude of the Net Force:
We can use the Pythagorean theorem to find the magnitude of the resultant force:
* Magnitude = sqrt((60N)^2 + (69.28N)^2)
* Magnitude ≈ 90.48N
Finding the Direction of the Net Force:
We can use trigonometry (specifically, the arctangent function) to find the angle of the resultant force:
* Angle = arctan(69.28N / 60N)
* Angle ≈ 49.1 degrees (This angle is measured from the east direction towards the south)
Conclusion
The net force applied to the box is approximately 90.48N, acting at an angle of 49.1 degrees south of east.
