Question

The red vector represents a 2 Newton force. The green vector represents a 3 Newton force. In which of the following arrangements is the net force greatest?

a) Red vector and green vector in the same direction.
b) Red vector and green vector in opposite directions.
c) Red vector and green vector at right angles to each other.
d) Net force is the same in all arrangements.

Answer 1

The greatest net force occurs when the red vector (2 Newtons) and green vector (3 Newtons) are in the same direction, yielding a net force of 5 Newtons.

Step-by-step explanation:

The question deals with the vector addition of forces and which arrangement results in the greatest net force. To find the net force, you must add the vectors together. When two vectors are in the same direction, you simply add their magnitudes to get the net force. So with a red vector representing a 2 Newton force and a green vector at 3 Newtons, the net force when they are both in the same direction is 2N + 3N = 5N, which is the largest net force possible from these two forces.

If the vectors are in opposite directions, you subtract the smaller from the larger to get a net force of 1N (3N - 2N = 1N). When at right angles, the net force is found using the Pythagorean theorem. You would calculate the net force as the square root of the sum of the squares of the individual forces (√(2² + 3²) ≈ 3.61N), which is not as large as when they are in the same direction.

Therefore, the greatest net force occurs when the red vector and green vector are in the same direction (option a).