Final answer:
The force that would produce a torque of 3 N·m, directed south, with a position vector of 1 m, west, would be 3 N directed north. The northward direction of the force is determined using the right-hand rule for cross products.
Step-by-step explanation:
The question is related to the concept of torque and forces in physics, particularly how to determine the force involved given a torque and a position vector. Using the definition of torque, which is the cross-product of the position vector (ρ) and the force (F), the torque (τ) can be expressed as τ = ρ x F. In the case provided, the torque is 3 N·m, directed south, and the position is 1 m, west. To find the force that would produce this torque, we must consider that for the maximum torque produced by a force, the force must act perpendicularly to the position vector. Therefore, if the position vector is west, the force vector must be directed north or south to be perpendicular. Given that the torque is directed south, and considering the right-hand rule for cross products, the force must be pointing north since it needs to follow the direction such that ρ (west) x F (north) yields a southward torque.
The magnitude of the force can be calculated by rearranging the torque formula: F = τ / ρ. So, F = 3 N·m / 1 m = 3 N. Hence, the force has a magnitude of 3 N and is directed north, making option d: 1 N, north the correct answer to this question. It's important to note that the options given seem to contain a discrepancy in the force magnitude, offering both 3 N and 1 N as possible answers for the north direction, but based on the calculation, the correct magnitude should be 3 N directed north.