Final answer:
The moment of a force about a point (torque) is calculated with the formula T = r × F × sin(θ); for a force applied perpendicular to the lever arm, the sine term is 1. The smallest force to create the same torque is found by dividing the torque by the new distance from the pivot point.
Step-by-step explanation:
The student has asked two questions related to force and moments, specifically about finding the moment created by a force and the required force to create the same moment at a different point. To answer part (a), the moment of force, also known as torque, is determined by the equation torque (T) = r × F × sin(θ), where r is the perpendicular distance from the point of rotation (D) to where the force is applied (A), F is the magnitude of the force, and θ is the angle between the force vector and the lever arm. In this case, assuming the force is applied perpendicular to the lever arm, θ would be 90 degrees, and the sine of 90 degrees is 1, simplifying the formula to T = r × F.
For part (b), the smallest force applied at B that creates the same moment about D can be found by rearranging the torque formula to solve for force: F = T / r. The perpendicular distance from B to D needs to be used for r in this case.
If further details regarding the distances were provided, numerical answers could be given. Without those, we have to leave the solutions in terms of the equations.