Question

Consider the two points A(-4, -1) and B(2, 7) in the xy-plane. Distances are given in centimeters.

The line of action of a 75 N force goes through the linear segment AB.

Determine the magnitude of the moment of the force (in N*cm) about the origin (0, 0).

Answer should be 195

Answer 1

The magnitude of the moment of the force about the origin is 750 N×cm.

Step-by-step explanation:

To determine the magnitude of the moment of the force about the origin, we first need to find the distance between the origin and the line segment AB. Using the distance formula, we can calculate the distance between A(-4, -1) and B(2, 7) as:

d = sqrt((2-(-4))^2 + (7-(-1))^2)

d = sqrt(6^2 + 8^2) = sqrt(36 + 64) = sqrt(100) = 10 cmNext, we can calculate the moment of the force by multiplying the magnitude of the force (75 N) by the distance (10 cm) and the perpendicular distance from the origin to the line of action of the force. Since the force line is passing through the origin, the perpendicular distance is equal to the distance between the origin and any point on the line segment AB, which is 10 cm.

Moment of the force = 75 N × 10 cm = 750 N×cm.

Therefore, the magnitude of the moment of the force about the origin is 750 N×cm.