Question

A 3-m long plank with a weight of 130 N is placed on a dock with 1 m of its length extended over the water, as in the diagram. The plank is uniform in density so the center of gravity of the plank is located at the center of the plank. A boy with a weight of 180 N is standing on the plank and moving out slowly from the edge of the dock. a) How far from the pivot point at the edge of the dock is the center of the plank?

Answer 1

The center of the plank is located 1.5 meters from the pivot point at the edge of the dock since it is positioned at the midpoint of the 3-meter long uniform plank.

Step-by-step explanation:

The student's question pertains to a situation involving a uniform 3-m long plank of wood, with part of it extending over the edge of a dock and a boy walking on it. The objective is to find how far the center of the plank is from the pivot point at the edge of the dock.

Since the plank is uniform and has a length of 3 metres, the center of gravity of the plank will be at its midpoint, which is 1.5 m from either end. Considering that 1 m of the plank extends over the water, the pivot point at the edge of the dock is also 1 m from one end of the plank. Therefore, the distance from the edge of the dock (pivot point) to the center of the plank (center of gravity) is 1.5 m.