Person stands at the middle point of a wooden ladder which starts slipping between a vertical wall and the floor of a room Why is the path traced by a person standing at the middle of ladder circular?

Answer 1

The path traced by a person standing at the middle of a slipping ladder is circular due to the conservation of angular momentum. As the ladder slips, the angular momentum of the system remains constant. The centripetal force required to maintain this angular momentum results in the circular path traced by the person. This phenomenon is a result of the rotational motion of the ladder around the point of contact with the floor.

Answer 2

The path traced by a person standing at the middle of a slipping ladder is circular due to the conservation of angular momentum. As the ladder starts to slip, the angular momentum of the system is conserved, causing the person to move in a circular path around the point where the ladder contacts the ground. This circular motion is a result of the changing forces and torques acting on the ladder as it slips.

Answer 3

Suppose the wall is represented by the y-axis and the ground as the x-axis. Let the position of the man be given by M = (x, y).

Then,

since M is the midpoint of the ladder, the base of the ladder is at A = (2x, 0).

also, the point where it touches the wall is B = (0, 2y).

Now, AB is the length of the ladder so AB = constant.

Using Pythagoras's theorem,

(2x - 0)2 + (0 - 2y)2 = c

(2x - 0)2 + (2y - 0)2 = c

This is the equation of [a quadrant of] a circle with centre (0, 0) and radius = sqrt(c).