A 6.5 m long ladder rests against a vertical wall reaching a height of 6.0 m. A 60 kg man stands half way up the ladder. (a) Find the torque of the force exerted by the man on the ladder about the upper end of the ladder. (b) Assuming the weight of the ladder to be negligible as compared to the man and assuming the wall to be smooth, find the force exerted by the ground on the ladder.

The torque developed by the ladder is 750Nm


The force exerted by the ladder on the ground is 600N


Given


The length of the ladder is given as 6.5m resting at a wall of 6 meters, the weight of the man is 60kg, the torque is exerted at the upper end of the ladder and the there is no friction against the wall.


Formula Used


The torque applied by the mass and radius of the ladder is the product of the force and the radius of rotation of the ladder falling



where


is the torque of the ladder, F is the force in terms of tension, r is the length of the weight suspended at certain distance, is the angular turning distance of the ladder is rotated.


Explanation


a. The torque developed due to the weight of the body is described as






b. Now finding the force exerted by the man through the ladder on the ground is



1