Solve Moment Question: Find Force at Bottom of Ladder

[jckjmes]

Homework Statement

A uniform ladder 5m long and of mass 40kg rests with its upper end against a smooth vertical wall and with its lower end 3m from the wall on rough ground. Find the magnitude and direction of the force exerted at the bottom of the ladder. (G=9.81ms^-2)

Homework Equations

ACM=CM
moment=force x distance from the pivot

The Attempt at a Solution

w(moment) = (40 x 9.81) x 2.5 =981 Nm clockwise

ACM=CM

therefore: reaction moment = 981Nm
and force = 981/3 =327N anticlockwise

Is this right or am i very far off??

 

[Orodruin]

moment=force x distance from the pivot

This is not correct. It should be moment = force x moment arm. The moment arm is equal to the distance from the pivot only if the force is orthogonal to the separation from the pivot.

w(moment) = (40 x 9.81) x 2.5 =981 Nm clockwise

What is the moment arm of the gravitational force?