Solve Moment Question: Find Force at Bottom of Ladder

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To find the force at the bottom of a ladder resting against a wall, the moment created by the ladder's weight must be balanced by the reaction force at the base. The weight of the ladder is calculated as 40 kg multiplied by the gravitational acceleration of 9.81 m/s², resulting in a moment of 981 Nm clockwise. The reaction moment is then determined to be 981 Nm anticlockwise, leading to a calculated force of 327 N. However, it is emphasized that the moment arm must be considered correctly, as it only equals the distance from the pivot when the force acts orthogonally. Accurate assessment of the moment arm for the gravitational force is crucial for determining the correct force at the bottom of the ladder.
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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??
 
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jckjmes said:
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.

jckjmes said:
w(moment) = (40 x 9.81) x 2.5 =981 Nm clockwise
What is the moment arm of the gravitational force?
 

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