Solve Moment Question: Find Force at Bottom of Ladder

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In summary, in this conversation, the question is about finding the magnitude and direction of the force exerted at the bottom of a ladder resting against a wall. The equations used are ACM=CM and moment=force x moment arm, and the gravitational force is 40 x 9.81 = 392.4 N. The correct solution is to calculate the moment arm and use it to find the magnitude and direction of the force, which is 327 N anticlockwise.
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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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  • #2
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?
 

FAQ: Solve Moment Question: Find Force at Bottom of Ladder

1. What is the definition of a moment in physics?

A moment, also known as a torque, is a measure of the tendency of a force to rotate an object about an axis or pivot point. It is calculated by multiplying the magnitude of the force by the perpendicular distance from the axis to the line of action of the force.

2. How is the moment of a force related to the force's distance from the pivot point?

The moment of a force is directly proportional to the distance of the force from the pivot point. This means that the farther the force is from the pivot point, the greater the moment will be.

3. How do you find the force at the bottom of a ladder?

To find the force at the bottom of a ladder, you can use the equation: F = W x L / d, where F is the force at the bottom of the ladder, W is the weight of the ladder, L is the length of the ladder, and d is the distance from the top of the ladder to the point where the force is applied.

4. What information do you need to solve a moment question?

To solve a moment question, you will need to know the magnitude and direction of the force, as well as the location of the force relative to the pivot point. This can be represented by the force's distance from the pivot point and its angle of application.

5. What are the common units used to measure moment?

The common units used to measure moment are newton-meters (N*m) in the SI system and pound-feet (lb*ft) in the imperial system. These units represent the product of force and distance, which is the standard equation for calculating moment.

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