Calculating Moment & Horizontal Force at O for 100 lb Force

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To calculate the moment of a 100 lb vertical force about point O, the correct approach involves using the perpendicular distance from O to the line of action of the force. The moment is determined using the formula Mo = Fd, where d is the distance calculated as 24 inches multiplied by the cosine of 60 degrees. This is because the cosine function provides the horizontal component of the distance relevant for moment calculations. The discussion clarifies that using sine would be incorrect as it does not represent the necessary perpendicular distance. Understanding the geometry of the lever and the force application is crucial for accurate moment calculations.
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Homework Statement


A 100 lb vertical force is applied to the end of a lever, which is attached to a shaft at O. Determine (a) the moment of the 100 lb force about O (b) the horizontal force applied at a that creates the same moment about O.

Homework Equations

The Attempt at a Solution


I know the solution but I'm still a bit confused as to what I'm doing for part (a) I have Mo = Fd = 24in*cos(60) * 100 lb
But I don't understand why I'm using
24in*cos(60) and not 24in*sin(60)...

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David Donald said:
But I don't understand why I'm using
24in*cos(60) and not 24in*sin(60)...
You need the perpendicular distance between O and the line of action of the force.
 
Thread 'Correct statement about size of wire to produce larger extension'

Thread 'Correct statement about size of wire to produce larger extension'

The answer is (B) but I don't really understand why. Based on formula of Young Modulus: $$x=\frac{FL}{AE}$$ The second wire made of the same material so it means they have same Young Modulus. Larger extension means larger value of ##x## so to get larger value of ##x## we can increase ##F## and ##L## and decrease ##A## I am not sure whether there is change in ##F## for first and second wire so I will just assume ##F## does not change. It leaves (B) and (C) as possible options so why is (C)...
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