Mechanics statics couple moment problem

In summary, to find the force P and angle alpha in this problem, you need to use the equation M=rXf, where M is the couple moment and r is the moment arm. Subtract force B from force A to find the resultant force P, then use trigonometry to calculate the angle alpha.
  • #1
hurricane123
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Homework Statement



Find the force 'p' and angle 'alpha'.

Homework Equations



m=rXf

The Attempt at a Solution


I calculated the couple moment by using M=rXf, I plugged r=12 and f=8 and the answer come out to be 96 lb.m. After finding the couple moment I am stuck now, I could not figure what I am suppose to do with the vectors A and B to calculate p and alpha, do I have to use this formula again M=rXp, if yes the what value I should for r?
 

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  • #2
Please help me out.The vector diagram shows two forces A and B acting on a body. r is the moment arm, or the lever arm, and f is the force. To find the force P and angle alpha, you need to use the equation M=rXf (where M is the couple moment). Subtract the force B from the force A to get the resultant force P, then calculate the angle alpha by using trigonometry.
 

1. What is a couple moment in mechanics statics?

A couple moment is a type of force that consists of two equal and opposite forces acting on a body at different points. It causes a rotational motion around an axis perpendicular to the plane of the forces.

2. How do you calculate the magnitude of a couple moment?

The magnitude of a couple moment can be calculated by multiplying one of the forces by the perpendicular distance between the two forces. This distance is also known as the moment arm or lever arm.

3. What is the difference between a couple moment and a single force?

A single force causes a translational motion, while a couple moment causes a rotational motion. Additionally, a single force has a point of application, while a couple moment has two points of application.

4. Can a couple moment be balanced?

Yes, a couple moment can be balanced if an equal and opposite couple moment is applied to the body. This will result in a net moment of zero, causing the body to remain in static equilibrium.

5. How is a couple moment represented in mechanics statics?

A couple moment is typically represented by a vector pointing along the axis of rotation, with a magnitude equal to the product of one of the forces and the distance between the forces. It is also commonly represented by a clockwise or counterclockwise moment diagram.

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