Analyzing Structural Forces: Understanding Reactions and Moments in Mechanics

In summary: It is not that the answer doesn't match in magnitude, but it also says that the reaction has an angle of 61.3°.In summary, the equation ∑Fx=0∑Fx=0\sum F_{x}=0 says that the only force acting upon the x-axis is the horizontal component Ax that becomes zero. Then for the other equation ∑Fy=0∑Fy=0\sum F_{y}=0 there are two forces: the 250 N that goes downwards and the Ay that I supposed that goes upwards.
  • #1
thegreengineer
54
3
<<Mentor note: Missing template due to being moved from other forum.>>

I took this problem from Vector Mechanics for Engineers by Beer et al. The reason why I am writing this is because I don't understand where I am wrong in this problem, yet I know I am wrong.

This is problem 6.123 and it's a problem concerning analysis of structures (in this case a machine).
https://scontent-lax3-1.xx.fbcdn.net/v/t1.0-9/13590368_1744245399193330_1531717957213866948_n.jpg?oh=b73b768c39128c189fcca2f3a5d3e3f4&oe=5835700D
So the first thing I did was calculating the reactions the system has. In this case there is a reaction in node A which consists of a rough surface. Therefore there are two forces which is in fact one single force but decomposed into its horizontal and vertical components which I called Ax and Ay respectively.
https://scontent-lax3-1.xx.fbcdn.net/v/t1.0-9/13567002_1744248252526378_7606622242639327423_n.jpg?oh=23ec4d5bd163fcbba959ba52711e8d41&oe=57F96698
This is where my problem begins, let's suppose I just considered the reactions Ax and Ay in node A and the 250 N load acting in node C. Then I work with equilibrium equations:
[itex]\sum F_{x}=0[/itex]
[itex]\sum F_{y}=0[/itex]
For the equation [itex]\sum F_{x}=0[/itex] we find out that the only force acting upon the x-axis is the horizontal component Ax that becomes zero. Then for the other equation [itex]\sum F_{y}=0[/itex] I see that there are two forces: the 250 N that goes downwards and the Ay that I supposed that goes upwards. When I perform the operations required I get that the Ay force is 250 N that goes upwards. Since the vertical component is the only component for the reaction in node A then I conclude that the reaction in node A is 250 N upwards.
So far we have answered part b).
When I consult the answers to selected problems section just to verify I am right I see that the answer doesn't match:
https://scontent-lax3-1.xx.fbcdn.net/v/t1.0-9/13511060_1744249799192890_8621689707186190488_n.jpg?oh=cd46cd6c0101d44c8d8a4d65b6dd0a2b&oe=57FB23BC
It is not that the answer doesn't match in magnitude, but it also says that the reaction has an angle of 61.3°.
I don't know where I am wrong.
 
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  • #2
MarcusAu314 said:
For the equation ∑Fx=0∑Fx=0\sum F_{x}=0 we find out that the only force acting upon the x-axis is the horizontal component Ax that becomes zero. Then for the other equation ∑Fy=0∑Fy=0\sum F_{y}=0 I see that there are two forces: the 250 N that goes downwards and the Ay that I supposed that goes upwards.

You've ignored what's going on at B (and/or D). They contribute forces in both x and y.

Complete question a) before proceeding to b).
Taking moments about A is a good first step.
 

1. What is a vector in mechanics?

A vector in mechanics is a quantity that has both magnitude and direction. It is represented by an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction of the vector.

2. How do you solve vector problems in mechanics?

To solve vector problems in mechanics, you first need to break down the vectors into their components using trigonometry. Then, you can use the laws of vector addition, subtraction, and multiplication to calculate the resulting vector. Finally, use the Pythagorean theorem and inverse trigonometric functions to find the magnitude and direction of the resulting vector.

3. What is the difference between scalar and vector quantities in mechanics?

A scalar quantity in mechanics only has magnitude and no direction, such as speed or temperature. A vector quantity has both magnitude and direction, such as velocity or force.

4. How do you represent vectors in mechanics?

Vectors in mechanics are represented by arrows. The length of the arrow represents the magnitude of the vector, and the direction of the arrow represents the direction of the vector.

5. What are some common applications of vector problems in mechanics?

Vector problems in mechanics are commonly used in calculating forces and motion in physics and engineering. They are also used in designing structures and analyzing their stability and strength.

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