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Mechanics vector problem

  • #1
<<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, lets 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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Answers and Replies

  • #2
billy_joule
Science Advisor
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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.
 

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