Determine the magnitude of force at pin A as a function of position d.

In summary, the problem involves determining the magnitude of force at pin A as a function of position d, with a weight of 700 kg and d ranging from 1.7 m to 3.5 m. The force on member BC has been found to be 6.86d/1.2 from a previous problem. The equations for the summation of forces in the x and y directions were set up, but the weight was initially left out in the summation of the y forces. Once included, the correct answer was obtained.
  • #1
Colts
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Homework Statement


Refer to link for picture of problem.
http://session.masteringengineering.com/problemAsset/1127894/8/Prob.5-29.jpg
Determine the magnitude of force at pin A as a function of position d.
The mass of the weight is 700 kg and d goes from 1.7 m to 3.5 m

I have found Fbc (Force on member b c) from an earlier problem to be 6.86d/1.2 and it is correct.
I can't seem to get Fa (Force on pin a) though.

Homework Equations


Summation of forces


The Attempt at a Solution



I tried to sum the forces in the x direction and y direction and got the equations.
ƩFx=0: Ax - cos(53.13)Fbd = 0
ƩFy=0: Ay - sin(53.13)Fbd = 0

I then found Ax and Ay then squared them added them together and took the square root.
I got 5.716d. That is not the correct answer. Where did I go wrong?
 
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  • #2
Nevermind. I forgot to put the weight in the summation of the y forces. I got it
 

1. What is the significance of determining the magnitude of force at pin A?

Determining the magnitude of force at pin A is important for understanding the overall strength and stability of a structure or system. It can also help in predicting potential failures or determining the appropriate materials and design for a particular application.

2. How is the magnitude of force at pin A calculated?

The magnitude of force at pin A is calculated using the equation F = k*d, where F is the force at pin A, k is the spring constant, and d is the position of the pin from its equilibrium point. This equation follows Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position.

3. What factors can affect the magnitude of force at pin A?

The magnitude of force at pin A can be affected by various factors, such as the material and stiffness of the spring, the distance from the equilibrium position, and any external forces acting on the system. Additionally, the angle and direction of the force can also impact the overall magnitude.

4. How does the position of pin A impact the magnitude of force?

The position of pin A directly affects the magnitude of force because it determines the distance from the equilibrium point. The further the pin is from its equilibrium position, the greater the force will be. This is because the displacement of the spring increases, causing the force to increase proportionally.

5. Can the magnitude of force at pin A be negative?

Yes, the magnitude of force at pin A can be negative. This would occur when the direction of the force is opposite to the direction of displacement. In this case, the force would be pulling in the opposite direction, resulting in a negative value for the magnitude of force.

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