What is the tension required for the crosspiece in an A-frame structure?

In summary, the task is to design the crosspiece for an A-frame structure with beams of 5.00 m length and 375.0 kg mass each. The crosspiece must withstand a certain amount of tension, assuming negligible mass and friction. The solution involves considering the first half of the frame and using equations involving forces and angles to calculate the tension needed. The final answer is 4941.08.
  • #1
iPromise
3
0
∑

Homework Statement



You are designing the crosspiece for the A-frame structure in the figure below. Beams AB and AC are 5.00 m long and have a mass of 375.0 kg each. How much tension must the crosspiece EF withstand? Assume that the mass of the crosspiece and the friction at points B and C are negligible.

http://oi57.tinypic.com/2zfq4y8.jpg

Homework Equations



T = F*R*sinΘ
∑T = 0

The Attempt at a Solution



I took the first half of the frame into consideration. I chose point A to be my pivot point. There are three forces acting on the first-half of the frame:

http://oi59.tinypic.com/fu7sw0.jpg

My initial equation:

(N)(4.75)(cosΘ) - (Mg)(2.375)cosΘ = (T)(1.4)

Θ = sin-1 ( 2.2 / 4.75 )
= 27.59

N = the force of gravity of the first half of the structure
= Mg = 335 * 9.81

I solve for T:

T = 4941.08

The answer: 8650
 
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  • #2
iPromise said:
(N)(4.75)(cosΘ) - (Mg)(2.375)cosΘ = (T)(1.4)
Where are you getting 4.75 and 1.4?
 
  • #3
4.75 is the length of the ladder. 1.4 was the radius from the pivot point. That was my mistake, 1.4 is NOT the radius, 0.8 is.
 
  • #4
iPromise said:
4.75 is the length of the ladder.
Isn't it given as 5 m?
 
  • #5
Sorry I was thinking of the last practise version I did. Each version has different values.
 

Related to What is the tension required for the crosspiece in an A-frame structure?

1. What is torque?

Torque is a measure of the turning or twisting force on an object. It is calculated by multiplying the force applied to an object by the distance from the point of rotation to the point where the force is applied.

2. How is torque related to equilibrium?

Torque plays a crucial role in determining whether an object is in equilibrium or not. If the net torque on an object is zero, then the object is in rotational equilibrium. This means that the object is not rotating or is rotating at a constant speed.

3. What is the difference between static equilibrium and dynamic equilibrium?

In static equilibrium, the object is at rest and not moving. The net force and net torque on the object are both equal to zero. In dynamic equilibrium, the object is moving at a constant speed in a straight line, and the net force and net torque are still equal to zero.

4. How can you calculate the torque on an object?

To calculate the torque on an object, you need to know the force applied to the object and the distance from the point of rotation to the point where the force is applied. The torque is then calculated by multiplying the force by the distance (T = F x d).

5. What is the unit of measurement for torque?

The unit of measurement for torque is Newton-meters (Nm) in the SI system, or pound-feet (lb-ft) in the imperial system. Both units represent the amount of force needed to cause an object to rotate around a specific point.

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How to calculate the tension needed for a crosspiece in an A-frame structure?
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