Beam hinged to wall with a cable (torque, etc)

In summary, the conversation discusses a problem involving a 48 kg beam at an angle of 24 degrees with respect to the horizontal, supported by a pin and horizontal cable. The goal is to find the magnitude of the total force exerted by the pin on the beam, and the conversation includes equations and calculations to solve the problem. Ultimately, the correct solution is found by adjusting the last equation to include the correct moment arm.
  • #1
lizzyb
168
0
Hi. I've tried to answer this questions four times and so far none of my answers have been correct. Any help is greatly appreciated!

A uniform 48 kg (m) beam at an angle of 24 degrees (theta) with respect to the horizontal has length of 38 m (L). It is supported by a pin and horizontal cable. The acceleration of gravity is 9.8 m/s^2 (g). What is the magnitude of the total force exerted by the pin on the beam?

So far:

[tex]\sum F_x = F_h - T = 0[/tex] horizontal component of pin - tension of cable
[tex]\sum F_y = F_v - mg = 0[/tex] vertical component of pin - mass of beam * gravity
[tex]\sum \tau = \sin \theta L T - \cos \theta L m g = 0[/tex]

Does this look ok to you? For the torque, I'm trying to use the moment arm times the magnitude of the force.

Thank you.
 
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  • #2
The last equation should have been:
[tex]\sum \tau = \sin \theta L T - \cos \theta \frac{L}{2} m g = 0[/tex]
and that took care of it.
 
  • #3


Hi there,

Based on the information provided, your equations and approach seem correct. To find the magnitude of the total force exerted by the pin on the beam, you can use the Pythagorean theorem:

F_total = \sqrt{F_h^2 + F_v^2}

Where F_h is the horizontal component of the pin and F_v is the vertical component of the pin. This will give you the total force exerted by the pin on the beam, taking into account both the horizontal and vertical components.

As for the torque equation, it looks like you are using the right formula, which is the moment arm (in this case, the length of the beam) multiplied by the magnitude of the force (tension of the cable or weight of the beam). Just make sure to use the correct sign conventions for the angles and directions of the forces.

I hope this helps! Let me know if you have any further questions. Keep up the good work!
 

1. What is a beam hinged to wall with a cable?

A beam hinged to wall with a cable is a structural system where one end of a beam is attached to a wall via a hinge or pinned connection, while the other end is connected to a cable or wire. This type of system is commonly used in construction to support and distribute loads.

2. How does the cable affect the beam's behavior?

The cable attached to the beam creates a tension force, which helps to stabilize the beam and prevents it from bending or sagging under the weight of a load. The cable also helps to distribute the load along the length of the beam, reducing the stress on any one point.

3. What is the purpose of the hinge or pinned connection?

The hinge or pinned connection allows the beam to rotate freely at one end, while still providing support and stability. This allows the beam to better distribute the load and reduces the risk of failure or collapse.

4. How is torque affected in this type of system?

In a beam hinged to wall with a cable, the torque is reduced due to the presence of the cable. This is because the cable creates a counterbalancing force, which helps to prevent the beam from rotating excessively and reduces the torque on the hinge or connection.

5. What are the advantages of using a beam hinged to wall with a cable?

Some potential advantages of this type of system include increased stability, better load distribution, and reduced risk of failure. It can also allow for longer and thinner beams to be used, as the cable helps to support the weight of the load. Additionally, this system can be more cost-effective compared to traditional beam supports, as it requires less material and labor to construct.

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