What is the Magnitude of F2 in a Hinged Beam Torque Problem?

I made a mistake. The correct solution is F2 = 31*2.30*sin28/(1.00*cos28) = 43.35 NIn summary, the massless bar, hinged at A and inclined at an angle θ = 28.0°, is in static equilibrium when subjected to horizontal force F1 = 31 N and an unknown vertical force F2. Using the equations for forces and torques, the magnitude of F2 is calculated to be 43.35 N.
  • #1
NoobeAtPhysics
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Homework Statement



302sape.gif


The massless bar, hinged at A, is inclined at an angle θ = 28.0° and subjected to horizontal and vertical forces F1 and F2, as shown. If L1 = 2.30 m, L2 = 1.00 m, F1 = 31 N, and the beam is in static equilibrium, what is the magnitude of F2?


Homework Equations



T=Fr

The Attempt at a Solution



sum of forces and torques must be null
forces
F1+Rx=0
F2+Ry=0
torques
F2L2cosθ-F1L2sinθ=0
F2=F1L2sinθ/(L2cosθ)
F2=31*1*sin28/(2.30*cos28)=7.17 N
 
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  • #2
Are you sure the torque produced by F1 about point A depends on L2 and not L1?
 
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  • #3
Thanks
 
Last edited:

1. What is torque and how is it related to the hinge problem?

Torque is the measure of the force that causes an object to rotate around an axis or pivot point. In the case of a hinge, the torque is the force applied to the door or gate that causes it to rotate around the hinge point.

2. How does the weight of the door or gate affect the torque in the hinge problem?

The weight of the door or gate exerts a force downward, which increases the torque on the hinge. This is because the weight creates a greater moment arm, or distance, from the hinge point to the force of the weight.

3. Can the length of the hinge affect the torque in the hinge problem?

Yes, the length of the hinge can affect the torque in the hinge problem. A longer hinge will have a greater moment arm, or distance, from the hinge point to the force of the door or gate, resulting in a higher torque.

4. What are some ways to reduce the torque on a hinge?

One way to reduce the torque on a hinge is to distribute the weight of the door or gate more evenly. This can be done by adding additional hinges or by using a lighter material for the door or gate. Additionally, using a shorter hinge or moving the hinge closer to the center of the door or gate can also decrease the torque.

5. How can I calculate the torque on a hinge in a specific situation?

To calculate the torque on a hinge, you will need to know the force applied to the door or gate, the distance from the hinge point to the force, and the angle at which the force is applied. The formula for torque is T = F x d x sinθ, where T is torque, F is force, d is distance, and θ is the angle between the force and the moment arm.

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