Basic Torque - Hinge and Cable

In summary, the problem involves a 15 meter beam held by a hinge and a cable, with an object placed on the beam. Using the equations for equilibrium, the cable tension is calculated to be 2973.44 N. The reaction force at the hinge is found to be 1750.95 N at an angle of 31.88° with the horizontal axis. The resultant force at the hinge is determined to be 1751 N at an angle of 32° with the horizontal axis.
  • #1
sinequanon
6
0

Homework Statement



A 15 meter beam jutting out of the side of a building is held by a hinge (at the wall) and a cable at 10 meters from the wall. The angle between the beam and the cable is 60 degrees and the mass of the beam is 250 kg. If a 1000 N object is located on the beam, 7 meters from the wall, what is the reacting force R from the hinge and at what angle is it applied? Assume the system is in equilibrium.

Homework Equations



1. ΣFx = Rx - TcosΘ = 0

2. ΣFy = Ry + TsinΘ - Fobject - Fbeam = 0

3. TsinΘ(dcable) - Fbeam(dbeam) - Fobject(dobject)

*Use 10 m/s2 for the value of gravitational acceleration.

The Attempt at a Solution



Alright, so I just wanted to double check to see if I'm actually doing this correctly.

First I substitute into the third equation in order to find the cable tension.

Tsin60(10 m) - (2500 N)(7.5 m) - (1000 N)(7 m) = 0
T = 2973.44

Then, I would substitute the T value into the other equations.

ΣFx = Rx - 2973.44cos60 = 0
Rx = 1486.72 N

ΣFy = Ry + 2973.44sin60 - 1000 - 2500 = 0
Ry = 924.925 N

From here, it appears to be a simple matter of using the Pythagorean Theorem and then just using inverse cosine to find ΘR.
R = [tex]\sqrt{1486.72^2 + 924.925^2}[/tex] = 1750.95 N

cos-1Θ = 1486.72/1750.95
Θ = 31.88°

I was hoping someone would be able to double check to see if my understanding of this matter is correct or otherwise. I was also wondering if someone could tell if my final answer R should be positive or negative, as that is one thing I haven't a clue about.
 
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  • #2
Looks real good to me. Often it is best to leave the reaction force at the hinge in terms of its x and y components, that is, Rx = +1486 N (or 1486 N pointing right) , and Ry = +925 N (or 925 N pointing up). The sign of the reaction force components is largely a matter of convention; its direction as shown on a sketch is the important part. Now since the problem asked you to provide the Resultant force and angle at the hinge, your calc is correct for the magnitude of that value: R = 1751 N pointing up and to the right at a 32 degree angle with the horizontal axis. The resultant force really is a magnitude only without a sign, the direction shown is is what is important. Good work!
 
  • #3


Thank you!



Your understanding of this problem and the equations involved is correct. Your calculations and final answer for R also appear to be correct. In terms of whether R should be positive or negative, it depends on the direction you choose for the x-axis. If you choose the positive x-axis to be pointing away from the building, then R would be positive. If you choose the positive x-axis to be pointing towards the building, then R would be negative. As long as you are consistent in your choice of direction, either answer would be acceptable. Keep up the good work!
 

Related to Basic Torque - Hinge and Cable

1. What is torque and how is it related to hinges and cables?

Torque is a measure of the twisting force applied to an object. In the context of hinges and cables, torque is the force that is required to rotate or move a door or other object attached to the hinge or cable.

2. How do hinges and cables work together to create torque?

Hinges and cables work together to create torque through the principle of leverage. The hinge acts as a pivot point, while the cable, when attached at different points along the door, creates a longer lever arm and increases the torque applied to the door.

3. What factors affect the amount of torque produced by hinges and cables?

The amount of torque produced by hinges and cables is affected by several factors, including the length of the lever arm, the distance between the hinge and cable attachment points, and the weight of the object being moved. Additionally, the type and quality of the hinge and cable materials can also impact the amount of torque produced.

4. Are there different types of hinges and cables that produce different levels of torque?

Yes, there are various types of hinges and cables that can produce different levels of torque. For example, a longer hinge or a thicker cable will typically produce more torque than a shorter hinge or thinner cable. Additionally, the materials used in the construction of the hinge and cable can also affect the amount of torque produced.

5. How is torque measured and expressed in the context of hinges and cables?

Torque is typically measured and expressed in units of force multiplied by distance, such as newton-meters or pound-feet. In the context of hinges and cables, this would refer to the amount of force applied to the door or object multiplied by the distance from the pivot point to the point where the force is being applied.

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