Tension of Two Ropes on an Object

  • Thread starter merzperson
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In summary, the conversation discusses the tension of two ropes supporting a 1400kg steel beam. The angles of the ropes from the vertical axis are given as 20 degrees and 30 degrees. The individual vector components of each rope are being calculated, but the person is having trouble solving the system of equations. After getting incorrect answers, they receive help and are able to correctly solve the system.
  • #1
merzperson
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1. A 1400kg steel beam is supported by two ropes. Find the tension of each rope.
Rope 1 is 20 degrees from the vertical axis and Rope 2 is 30 degrees from the vertical axis.

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2. I am getting lost trying to find the vector components of each rope. More specifically, I am having trouble solving the system of equations as I can't remember the last time I've done this.

Here's my set-up:
T1cos(20) + T2cos(30) = 13720
T1sin(20) + T2sin(30) = 0

When I solve the system of equations I get T1=39505 and T2=-27023. These do not seem to be the correct answers according to MasteringPhysics, and if I'm not mistaken they don't make sense either.


 
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  • #2
The horizontal components of the tensions are opposite.

T1sin(20) - T2sin(30) = 0

ehild
 
  • #3
Thank you ehild, that did it.
 

1. What is tension?

Tension is a force that is exerted on an object by a string, rope, or cable that is attached to it on both ends. It is a pulling force that occurs in the direction of the string or rope and is responsible for keeping an object in equilibrium.

2. How is tension calculated?

Tension is calculated by using the formula T = F * sin(θ), where T is the tension force, F is the applied force, and θ is the angle between the string and the direction of the applied force. This formula applies to situations where the rope or string is at an angle to the object.

3. What factors affect the tension of two ropes on an object?

The tension of two ropes on an object is affected by the magnitude of the applied force, the angle of the ropes with respect to the object, and the weight of the object itself. The tension will also change if the length or elasticity of the ropes is altered.

4. How does the angle of the ropes affect the tension?

The angle of the ropes has a direct impact on the tension. The greater the angle between the ropes and the object, the greater the tension will be. This is because the applied force is spread out over a larger area, resulting in a larger tension force.

5. Can the tension on an object be greater than the applied force?

Yes, in some cases, the tension on an object can be greater than the applied force. This is due to the vector components of the applied force and the angle between the ropes and the object. If the ropes are at an angle, the tension force will have a vertical component that is greater than the applied force, resulting in a greater overall tension force.

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