Calculating tensions in ropes suspending an onject

In summary, the problem involves determining the tensions in two ropes suspending a 20 kg mass from a ceiling at angles of 30° and 45°. Using the equations Fg=mg and ∑F=ma, the y-components of the tensions are set equal to the weight of the object, while the x-components provide a second equation for solving the two unknown tensions.
  • #1
novae
15
1

Homework Statement


A mass of 20 kg is suspended from a ceiling by two lengths of rope that make angles of 30° and 45° with the ceiling . Determine the tension in each of the strings.

2.Relevant equations

Fg= mg

The Attempt at a Solution


Fg= 20 x 9.8 = 196 N

∑F= fnet=ma
Fg-FTtotal= 0
196= FTtotal
196= FT1y+ FT2y (y components of each of the tensions)
196= (cos60)(FT1) + (cos45)(FT2)
I think I'm doing something wrong and I don't knownwhat. In the textbook, instead of using the y components of the tensions, they just use the tensions, which doesn't make sense to me because it's the y components of the tensions that give the equilibrant force to Fg.
 
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  • #2
What you're doing is fine, but don't forget the x-components. That will give you the second equation that you need to solve for your two unknowns.
 
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  • #3
Doc Al said:
What you're doing is fine, but don't forget the x-components. That will give you the second equation that you need to solve for your two unknowns.
Ohhhhh right! I forgot about that! And then it's substitution and stuff from there, thank you!
 

1. How do I calculate the tension in a rope suspending an object?

To calculate the tension in a rope, you will need to know the weight of the object being suspended, the angle at which the rope is suspended, and the acceleration due to gravity. You can then use the formula T = mg/sinθ, where T is tension, m is mass, g is acceleration due to gravity, and θ is the angle of the rope.

2. Can I calculate the tension in a rope without knowing the weight of the object?

No, the weight of the object is an important factor in calculating tension in a rope. Without knowing the weight, you will not be able to accurately determine the tension.

3. How does the angle of the rope affect the tension?

The angle of the rope affects the tension because it changes the amount of force that is being applied to the rope. The greater the angle, the more force is being applied, resulting in a higher tension.

4. What units are used to measure tension?

Tension is typically measured in units of force, such as newtons or pounds. However, it can also be measured in units of weight, such as kilograms or pounds.

5. Can I use the same formula to calculate tension in all types of ropes?

Yes, the formula T = mg/sinθ can be used to calculate tension in all types of ropes, as long as the weight and angle are known. However, keep in mind that different types of ropes may have different weight capacities and may stretch or deform under tension, so it is important to choose the appropriate rope for the specific situation.

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