Simple hanging tension problem

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In summary, a simple hanging tension problem involves calculating the tension force in a rope or cable supporting an object or hanging between two points. The key factors affecting tension are the weight of the object, the angle of the rope, and the length and stiffness of the rope. Tension can be calculated using the formula T = mg + ma or T = mg. Some real-world applications include suspension bridges, cranes, and rock climbing ropes. Tips for solving these problems include drawing a free-body diagram, breaking the problem into smaller parts, and being mindful of units. Practice and familiarity with the concepts are also helpful.
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dolerka
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Homework Statement


A ball of mass 0.850 kg is dangling as shown. The angle created with String 1 and ceiling is 30 degrees. The angle created with the second and the ceiling is 45 degrees. What is the tension in each string?


Homework Equations


F=ma


The Attempt at a Solution


T1=tension in string 1
T2=tension in string 2
W=weight of ball

I determined the the x and y acceleration to be zero. T1y+T2y=0. and T1x+T2x+W=0. i then used trigonometric identities.

T1y=T1sin(120)
T2y=T2sin(45)

T1x=T1cos(120)
T2x=T2cos(45)
W=8.33N

i then did substitution with the formulas and i found the tension in string 1 to be 6.10 i know this to be correct. and substituting in for the second tension i get 4.31 but i am being told that this is wrong so what exactly am i doing wrong?
 
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  • #2
dolerka said:
T1=tension in string 1
T2=tension in string 2
W=weight of ball

I determined the the x and y acceleration to be zero. T1y+T2y=0. and T1x+T2x+W=0. i then used trigonometric identities.

T1y=T1sin(120)
T2y=T2sin(45)

T1x=T1cos(120)
T2x=T2cos(45)
W=8.33N

i then did substitution with the formulas and i found the tension in string 1 to be 6.10 i know this to be correct. and substituting in for the second tension i get 4.31 but i am being told that this is wrong so what exactly am i doing wrong?

Suppose, for an experiment, the ball was substituted with one of twice the weight. What would be the tension in the strings?
 
  • #3
welcome to pf!

hi dolerka! welcome to pf! :smile:

(have a degree: ° and try using the X2 icon just above the Reply box :wink:)
dolerka said:
I determined the the x and y acceleration to be zero. T1y+T2y=0. and T1x+T2x+W=0. i then used trigonometric identities.

T1y=T1sin(120)
T2y=T2sin(45)

T1x=T1cos(120)
T2x=T2cos(45)
W=8.33N

if y is up, then your W is in the wrong equation :redface:

and whyever are you using 120° ? :confused:
 
  • #4


tiny-tim said:
hi dolerka! welcome to pf! :smile:

(have a degree: ° and try using the X2 icon just above the Reply box :wink:)if y is up, then your W is in the wrong equation :redface:

and whyever are you using 120° ? :confused:

bleh yes first time post. and the equation read T1y+T2y=0 should be T1x+T2x=0. and T1x+T2x+W=0 should be T1y+T2y+W=0. also i used 120o only because my book gives an example of a similar problem and also does this but that example on solved for one side.
 
Last edited:
  • #5
the system is in equilibrium.
draw components of both the tensions...we get
T2sin30+T1sin45=ma...1
T2cos30=T1cos 45 ...2
solve de 2 eq. to get T1 and t2...please correct me...if i m wrong...i m new here!
 
  • #6
welcome to pf!

hi Kartikc! welcome to pf! :wink:

(try using the X2 icon just above the Reply box :wink:)
Kartikc said:
the system is in equilibrium.
draw components of both the tensions...we get
T2sin30+T1sin45=ma...1
T2cos30=T1cos 45 ...2
solve de 2 eq. to get T1 and t2...

yes, that looks fine :smile:

(with "mg" of course)
 

What is a simple hanging tension problem?

A simple hanging tension problem is a physics problem that involves calculating the tension force in a rope or cable that is supporting an object or hanging between two points. It is a common problem in introductory physics courses and is used to illustrate the concept of tension in a system.

What are the key factors that affect the tension in a hanging rope?

The key factors that affect the tension in a hanging rope are the weight of the object being supported, the angle at which the rope is hanging, and the length and stiffness of the rope. The greater the weight of the object or the steeper the angle of the rope, the greater the tension will be. A longer or stiffer rope will also experience higher tension.

How do you calculate tension in a simple hanging tension problem?

To calculate the tension in a simple hanging tension problem, you can use the formula T = mg + ma, where T is the tension force, m is the mass of the object, g is the acceleration due to gravity (9.8 m/s^2), and a is the acceleration of the object. If the object is not accelerating, the formula simplifies to T = mg.

What are some real-world applications of simple hanging tension problems?

Simple hanging tension problems have many real-world applications, such as determining the tension in cables used in suspension bridges, calculating the force required to lift objects with a crane, and understanding the forces acting on a person hanging from a rock climbing rope. They are also used in engineering and construction to ensure that structures can withstand the tension forces they will experience.

What are some tips for solving simple hanging tension problems?

Some tips for solving simple hanging tension problems include drawing a free-body diagram to visualize the forces acting on the system, breaking the problem down into smaller parts if necessary, and carefully considering the units when plugging values into equations. It is also important to double-check your calculations and make sure they make sense in relation to the problem. Practice and familiarity with the concepts will also help in solving these types of problems.

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