How Do You Calculate Wire Tension in the Hanging Bowling Balls Problem?

In summary, two identical, perfectly smooth 71.2 {\rm N} bowling balls 21.7 {\rm cm} in diameter are hung together from the same hook in the ceiling by means of two thin, light wires. The balls are touching with an angle of 50 degrees between the two wires split evenly between the balls. The tension in each wire can be found by using trigonometry and is equal to 78.6 Newtons. The balls exert a force on each other in the x direction, which is equal to 33.2 Newtons. The ball diameter is not needed to solve this problem.
  • #1
kirby27
32
0
Two identical, perfectly smooth 71.2 {\rm N} bowling balls 21.7 {\rm cm} in diameter are hung together from the same hook in the ceiling by means of two thin, light wires, as shown in the figure. The balls are touching with an angle of 50 degrees between the two wires split evenly between the balls.

find the tension in each wire:

i know that the top angle is 50 so each right triangle must be 25,65,90. the force opposing tension is gravity so if i find gravity i can change the sign and find tension. i did cos(65)*71.2 and got 30 Newtons. is this method correct?
 
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  • #2
You are on track, but check your trig, geometry, and pythagorus...if the force opposing gravity is the vertical tension component, shouldn't the Tension in the ( diagonal ) cord be greater than that?
 
  • #3
i think i see my mistake. should it be cos(25)*71.2 = 64.5 Newtons?
 
  • #4
No-o. If the vertical component of the tension force is 71.2 N, as you stated, then the tension in the wire must be greater than 71.2 N.
 
  • #5
  • #6
kirby27 said:
the tension force is diagonal. 71.2 is the weight of each ball. here is the diagram:

http://i.imgur.com/Q5dXO.jpg
Draw a sketch of one of the balls and identify the forces acting on it. As you noted in your original post (I think), the gravity force of 71.2 N acts down, and the vertical component of the tension force, Ty, is 71.2 N, equal and opposite to the gravity force, correct? You have also correctly identified that the angle the cord makes with the vertical is 25 degrees. The resultant tension force acting along the diagonal is the unknown, T. Solve for T, using Trig. .
 
  • #7
ok i think i got it. is it 71.2/cos(25) = 78.56?
 
  • #8
kirby27 said:
ok i think i got it. is it 71.2/cos(25) = 78.56?
Yes. Call it 78.6. Newtons.
 
  • #9
thank you very much
 
  • #10
the second part of the questions asks "Find the force the balls exert on each other." i think the only force they have on each other is the x component of tension. so I am guessing the answer is 78.6cos(65)=33.2. but the problem gives the diameter of the balls and i haven't used that number so i think I am doing something wrong
 
  • #11
kirby27 said:
the second part of the questions asks "Find the force the balls exert on each other." i think the only force they have on each other is the x component of tension. so I am guessing the answer is 78.6cos(65)=33.2. but the problem gives the diameter of the balls and i haven't used that number so i think I am doing something wrong
Your answer is correct. You don't need the ball diameter information.
 

FAQ: How Do You Calculate Wire Tension in the Hanging Bowling Balls Problem?

1. What is the hanging balls tension problem?

The hanging balls tension problem, also known as the "hanging chain problem" or "hanging cable problem", is a classic physics problem that involves calculating the tension in a cable or chain that is supporting a series of hanging objects of equal mass.

2. How do you solve the hanging balls tension problem?

To solve the hanging balls tension problem, you need to use the principles of static equilibrium. This means that the sum of all the forces acting on the system (in this case, the hanging objects and the cable) must equal zero. You also need to consider the weight of the objects and the tension in the cable as two separate forces acting on the system.

3. What factors affect the tension in the cable in the hanging balls tension problem?

The tension in the cable in the hanging balls tension problem is affected by several factors, including the weight of the hanging objects, the distance between the objects, and the angle at which the cable is suspended. The longer the chain or cable, the greater the tension will be. Additionally, a steeper angle of suspension will result in a higher tension.

4. Can the hanging balls tension problem be applied to real-world scenarios?

Yes, the hanging balls tension problem can be applied to real-world scenarios, such as determining the tension in a suspension bridge or the tension in a cable supporting a cable car. It can also be used to calculate the tension in ropes or cables used in construction or rock climbing.

5. Are there any limitations to the hanging balls tension problem?

One limitation of the hanging balls tension problem is that it assumes a perfectly uniform and symmetrical system, which may not always be the case in real-world scenarios. Additionally, it does not take into account the effects of friction or air resistance, which can impact the accuracy of the calculations.

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