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

[kirby27]

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?

 

[PhanthomJay]

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?

 

[kirby27]

i think i see my mistake. should it be cos(25)*71.2 = 64.5 Newtons?

 

[PhanthomJay]

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.

 

[kirby27]

the tension force is diagonal. 71.2 is the weight of each ball. here is the diagram:

http://i.imgur.com/Q5dXO.jpg

 

[PhanthomJay]

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, T_y, 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. .

 

[kirby27]

ok i think i got it. is it 71.2/cos(25) = 78.56?

 

[PhanthomJay]

ok i think i got it. is it 71.2/cos(25) = 78.56?

Yes. Call it 78.6. Newtons.

 

[kirby27]

thank you very much

 

[kirby27]

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

 

[PhanthomJay]

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.