Question

Two identical, perfectly smooth 71.2 N bowling balls 21.7 cm in diameter are hung together from the same hook in the ceiling by means of two thin wires. Hint: draw the free body diagram at the center of the ball.

(a) What is the tension in each wire? (b) What is the force the balls exert on each other?

500

Answer 1

the angle on top= 50 degrees?

If so, the other two angles at the bottom must be 65 degrees each, which adds up to 65+65+50 = 180...

The tension for each of the wires must be equal, since it is an isosceles triangle. Therefore, T1=T2=T

Set up the equations for the two wires:
T= T*sin(65) - 71.2N
T= T*sin(65) - 71.2N

Now add the two equations:
(T*sin(65) - 71.2N) + (T*sin(65) - 71.2N) = 0
T*sin(65) + T*sin(65) = (71.2N + 71.2N)
Now solve algebraically for T:
2T*sin(65)= 142.4 N
T= 142.4N ÷ ( 2*sin(65) ) = 78.56N.

Now, for part B:
F= T*cos(65)

=78.56 cos(65) 33.20 N