Answer to Question #311855 in Mechanics | Relativity for Chen

Question #311855

Two identical 15.0-kg balls, each 25.0 cm in diameter, are suspended by two



35.0-cm wires. The entire apparatus is supported by a single 18.0-cm wire,



and the surfaces of the balls are perfectly smooth.



a) Find the tension in each of the three wires.



b) How hard does each ball push on the other one?

1
Expert's answer
2022-03-18T09:16:23-0400

Explanation & Calculations


a)

  • Take the system as a whole so that only the two weights of the ball and the single thread is seen, and consider the equilibrium.

T2mg=0T=294N\qquad\qquad \begin{aligned} \small T-2mg&=\small 0\\ \small T&=\small 294\,N \end{aligned}

  • If the two threads make θ\small \theta angles with the horizontal (they are identical as the system is symmetrical about the vertical)

cosθ=rr+35.0=12.512.5+35.0=0.263sinθ=0.945\qquad\qquad \begin{aligned} \small \cos\theta &=\small \frac{r}{r+35.0}=\frac{12.5}{12.5+35.0}=0.263\\ \small \sin\theta &=\small 0.945 \end{aligned}

  • Now consider the equilibrium of a ball under the act of its weight and one of the two threads.

T1sinθmg=0T1=155.6N\qquad\qquad \begin{aligned} \small \uparrow\\ \small T_1\sin\theta-mg&=\small 0\\ \small T_1&=\small 155.6\,N \end{aligned}


b)

  • Consider the horizontal equilibrium of a ball under the same act and say the force the balls are being pushed is R,

T1cosθR=0R=40.9N\qquad\qquad \begin{aligned} \small \to\\ \small T_1\cos \theta-R&=\small 0\\ \small R&=\small 40.9\,N \end{aligned}


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