A 3m long uniform density boom of mass 14 kg is horizontally mounted to a wall,

Question

A 3m long uniform density boom of mass 14 kg is horizontally mounted to a wall, and is supported by a cable that makes a 35 angle with respect to the boom and attached at the 2 m mark. At the end of the boom, on an o.8 m tether is a 0.6 kg ball that spins in a vertical loop. The support cable can only support a tension of 1000 N. a) what is the max speed of the ball at the bottom of its rotation before it breaks the support cable? (Hint: First figure out the max tension in the tether, then create that tension with centripetal acceleration). b) What is the reaction force at the base of the boom at that moment?

Explanation / Answer

I don't know why cramster won't create my image. It says error. If you draw a free body diagram on the boom, you will have its weight acting downwards and Tension T in support cable as well as Tt, the tension in tether.You will also have Ry and Rx, the reaction forces in y and x direction respectively. The verticle component of T will be T sin(35) and its perpendicular distance from base is given as 2 meters. Thus, it will produce anticlockwise moment of 1000sin(35) x 2 = 2000sin(35). The weight (14x9.8) acts at the middle of the boom so its clockwise moment will be (14x9.8x1.5). The tether also produces a clokwise moment of 3Tt since its distance from base is 3. Thus, (14x9.8x1.5) + 3Tt = 2000sin(35). You can now find tension in tether. If we draw free body diagram of ball, there is Tt acting upwards and weight acting downwards. this is what provides the centripetal force mv^2/R where r is radius of its circular path. that is basically the length of the tether. Thus, Tt - (0.6x9.8) = 0.6v^2/0.8. Find v. (b) Reaction force consists of Rx and Ry. For Ry, consider sum of verticle forces.Assume Ry is upwards and Rx is to the right. Thus, Ry + Tsin(35) = weight of boom + Tt Thus, Ry = (14x9.8x1.5) + Tt - 1000sin(35). Similarly, in horizontal direction, Rx = 1000cos(35) where 100cos(35) is horizontal component of tension. you can easily find Rx.

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