Frederick the amazing cat (mass: 10 kg) is sitting on a horizontal beam of weigh

Question

Frederick the amazing cat (mass: 10 kg) is sitting on a horizontal beam of weight 50 N and length 2.2 m. the beam is supported at one end by a vertical cord which is fastened securely to the ceiling. the cord has a breaking strength of 100 N (meaning that is the tension in the cord exceeds this value, the cord will break!). At the other end, the beam is fastened to a wall 1 means of a steel pin which keeps the beam from moving horizontally or vertically, but which allows the beam to rotate about the end. (The pin exerts a horizontal force to the right and a vertical force upwards on the beam in the figure below.) Find the maximum distance x that Frederick can move along the beam from the wall without breaking the cord.

Explanation / Answer

m = 10 kg ; W(beam) = 50 N ; L = 2.2 m ; T = 100 N

W(fred) = 10 x 9.8 = 98 N

The sum of torques about the point should be zero.

W(beam) x L/2 + W(Fred) x X - T x L = 0

50 x 2.2/2 + 98 X - 100 x 2.2 = 0

X = (220 - 55)/98 = 1.68 m

Hence, X = 1.68 m

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