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Answer :
Final answer:
The tension in the cable at the lowest point of the swing of demolition ball is -34716.3 N. This means the tension is directed upwards, opposing the force of gravity.
Explanation:
In the scenario described, the demolition ball is experiencing two forces at the lowest point: the tension in the cable, and its weight due to gravity. The total force acting on the demolition ball (which we can also understand as the net centripetal force necessary to keep the ball moving in a circular path) is the sum of its gravity and the tension in the cable. Using the formula for centripetal force (Fc = mv^2/r), where m is mass, v is velocity, and r is radius, and knowing that the weight of the ball is mg (mass * gravity), we can find the tension (T). Thus: T = Fc - mg = m(v^2/r) - mg.
Substituting the given values: T = (4690kg)*(8.90 m/s)^2/(37.1m) - (4690kg)*(9.8 m/s^2) = 11245.7N - 45962N which gives us a tension of -34716.3N. The negative sign indicates that the tension force is directed upwards, in the opposite direction to the gravitational force.
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