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A 75.0-kg wrecking ball hangs from a uniform, heavy-duty
Chapter 8, Problem 3E(choose chapter or problem)
A 75.0-kg wrecking ball hangs from a uniform, heavy-duty chain of mass 26.0 kg.
(a) Find the maximum and minimum tensions in the chain.
(b) What is the tension at a point three-fourths of the way up from the bottom of the chain?
Questions & Answers
QUESTION:
A 75.0-kg wrecking ball hangs from a uniform, heavy-duty chain of mass 26.0 kg.
(a) Find the maximum and minimum tensions in the chain.
(b) What is the tension at a point three-fourths of the way up from the bottom of the chain?
ANSWER:Solution 3E Step 1 (a) The tension on a chain due to its own weight, at a point y is given by T (y) = mg(1 y/L) c Here y is measured from the top of the string, m = 26.0 kg is the mass and L is the length of the string. So the total tension will be T ty) = Mg + mg(1 y/L) Here M = 75 kg is the mass of ball. So the maximum tension will be at y = 0, hence the maximum tension is 2 T m = Mg + mg = (M + m)g = (75.0 kg + 26.0 kg)(9.8 m/s ) = 990 N And the minimum tension will be at y = L, and the minimum tension is 2 T min = Mg + mg(1 L/L) = Mg = (75 kg)(9.8 m/s ) = 735 N