A bungee cord can stretch, but it is never compressed. When thedistance be- twee
ID: 1722504 • Letter: A
Question
A bungee cord can stretch, but it is never compressed. When thedistance be-tween the two ends of the cord is less than its unstretched lengthL0, the cord folds and
its tension is zero. For simplicity, neglect the cord’s ownweight and inertia as well as the
air drag on the ball and the cord. A bungee cord has lengthL0 = 33 m when
unstretched; when it’s stretched to L > L0, thecord’s tension obeys Hooke’s law with
“spring” constant 39 N/m. To test the cord’sreliability, one end is tied to a high bridge of
height 94 m above the surface of a river) and the other end is tiedto a steel ball of mass
75 kg. The ball is dropped off the bridge with zero initial speed.Fortunately, the cord works and the ball stops in the air a fewmeters before it hits the water — and then the cord pulls itback up.
The acceleration of gravity is 9.8 m/s2 . Calculate theball’s height above the wa-
ter’s surface at this lowest point of its trajectory. Answerin units of m. What is the tension of the bungee cord when the ballis at its lowest point? Answer in units of N.
Explanation / Answer
A bungee cord can stretch, but it is never compressed. When thedistance be- tween the two ends of the cord is less than its unstretched lengthL0, the cord folds and its tension is zero. For simplicity, neglect the cord’s ownweight and inertia as well as the air drag on the ball and the cord. A bungee cord has lengthL0 = 33 m when unstretched; when it’s stretched to L > L0, thecord’s tension obeys Hooke’s law with “spring” constant 39 N/m. To test the cord’sreliability, one end is tied to a high bridge of height 94 m above the surface of a river) and the other end is tiedto a steel ball of mass 75 kg. The ball is dropped off the bridge with zero initial speed.Fortunately, the cord works and the ball stops in the air a fewmeters before it hits the water — and then the cord pulls itback up. The acceleration of gravity is 9.8 m/s2 . Calculate theball’s height above the wa- ter’s surface at this lowest point of its trajectory. Answer in units of m. the velocity of ball at the end of33m=0+2*9.8*33=25.43m/sec up to this point stretching of bungee cord wont happen now 1/2*75*25.43*25.43=1/2*39*x*x calculating x=35.26m hence the ball’s height above the water’s surface at this lowest point of itstrajectory.=94-(33+35.26)=25.74m What is the tension of the bungee cord when the ball is atits lowest point? Answer in units of N. tension=75*9.8+39*35.26=2110.14N
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