I\'m having a tough time with my general physics class, and I\'ma little stuck o

Question

I'm having a tough time with my general physics class, and I'ma little stuck on this question. If anyone could show me how to doit so that I can do the rest of my homework problems, it would begreatly appreciated! It's a nontextbook question (just a questionmy professor wrote). Thank you! Also, the link to theillustration was broken on his website, but I'm pretty sure you cando it without the illustration! Consider a bungee jump (illustration).A bungee cord acts like a spring when stretched: its tensionT depends on length L asT=k(L-L0) for someforce constant k and un-stretched lengthL0. However, forL<L0 the cord folds instead ofbecoming compressed, so there is no tension force and no elasticenergy.
(a) To test the reliability of a bungee cord, it's tied to a 120 kgsteel ball on one end and to a 61 m high bridge on the other end.The ball is dropped off the bridge (with zero initial velocity) andfalls down, but the bungee cord slows down the fall and eventuallystops the ball and yanks it back up. The lowest point reached bythe ball is 1 m above the water, 60 m below the bridge. The bungeecord has un-stretched length L0=20m; what is its force constant k?
(b) Once the cord is tested, a 60 kg student ties himself to thecord instead of the steel ball and jumps off the same bridge. Howclose to the water below the bridge does he get before the bungeecord yanks him up? I'm having a tough time with my general physics class, and I'ma little stuck on this question. If anyone could show me how to doit so that I can do the rest of my homework problems, it would begreatly appreciated! It's a nontextbook question (just a questionmy professor wrote). Thank you! Also, the link to theillustration was broken on his website, but I'm pretty sure you cando it without the illustration! Consider a bungee jump (illustration).A bungee cord acts like a spring when stretched: its tensionT depends on length L asT=k(L-L0) for someforce constant k and un-stretched lengthL0. However, forL<L0 the cord folds instead ofbecoming compressed, so there is no tension force and no elasticenergy.
(a) To test the reliability of a bungee cord, it's tied to a 120 kgsteel ball on one end and to a 61 m high bridge on the other end.The ball is dropped off the bridge (with zero initial velocity) andfalls down, but the bungee cord slows down the fall and eventuallystops the ball and yanks it back up. The lowest point reached bythe ball is 1 m above the water, 60 m below the bridge. The bungeecord has un-stretched length L0=20m; what is its force constant k?
(b) Once the cord is tested, a 60 kg student ties himself to thecord instead of the steel ball and jumps off the same bridge. Howclose to the water below the bridge does he get before the bungeecord yanks him up?

Explanation / Answer

(a) To test the reliability of a bungee cord, it's tied to a120 kg steel ball on one end and to a 61 m high bridge on the otherend. The ball is dropped off the bridge (with zero initialvelocity) and falls down, but the bungee cord slows down the falland eventually stops the ball and yanks it back up. The lowestpoint reached by the ball is 1 m above the water, 60 m below thebridge. The bungee cord has un-stretched lengthL0=20 m; what is its forceconstant k?

force constant=mg/X
mg=120*9.8N
X=(61-1)-20=40m
so force constant=120*9.8/40=29.4N/m
(b) Once the cord is tested, a 60 kg student ties himself to thecord instead of the steel ball and jumps off the same bridge. Howclose to the water below the bridge does he get before the bungeecord yanks him up?
in the case
k remains constant
k=60*9.8/x=29.4
so x= 60*9.8/29.4=20m
hence he will move down by 20+20=40m
so he will be at 61-40=21m from the water surface.

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