See picture for first part of problem and pictures.
II. You are to find:
a) The necessary un-stretched length of the bungee cord.
b) The maximum speed and acceleration achieved during the jump.
c) The spring constant of the bungee cord in relation to the jumper’s
- NCSLv 75 months agoFavorite Answer
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All quantities are in SI units.
person's GPE becomes spring PE:
m*g*(25 - 2) = ½kx²
where x is the maximum elongation of the cord,
h - 2 = L + x
where L is the unstretched length
At equilibrium, the stretch z is due only to the person's weight:
mg = kz
x = z + 8
mg = k(x - 8)
k = mg / (x-8)
m*g*23 = ½*[m*g/(x-8)]*x²
23*2 = x² / (x-8)
46(x - 8) = x²
x² - 46x + 368 = 0
is quadratic with roots at
x = 10.3 m ← solution
and x = 35.7 m ← outside of acceptable range
L = 23m - x = 12.7 m
b) the maximum speed is achieved just when the spring force is equal to the weight:
z = x - 8m = 2.3 m
KE = initial GPE - final GPE - SPE
KE = m*g*(12.7+2.3) - ½*[m*g/2.3]*(2.3)²
KE = m*g*(15 - 1.15) = m*g*14
and of course KE = ½mv²
so after canceling the mass we have
½v² = g*14 = 9.8*14 = 137
v² = 274
v = 17 m/s
c) k = mg / (x - 8) = m*9.8 / 2.3 = 4.26*m
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