Anonymous
Anonymous asked in Science & MathematicsPhysics · 5 months ago

Physics Question?

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

mass.

Relevance
• NCS
Lv 7
5 months ago

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

and

x = z + 8

so

mg = k(x - 8)

k = mg / (x-8)

m*g*23 = ½*[m*g/(x-8)]*x²

m*g cancels

23*2 = x² / (x-8)

46(x - 8) = x²

x² - 46x + 368 = 0

x = 10.3 m ← solution

and x = 35.7 m ← outside of acceptable range

a) so

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