Please show all work so I can follow along!! Your adventurous friend Lola goes b

Question

Please show all work so I can follow along!! Your adventurous friend Lola goes bungee jumping. She leaps from a bridge that is 100 m above a river. Her bungee cord has an un-stretched length of 50 m and a spring constant k = 600 N/m. Lola has a mass of48 kg. a) How fast is she falling when she just starts to stretch the cord? How long does it take for Lola to reach this point? b) Lola stretches the bungee cord and it brings her to a stop. She then bounces back up again. What type(s) of mechanical energy does the system (Lola and the bungee cord) have just before she jumps? (i.e., gravitational PE, elastic PE, kinetic energy, etc.)What type(s) of energy does the system have at the instant she comes to rest at her lowest point? c) What is her height above the river at her lowest point?

Explanation / Answer

Given data,

H=100m, L=50m, k=600N/m, m=48kg

a)

At the end of the cord Lola start to stretch. Thus after falling length L=50m she start to stretch.

vi=initial velocity when she jumps = 0m/s

vf= velocity when she start to jump

So using kinematic equation,

vf^2=vi^2+2*g*L

vf^2 = 0^2 -2*9.8*-50

vf= -31.3m/s …negative since directed downward

Now by second kinematic equation,

vf=vi –gt

31.3=0-9.8*t

t= 3.2 s

b)

Just before she jumps system have gravitational PE.

At the instant when she comes rest at lowest point system have elastic PE.

c)

At the lowest point we use conservation of energy,

PE(gravitational) = PE(gravitational)

mg(L+L) = ½*k* L2

48*9.8*(50+ L)=1/2*600* L2

48*9.8*(50+ L)=1/2*600* L2

L = 9.67m

Height above the river = H – L – L = 100 – 50 – 9.67 = 40.33 m

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