Question

A child bounces in a harness suspended from a door frame by three elastic bands.

(a) If each elastic band stretches 0.260 m while supporting a 8.15-kg child at rest, what is the force constant for each elastic band? Assume that each spring supports 1/3 of the child's weight.
N/m

(b) What is the time for one complete bounce of this child?
s

(c) What is the child's maximum velocity if the amplitude of her bounce is 0.260 m?
m/s

Answer 1

a) force on each band = (8.15/3)*9.8=26.62 N

elongation in each band = 0.26 m

Force constant of each band = 26.62/0.26=102.4 N/m

b)total force constant of the system = 3*102.4=307.2 N/m

mass=8.15 kg

angular velocity = sqrt(307.2/8.15)=6.14 rad/s

period of vibration = 2*pi/6.14=1.02 seconds

time for one complete bounce of child = 1.02 seconds

c)maximum energy stored = 3*0.5*102.4*0.26²=10.383 J

let maximum velocity of child be v

0.5*8.15*v² = 10.383

v=1.596 m/s