Please show work 9. Having successfully survived his first bungee jump, Ron is h
ID: 250918 • Letter: P
Question
Please show work
9. Having successfully survived his first bungee jump, Ron is hanging from rest at the end of the bungee chord. "I wonder what the spring constant of this bungee cord is?" he asks himself. So he decides to perform a simple experiment. He pulls himself up about 0.75 m and lets go. As he begins to bob up and down, he times his bounces and finds that he completes 4 oscillations in 20 seconds. He knows his mass is 75 kg. a) What is the period of his motion? b) What is the frequency of his motion? c) What total distance does Ron travel in 20 seconds? Explain your reasoning. d) What is the spring constant of the bungee chord?Explanation / Answer
(a) Period of his motion T = 20/4 = 5 Seconds
(b) Frequency of motion = 1/5 Seconds = 0.2 Hz
(d) Time period T = 2 SQRT (m/k)
K = spring constant of chord = m x 4 2/T2 = 75 x 4 x 3.142 / 52 = 118.32 N/m
(c) For maximum extension of chord kXmax = mg
Xmax = 75 x 9.8 /118.32 = 6.21 m
Total distance travelled in one oscillation = 4 X maximum extension of chord
So total distance travelled in one oscillation = 16 x Xmax = 99.39 meters