Physics challenge question! your adrenaline-junkie friend loves bungee jumping.
ID: 2286712 • Letter: P
Question
Physics challenge question!
your adrenaline-junkie friend loves bungee jumping. He wants to try something new, so is planning a static line (not elastic) swing jump. This will involve tying one end of the 50 m long rope to the center of a bridge 70 m over a river, walking down the bridge 50 m, so that the rope is fully extended, and then jumping off the bridge while harnessed to the other end of the rope so that you swing down in a circular arc. He decides that you, he, and three other friends can all do the jump at the same time harnessed together to the same rope. In total, all five of you have a mass of 375 kg. He has bought a rope that can support 9,000 N of tension without breaking. How do you think the jump goes and why? Will you be doing more jumps with him in the future? Support your answer with a calculation, considering the maximum force the rope must be able to support. (You can ignore any effects of air resistance.)
Explanation / Answer
Maximum tension on the rope will be at the bottom of the arc. The velocity at the bottom can be calculated by conservation of energy.
0.5mv^2=mgL
v=sqrt(2gL)=sqrt(2*9.81*50)=31.32m/s
Maximum tension=mg+mv^2/L=375*9.81+375*31.32^2/50=11035 N
Since this is greater than the maximum tension the rope can bear, the rope will break before it reaches the absolute bottom of the arc. Therefore, I am going to avoid doing such jumps in the future.