What is the maximum length a bungee rope with a spring constant of 100 Nm−1 can be for an 80kg man to be able to jump from 100m above a river without touching the water?

The key to solving this problem is realising that gravitational potential energy and elastic potential energy need to be equated. The gravitational potential energy of an object of mass m at height h above the Earth is equal to mgh. The elastic potential energy of a spring with spring constant k and extension x is 0.5kx^2. Equating these expressions gives mgh = 0.5kx^2. This assumes that all of the gravitational potential energy of the bungee jumper will be converted to elastic potential energy. To find the maximum extension of the rope, rearrange this expression to find x, giving x = (2mgh/k)^0.5. Substituting in the values given in the question gives the extension of the rope to be x = (2 x 80 x 9.81 x 100/100)^0.5 = 39.62m. To find the maximum original length the rope can be without the jumper touching the water, just subtract this extension from the height at which the jumper is jumping from, giving 100 - 39.62 = 60.38m. Therefore, the rope can be a maximum of 60.38m long for the jumper to be able to jump from 100m above the river and not touch the water.

SJ
Answered by Samuel J. Physics tutor

13957 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

How do you prove Kepler's Third Law?


Define Newtons law of Gravitation (in words or an equation).


An ideal gas undergoes a transformation in which both its pressure and volume double. How many times does the root mean square speed of the gas molecules increase?


What is the angular speed of a car wheel of diameter 0.400m when the speed of the car is 108km/h?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences