Mastering Physics Solutions- Bungee Jumping Mastering Physics Solutions PDF

Preview

Summary

Mastering physics solutions
...

Description

3/19/2019

Mastering Physics Solutions: Bungee Jumping | Mastering Physics Solutions

Mastering Physics Solutions Help and solutions to mastering physics problems.

Home Mastering Physics Solutions by Chapter Contact

Mastering Physics Solutions: Normal Force and Centripetal Force Ranking Task Mastering Physics Solutions: Pushing Too Hard

Mastering Physics Solutions: Bungee Jumping Mastering Physics Solutions: Bungee Jumping On October 11, 2013, in Chapter 05: Work and Energy, by Mastering Physics Solutions Bungee Jumping Part A = d = mg/k + L Part B = k = 2mgh / (h – L)^2 Solution Below: Kate, a bungee jumper, wants to jump off the edge of a bridge that spans a river below. Kate has a mass m, and the surface of the bridge is a height h above the water. The bungee cord, which has length L when unstretched, will first straighten and then stretch as Kate falls. Assume the following: The bungee cord behaves as an ideal spring once it begins to stretch, with spring constant k. Kate doesn’t actually jump but simply steps off the edge of the bridge and falls straight downward. Kate’s height is negligible compared to the length of the bungee cord. Hence, she can be treated as a point particle. Use for the magnitude of the acceleration due to gravity. Part A How far below the bridge will Kate eventually be hanging, once she stops oscillating and comes finally to rest? Assume that she doesn’t touch the water. Express the distance in terms of quantities given in the problem introduction. Remember that the force exerted by a spring is F = -kx. Since the cord is being stretched downwards (and will spring upwards), we can remove the negative sign since the force will be acting in the positive y direction. And x = (d – L), where d is the total (stretched) length of the bungee cord. Just set this equal to the gravitational force: F(spring) = k(d – L) F(gravity) = mg k(d – L) = mg (d – L) = mg/k d = mg/k + L d = mg/k + L Part B If Kate just touches the surface of the river on her first downward trip (i.e., before the firstbounce), what is the spring constant k? Ignore all dissipative forces. Express k in terms of L, h, m, and g. When Kate jumps, her gravitational potential energy will be converted to spring potential energy, as the cord stretches. Remember that gravitational potential energy is U = mgh, and that spring potential energy is E = 1/2kx^2. Just set the two equal to each other. Also remember from Part A that x = (d – L), except that in this part, ‘d’ is replaced by ‘h’, since the cord is extended all the way down to the river. So for x, you have: x = (h – L). U = mgh E = 1/2k(h – L)^2 mgh = 1/2k(h – L)^2 2mgh = k(h – L)^2 k = 2mgh / (h – L)^2 k = 2mgh / (h – L)^2 If you enjoyed this article, please consider sharing it! http://www.masteringphysicssolutions.net/mastering-physics-solutions-bungee-jumping/

1/4

3/19/2019

Mastering Physics Solutions: Bungee Jumping | Mastering Physics Solutions

Tagged with: Forces • Springs

2 Responses to Mastering Physics Solutions: Bungee Jumping 1.

Anonymous says: October 14, 2013 at 6:02 am Instead of “(d – L)^2″ is (h – L)^2 for the second part Reply Mastering Physics Solutions says: October 15, 2013 at 10:13 pm Good catch. Sorry for the confusion! Reply

Leave a Reply Your email address will not be published. Name Email Website

CAPTCHA Code *

Comment You may use these HTML tags and attributes:

http://www.masteringphysicssolutions.net/mastering-physics-solutions-bungee-jumping/

2/4

3/19/2019

Mastering Physics Solutions: Bungee Jumping | Mastering Physics Solutions

Like us on Facebook

Like 527

Share

 By Chapter

Chapter 03: Motion in Two Dimensions (9) Chapter 04: Force and Motion (21) Chapter 05: Work and Energy (27) Chapter 06: Linear Momentum and Collisions (17) Chapter 07: Circular Motion and Gravitation (20) Chapter 13: Vibrations and Waves (18) Chapter 14: Sound (15) Chapter 15: Electric Charge, Forces, and Fields (26) Chapter 16: Electric Potential, Energy, and Capacitance (18) Chapter 17: Electric Current and Resistance (17) Chapter 18: Basic Electric Circuits (22) Chapter 19: Magnetism (17) Chapter 20: Electromagnetic Induction and Waves (14) Chapter 22: Reflection and Refraction of Light (17) Chapter 24: Physical Optics: The Wave Nature of Light (17) Site News (7)  Tags

Angular/Circular Motion Capacitors Centripetal Force

Charges Circuits Current Diffraction Doppler Effect Electric Fields

Electricity Electric Potential Energy Forces Friction Fundamental

Frequency Gauss's Law

Gravity Harmonic

Motion Impulse Induction Kinematics Kinetic Energy Light / EM

Spectrum Magnetic Fields Magnetism Momentum Newton's Laws Pendulums Periodic Motion Potential Energy Power Reflection Refraction

Resistance Slits and Diffraction Gratings Sound Spring Potential Energy Springs Standing Waves Tension Transformers Vectors Voltage Waves Work  http://www.masteringphysicssolutions.net/mastering-physics-solutions-bungee-jumping/

3/4

3/19/2019

Mastering Physics Solutions: Bungee Jumping | Mastering Physics Solutions

http://www.masteringphysicssolutions.net/mastering-physics-solutions-bungee-jumping/

4/4...