My Math Forum  

Go Back   My Math Forum > Science Forums > Physics

Physics Physics Forum

Thanks Tree1Thanks
  • 1 Post By greg1313
LinkBack Thread Tools Display Modes
May 5th, 2015, 12:13 PM   #1
Joined: Jul 2014
From: Wrexham

Posts: 20
Thanks: 0

Spring question-Conservation of energy

A particle of mass 2 kg is attached to one end of a model spring that ishanging vertically from a fixed point O. The spring has stiffness 4 N m−1and natural length 1 m. The system is oscillating in a vertical line with theparticle below O. In this question use the approximation that themagnitude of the acceleration due to gravity is 10ms−2. Take the point Oas the datum for potential energy, and measure x downwards.
(a) Find an expression for the total mechanical energy function for the system.
(b) When the particle is 2 m below A, it has speed 1 m s−1. Use conservation of mechanical energy to establish whether the spring is ever in compression during the motion. (Hint: Try to determine the speed of the particle when the spring has its natural length.)

I get the energy of the system to be E= v^2 - 20x + 2(x-1)^2 for the first part. I also get E=-37 J when x=2 and v=1m/s. The problem is for b) when using the conservation of energy I get

v2 = -17

Does this mean I take the absolute value of v^2 and conclude the spring does compress as it has a velocity, or since square root of -17 gives a complex value do I conclude that this could not happen?
AJ235 is offline  
May 5th, 2015, 06:33 PM   #2
Math Team
Joined: Jul 2011
From: Texas

Posts: 2,751
Thanks: 1401


(b) When the particle is 2 m below A, it has speed 1 m s−1
A? Do you mean O?

$E_{total}=2-40+1=-37 \, J$

When $x=1$, the gravitational potential energy is $-20 \, J$. Since no energy is stored in the spring at its natural length, the kinetic energy would have to be $-17 \, J$, but kinetic energy cannot be less than zero. Therefore, the mass can never get to the height of $1 \, m$ below O.

Have a look at the potential energy curve shown ... $f_1(x)=2(x-1)^2-20x$ is the sum of the elastic & gravitational potential energy; $f_2(x)=-37$ is the total mechanical energy of the system. Note the intersection of the two graphs defines the max and min position for the mass while it oscillates. The vertical distance between the two graphs is the kinetic energy of the mass, a max at $x=6 \, m$, where $mg=kx$.
Attached Images
File Type: jpg image.jpg (68.3 KB, 5 views)
skeeter is offline  
May 5th, 2015, 10:35 PM   #3
Joined: Jul 2014
From: Wrexham

Posts: 20
Thanks: 0

Thanks very much skeeter that is a massive help. The question said A but I assume it is meant to say O! Thanks again
AJ235 is offline  
May 6th, 2015, 02:06 AM   #4
Global Moderator
greg1313's Avatar
Joined: Oct 2008
From: London, Ontario, Canada - The Forest City

Posts: 7,807
Thanks: 1045

Math Focus: Elementary mathematics and beyond
AJ235, please do not post duplicate topics.
Thanks from AJ235
greg1313 is offline  

  My Math Forum > Science Forums > Physics

energy, questionconservation, spring

Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Mechanical energy conservation Mr Davis 97 Physics 3 April 24th, 2015 10:16 AM
conservation of energy in an undamped driven harmonic oscillator inkliing Physics 2 August 26th, 2014 07:48 AM
Is the start of the Universe against the law of conservation of energy? Kavesat Physics 7 July 22nd, 2014 01:39 PM
Conservation of Energy Problem edwinandrew Physics 2 April 28th, 2014 02:16 AM

Copyright © 2018 My Math Forum. All rights reserved.