May 5th, 2015, 12:13 PM  #1 
Newbie Joined: Jul 2014 From: Wrexham Posts: 16 Thanks: 0  Spring questionConservation 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(x1)^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? 
May 5th, 2015, 06:33 PM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 2,722 Thanks: 1376 
$E_{total}=\frac{1}{2}k(x1)^2mgx+\frac{1}{2}mv^2$ Quote:
$E_{total}=240+1=37 \, J$ 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 ... $f_1(x)=2(x1)^220x$ 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 $mg=kx$.  
May 5th, 2015, 10:35 PM  #3 
Newbie Joined: Jul 2014 From: Wrexham Posts: 16 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

May 6th, 2015, 02:06 AM  #4 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,762 Thanks: 1010 Math Focus: Elementary mathematics and beyond  AJ235, please do not post duplicate topics.


Tags 
energy, questionconservation, spring 
Search tags for this page 
Maths questin 293, 678,Conservation of mechanical energy conservation of mechanical energy forest spring,CONSERVATION OF ENERGY QUES. ON SPRING,question based on conservation of energy in spring,spring questions based on conservation of mechanical energy
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 