If you plug in real values for the final equation on PART 2 of the question, you get root a negative number in any situation, except compression. Can someone explain this?
If you plug in real values for the final equation on PART 2 of the question, you get root a negative number in any situation, except compression.
No you don’t. Remember, x is the total length of the spring when it is pulled back, so the expression inside the square root is positive when x – l > 2gm/k.
It took me a while to understand the solution to the problem. I’ve tried different combinations of events, i.e. if the spring was compressed instead. Would the equation, assuming the natural length is ‘L’ for the spring, and this is taken as the reference point, of E initial = 1/2 K (L-X)^2 + Mg(L-X) and E final = 1/2 MV^2, giving you 1/2MV^2 = 1/2 K(L-X)^2 + Mg(L-X) be correct?
I think I need some clarification on why GPE is negative in the solution to the problem and does this have anything to do with the conservation of mechanical energy (0 = KE + GPE). If I use the work-energy principle and conservation of mechanical energy for the energy equations of compression, does that make the equation above incorrect since it now becomes 1/2 MV^2 – Mg(L-x)?
Sorry for the lengthy question! Thanks!
In part 2, the KE equals the elastic potential energy minus the gravitational potential energy. But in the GPE, why is the height given as x-l ? Is it not possible for the mass to exceed this height?
Hi Brook — thanks for your question.
In part 2, we’re talking about the point where the ball has its maximum velocity. (Writing capitals for X and L to make the text clearer) when the spring is extended to total length X, the ball is at its lowest point, and isn’t moving. The ball reaches its highest velocity at the point where the spring just becomes slack, i.e. when it has length L. So at this point the ball has been raised a total distance of X – L. So the GPE gained at the point of maximum velocity is mg(X – L), and the total KE at this point is the energy that was stored in the spring minus this quantity of GPE gained.
Is that OK? Add another comment if you think there’s a mistake or you need more clarification.
Your comments made it clearer, it makes sense now. Thanks a lot.
Fill in your details below or click an icon to log in:
You are commenting using your WordPress.com account. ( Log Out / Change )
You are commenting using your Twitter account. ( Log Out / Change )
You are commenting using your Facebook account. ( Log Out / Change )
You are commenting using your Google+ account. ( Log Out / Change )
Connecting to %s
Notify me of new comments via email.
Notify me of new posts via email.