Why Do Different Conservation Laws Give Different Results in SHM Problems?

AI Thread Summary
The discussion focuses on the application of conservation laws in simple harmonic motion (SHM) problems, specifically when a smaller mass is added to a larger mass in motion. When using conservation of momentum, the resulting amplitude ratio is derived as (M/(m+M))^(1/2), while conservation of energy yields a different ratio of (M/(m+M)). The discrepancy arises because the interaction between the two masses requires work to be done, leading to a loss of mechanical energy, similar to an inelastic collision. Thus, while momentum is conserved, energy is not conserved in this scenario. This highlights the importance of recognizing the conditions under which different conservation laws apply in SHM.
kushan
Messages
256
Reaction score
0
Conservation of energy ?

Homework Statement


I was trying to solve this question
" A mass M , attached to a horizontal spring , executes SHM with Amplitude A1 , when the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with Amplitude A2 , ratio of A1/A2 "
when i apply conservation of Momentum i get
(M/(m+M))^(1/2)
and if i apply conservation of energy
i get (M/(m+M)

Can somebody help me figure out what is going wrong ?
Thank you
 
Physics news on Phys.org


When you place the small mass on the big one while it is in motion, the small mass has to accelerate up, the bigger mass has to decelerate to the common speed. For that, some force of interaction is needed, and that force does work. Because of the work done by something else than the spring, the sum of the elastic energy and kinetic energy is not conserved.
The situation is similar to inelastic collision. If the small mass were put in front of the big one it would be exactly an inelastic collision. The momentum conserves but the energy does not.

ehild
 


thank you ehild :D
 
Last edited:


You are welcome.:smile:
 
Thread 'Collision of a bullet on a rod-string system: query'

Thread 'Collision of a bullet on a rod-string system: query'

In this question, I have a question. I am NOT trying to solve it, but it is just a conceptual question. Consider the point on the rod, which connects the string and the rod. My question: just before and after the collision, is ANGULAR momentum CONSERVED about this point? Lets call the point which connects the string and rod as P. Why am I asking this? : it is clear from the scenario that the point of concern, which connects the string and the rod, moves in a circular path due to the string...
View full post »
Thread 'A cylinder connected to a hanged mass'

Thread 'A cylinder connected to a hanged mass'

Let's declare that for the cylinder, mass = M = 10 kg Radius = R = 4 m For the wall and the floor, Friction coeff = ##\mu## = 0.5 For the hanging mass, mass = m = 11 kg First, we divide the force according to their respective plane (x and y thing, correct me if I'm wrong) and according to which, cylinder or the hanging mass, they're working on. Force on the hanging mass $$mg - T = ma$$ Force(Cylinder) on y $$N_f + f_w - Mg = 0$$ Force(Cylinder) on x $$T + f_f - N_w = Ma$$ There's also...
View full post »

Similar threads

Conservation of Momentum vs Constant k for an Ideal Spring
Replies
2
Views
1K
Energy conservation vs momentum conservation in SHM
Replies
4
Views
3K
Elastic potential energy - different methods, different results
Replies
2
Views
768
Angular Momentum- Conserved or not?
Replies
17
Views
337
Conservation of Energy in Trampoline Bounce
Replies
20
Views
2K
Question about the conservation of mechanical energy
Replies
7
Views
2K
An exploding cannon shell
Replies
4
Views
697
Spring Problem Involving Variables and Constants Only
Replies
3
Views
1K
Body attached to a block by a spring, shaped like an inclined plane
Replies
1
Views
884
Is energy conserved is this problem?
Replies
44
Views
3K

Hot Threads

Recent Insights

Back
Top