How do I calculate percent elasticity?

AI Thread Summary
To calculate percent elasticity in collisions, one must understand the distinction between elastic and inelastic collisions. Elastic collisions conserve both momentum and kinetic energy, resulting in 100% elasticity, while inelastic collisions result in energy loss and can be described as 0% elastic. The concept of percent elasticity can be framed as a spectrum between these two extremes, where energy is conserved in elastic collisions but dissipated as heat or sound in inelastic ones. The discussion emphasizes that while total energy is conserved, the form it takes changes in inelastic collisions. Understanding these principles is crucial for accurately calculating percent elasticity in various collision scenarios.
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Homework Statement


I was given a chart to figure out the different momentum and kinetic energies of different collisions (elastic and inelastic) and in the lab he posed the question "Calculate the percent elasticity for each of the collisions."

Homework Equations


conservation of momentum and energy

The Attempt at a Solution


I have never heard of this question before and have looked through all of my notes. Finding nothing, I turned to the internet and searched for "percent elasticity," "how to calculate percent elasticity," and multiple other relevant phrases to the problem. Nothing has come up so far and I'm not sure how to approach the question. Any help would be awesome. Thanks!
 
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How are elastic collisions different from inelastic collisions?
 
AlephNumbers said:
How are elastic collisions different from inelastic collisions?
Elastic collisions occur when objects of whatever mass or velocity collide and propel apart from each other with the exact same momentum and energy as the initial momentum and energy (p=p' and E=E'). Inelastic collisions are when objects of whatever mass or velocity collide and 'stick' together. For example, two tennis balls with Velcro stick together when they collide. In this system, energy is lost.
 
Right! Energy is not conserved in inelastic collisions. Think of a collision in which energy is conserved. This case could be described as being 100% elastic, right? Alternatively, think of a case in which the collision is completely inelastic. This case could be described as being 0% elastic. The final kinetic energy of the system is not zero, but the elasticity is still 0%.
 
Well, actually, the kinetic energy is not conserved. Energy is always conserved. Some of it just goes into heat or sound or what have you.
 
AlephNumbers said:
Right! Energy is not conserved in inelastic collisions. Think of a collision in which energy is conserved. This case could be described as being 100% elastic, right? Alternatively, think of a case in which the collision is completely inelastic. This case could be described as being 0% elastic. The final kinetic energy of the system is not zero, but the elasticity is still 0%.
Okay, yeah that makes sense! Thank you so much!
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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