Maximally Inelastic Collisions

Claimed by Colleen Becton.

Contents [hide]

1 The Main Idea

1.1 A Mathematical Model

2 Examples

2.1 Simple

2.2 Middling

2.3 Difficult

3 Connectedness

4 History

5 See also

5.1 Further reading

5.2 External links

6 References

1 The Main Idea

As with all inelastic collisions, internal energy does change during this collision. This could be shown as getting hot, deforming, rotating, vibrating, in an excited state, and so on. In the maximally inelastic case, however, the objects have maximum dissipation, though that does not mean they stop, as they still follow the conservation of momentum. The objects stick together.

1.1 A Mathematical Model

pi=pf

mvi=mvf

2 Examples

2.1 Simple

Two lumps of clay, both with mass of .5 kg are thrown at 3 m/s in opposite directions and stick together. What is their final velocity?

m1v1 + m2v2 = mtvf (.5)<3,0,0> + (.5)<-3,0,0> = (.5+.5)<vf> <1.5,0,0> + <-1.5,0,0> = (1)<vf> <0,0,0> = (1)<vf> <vf> = <0,0,0> m/s

2.2 Middling

A car of mass 1500 kg travelling at <30,-8,0> m/s and motorcycle of mass 700 kg travelling at <0,50,0> m/s collide and stick together. What is their final speed?

m1v1 + m2v2 = mtvf (1500)<30,-8,0> + (700)<0,50,0> = (1500+700)<vf> <45000,-12000,0> + <0,35000,0> = (2200)<vf> <45000, 23000,0> = (2200)<vf> <vf> = <20.45,10.45,0> m/s

Difficult

An asteroid of mass 800 kg and velocity <900,-600, 1200> m/s crashes into a small planet of mass 60000 kg travelling at <-200,100,2> m/s. What is their final speed?

m1v1 + m2v2 = mtvf (800)<900,-600,1200> + (60000)<-200,100,2> = (60000+800)<vf> <720000,-480000,960000> + <-12000000,6000000,120000> = (60800)<vf> <-11280000,5520000,1080000> = (60800)<vf> <vf> = <-185.53,90.79,17.76> m/s

Connectedness[edit] How is this topic connected to something that you are interested in? How is it connected to your major? Is there an interesting industrial application? History[edit] Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

See also[edit] Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

Further reading[edit] Books, Articles or other print media on this topic

External links[edit] [1]

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