Maximally Inelastic Collisions

Claimed by Colleen Becton.

Contents

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

2.3 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

3 Connectedness

This topic is connected to something I'm interested in because collisions have been one of my favorite topics in Physics 2211.

As a civil engineering major, physics will be vitally important, and collisions can be as it tells you the resultant velocity, from which you can find other things.

It can be industrially interesting, especially if someone is analyzing systems, like if they want to see how far something would travel after a collision.

4 History

This topic has been observed and studied for most of human history.

5 See also

Collisions

Elastic Collisions

5.1 Further reading

2211 Textbook, Matter & Interactions, Chabay and Sherwood, Wiley 2015

6 References

Matter & Interactions, Chabay and Sherwood, Wiley 2015