How Do You Calculate Kinetic Energy in Relativistic Dynamics?

[Scientist94]

Homework Statement

A particle of mass m and kinetic energy K strikes and combines with a stationary particle of mass 2m, producing a single composite particle of mass √17 m. Find the value of K

Homework Equations

E= γmc^2 , p = λmv

The Attempt at a Solution

I have tried many times at this and have used the conservation of energy and conservation of momentum but I seem to get nowhere. The equations are definitely solvable and this seems to just be algebraic manipulation. My question is whether there is any way to simplify these problems as I just cannot get an expression for K without the other variables, this problem keeps cropping up in other questions too!

 

[DataGG]

Show us what you've done please.

EDIT:

Also, check out this link. You should get used to writing in latex for physics/math.

 

[rude man]

Does the composite particle have zero K.E.?

 

[Chestermiller]

Does the composite particle have zero K.E.?

Hi Rudy. Not necessarily.

Chet

 

[Chestermiller]

Homework Statement

A particle of mass m and kinetic energy K strikes and combines with a stationary particle of mass 2m, producing a single composite particle of mass √17 m. Find the value of K

Homework Equations

E= γmc^2 , p = λmv

The Attempt at a Solution

I have tried many times at this and have used the conservation of energy and conservation of momentum but I seem to get nowhere. The equations are definitely solvable and this seems to just be algebraic manipulation. My question is whether there is any way to simplify these problems as I just cannot get an expression for K without the other variables, this problem keeps cropping up in other questions too!

You should be able to manipulate and combine the momentum balance and the energy balance into a single quadratic equation involving the variable x = K/(mc²). It takes some playing with the math to bring this about. So, as Strange said, show us what you did, and maybe we can give you some hints on manipulating the math.

Chet

 

[rude man]

Hi Rudy. Not necessarily.

Chet

Hi Chet, right. Hadn't realized.

I'll leave this one to you, assuming the OP responds. Lately the only responses I get are from other helpers ... bedides, I'd only invoke rest mass again, stirring that controversy up again probably.

rudy

 

[Chestermiller]

Hi Chet, right. Hadn't realized.

I'll leave this one to you, assuming the OP responds. Lately the only responses I get are from other helpers ... bedides, I'd only invoke rest mass again, stirring that controversy up again probably.

rudy

What's wrong with invoking rest mass? That seems to be a large part of what this problem is about.

Chet

 

[rude man]

What's wrong with invoking rest mass? That seems to be a large part of what this problem is about.

Chet

I learned 'modern physics' in the early '60's when there was a separate symbol for rest mass: m₀. Recently it was pointed out to me in these forums that that is no longer in vogue: there is only one mass, m. If at rest it's m, if moving it's γm. So among other casualties it's no longer E = mc² but γmc², and p = mv is no longer correct either. I find this change entirely pointless but found out to my distress that I was in the rank minority ... I suppose I made a mountain out of a molehill but still I see no reason to fix what isn't broke.

 

[Chestermiller]

I learned 'modern physics' in the early '60's when there was a separate symbol for rest mass: m₀. Recently it was pointed out to me in these forums that that is no longer in vogue: there is only one mass, m. If at rest it's m, if moving it's γm. So among other casualties it's no longer E = mc² but γmc², and p = mv is no longer correct either. I find this change entirely pointless but found out to my distress that I was in the rank minority ... I suppose I made a mountain out of a molehill but still I see no reason to fix what isn't broke.

Yes, I see. There used to be rest mass and relativistic mass. Now, for good reason, there's no meaningful quantity called relativistic mass. Rest mass and m are now one and the same.

Chet