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Relativistic Momentum

  • Thread starter Peter G.
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  • #1
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Hi,

I was given a question in which I had to work out the speed of an object given its momentum and its mass.

Now I had to answer what would be the new speed if the momentum doubled.

So, from what I understand, the rest mass can't change, it is like a constant for a given body. So, in other words, in this case, it is the velocity that is going to change.

In order to find by what factor v must be increased in order to yield an increase in momentum of two I tried to rearrange the following equation:

v/√1-(v2/c2 = 2

Is this what I should do?

Can anyone please maybe give me a hint of what step I should take?
 

Answers and Replies

  • #2
Curious3141
Homework Helper
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Hi,

I was given a question in which I had to work out the speed of an object given its momentum and its mass.

Now I had to answer what would be the new speed if the momentum doubled.

So, from what I understand, the rest mass can't change, it is like a constant for a given body. So, in other words, in this case, it is the velocity that is going to change.

In order to find by what factor v must be increased in order to yield an increase in momentum of two I tried to rearrange the following equation:

v/√1-(v2/c2 = 2

Is this what I should do?

Can anyone please maybe give me a hint of what step I should take?
The formula for the relativistic momentum is [itex]p = {\gamma}mv[/itex], where [itex]\gamma =\frac { 1 }{ \sqrt { 1-\frac { { v }^{ 2 } }{ { c }^{ 2 } } } }[/itex], which gives [itex]p = \frac { mv }{ \sqrt { 1-\frac { { v }^{ 2 } }{ { c }^{ 2 } } } }[/itex]

You're given that [itex]p_{new} = 2p_{old}[/itex].

So what you need to do is to solve this equation:

[tex]\frac { mv }{ \sqrt { 1-\frac { { v }^{ 2 } }{ { c }^{ 2 } } } } = 2\frac { mu }{ \sqrt { 1-\frac { { u }^{ 2 } }{ { c }^{ 2 } } } }[/tex]

where v is the new speed and u is the old speed (which you've already calculated). Solve for v.
 

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