Solve Equal & Opposite Velocities for Two Particles in Relative Frames

[cscott]

Homework Statement

In frame S , particle 1 is at rest and particle 2 is moving to the right with velocity v.
Consider frame S ′ , moving relative to S , with speed u. Find the value of u such that
the two particles appear in S ′ to be approaching each other with equal but opposite
velocities.

I don't see here how you can get the particles to approach each other.

Homework Statement

Calculate the range of speeds for a particle of mass m in which the classical relation
for kinetic energy is within 1% of the correct relativistic value.

For this can I use K/T = 0.01 and solve for the velocity of the mass, where K is Newtonian KE and T is relativistic KE?

 

[badphysicist]

What equations do you think you should use on the first question? You're kind of close on the second part, but you want the difference in K and T to be 0.01 of the relativisitic..

 

[cscott]

The velocity transforms could be used for the first question. Can I just set the S' frame velocity to -1/2v or -v (not sure here) then solve for the frame speed u given that the S frame speed is v?

Thanks, I'll work on the second one.

 

[Dick]

Be careful! If v=c then there is no such frame. So the answer clearly isn't c/2. You have to use the relativistic formula for velocity addition.