[Francis Tapon]

Francis Tapon  asked the Naked Scientists:

Loved your show on the LHC!

When two cars going 50 kph run into each other, it's said that it's the
same as a single car running into a wall at 100 kph.

If two particles are going at nearly the speed of light and they smash into
each other, then can one say that it's like a single proton running into a
wall at two times the speed of light (i.e., 600,000 kps)?

Francis Tapon

What do you think?

[lightarrow]

Francis Tapon  asked the Naked Scientists:

Loved your show on the LHC!

When two cars going 50 kph run into each other, it's said that it's the
same as a single car running into a wall at 100 kph.

If two particles are going at nearly the speed of light and they smash into
each other, then can one say that it's like a single proton running into a
wall at two times the speed of light (i.e., 600,000 kps)?

Francis Tapon

What do you think?

The correct formula for adding two velocities v₁ and v₂ is this:

V = (v₁ + v₂)/(1 + v₁*v₂/c²)

when v₁ and v₂ are little with respect to c, v₁*v₂/c² becomes little with respect to 1, so you can neglect the term v₁*v₂/c² and so you have:

V ≈ v₁ + v₂

Use the correct formula in these cases:

1. v₁ = v₂ = 100 m/s
2. v₁ = 100 m/s; v₂ = c
3. v₁ = v₂ = c

then write the answers here.

[chrisdsn]

No.

> "When two cars going 50 kph run into each
> other, it's said that it's the
> same as a single car running into
> a wall at 100 kph."

It isn't; it's just *almost* the same. So, close that
at that speed you couldn't tell. However, it will be
very slightly less than 100 kph. At 500kph + 500kph
it would be even more less than 1000kph, to the point
that as you get faster and faster, you will never
get a combined speed faster than the speed of
light. From this basic fact you can work out a lot
of the crazy consequences of special relativity: to
keep things consistent things that move faster get
shorter and time moves slower for them, for example.

Since everything we deal with in our lives moves
way slower than the speed of light, all this seems
very counterintuitive. However, it is true. For example:
the gps satellites orbit fast enough that you need to
take into account for the fact that time moves slower
for them, for them to give you an accurate position.