So, what energy or what momentum should the incoming projectile have?

入射粒子的能量和动量应该取什么值呢
Let's see. So, here are four protons,

现在有四个质子
and in the cheapest collision

在最省能量的碰撞中
what will they be doing in the end?

它们最后处于什么状态
Sitting in a clump.

团聚在一块儿
And what will be the energy of that clump?

那么这种团聚的能量是多少
Do you agree that's 4m?

是 4m 吗
Okay, this guy brings energy m into the collision,

这个粒子作为静态靶
being the static target.

本身有能量 m
So, you would conclude the energy of this should be 3m.

这样推出它的能量应当是 3m
By that we'll mean

也就是说
m·c^2 divided by 1-v^2/c^2

m·c^2 除以 1-v^2/c^2