The spring is compressed after the bullet enters the hole. At the same time, the object M accelerates and the bullet M decelerates. At a certain moment, the speed of T and Mm is the same, and the spring is compressed by L. Then, in the process of spring recovery, M continues to accelerate and M continues to decelerate. Finally, the Mm moves at its own speed, and the spring returns to its original state. The energy of all this comes from the initial kinetic energy of the bullet.

Let the muzzle velocity of the bullet be u 1,

At the same speed, the speed of Mm is u2,

Finally, the speed of the bullet is u3, and the speed of the object is U.

(The coefficient 1/2 is omitted from the following formula)

Mu12 = (m+m) u2 2+Ex (elastic potential energy ex is analyzed separately).

=mu3^2+MU^2

The above is an analysis from the perspective of energy. Let's analyze it from the perspective of momentum.

MU 1 = mu3+μ

Momentum theorem is only suitable for studying the results before and after collision. Due to the existence of elastic potential energy, the moment in the collision process is not conserved.

Personally, I think that the conservation of energy is the essence, and the conservation of momentum is a phenomenon, which can even be said to be a calculation tool.

Finally, let's talk about elastic potential energy Ex.

I really haven't analyzed it carefully in the past. First of all, this is a process of changing force to do work. The accumulation of potential energy and the acceleration of two colliding objects are not constants. Strictly speaking, it should be

f=kl

One bullet =kl/m

An object =kl/M

L=l bullet -l object

Then the analytical formulas of bullet deceleration and object acceleration are obtained, and then the compression length of spring and the motion speed of two objects colliding at the same speed are solved.

I omitted this section when I was reading. Because it requires more advanced mathematical knowledge.

For reference only.

The latter problem is to calculate the position of an object in the X direction and the Y direction at a certain moment. It is also a problem of changing force to do work. At a certain moment, the X direction reaches 2 and the Y direction reaches 6. I seem to be at the end of my rope.