碰撞和保护原理

A collision is exactly what it sounds like- two or more objects colliding with each other.

More technically, a collision involves one mass moving at some velocity towards another mass with some velocity, the two hitting each other, and then continuing off at different velocities. The collision itself occurs because as the masses hit each other, their internal structure of atoms compresses like a series of tiny springs. This force causes a change in momentum, first decelerating the objects, then accelerating them in the opposite direction with what we can understand to be a restoring force caused by the compression of the matter in the objects. The change in momentum that occurs when two objects collide is called impulse.

Collision are most often conceptualized using billiard balls. If one billiard ball sits in the middle of the table, and another one is moving towards the first at some velocity, the two will collide, and move off in different directions at new velocities.

Perfectly elastic collisions, such as the one described above, have the properties of conservation of momentum and conservation of mechanical energy. They bounce off each other with no loss of energy.

Conservation of momentum states that the total momentum of an isolated system (one with no external force) remains constant. The sum of the momentum of each object before the collision and the sum of the momentum of each object after the collision are equal. In equation form (remember, momentum is a vector): $$\overrightarrow{(P_i)_1}+\overrightarrow{(P_i)_2}=\overrightarrow{(P_f)_1}+\overrightarrow{(P_f)_2}$$

The law of conservation of mechanical energy states that the total mechanical energy of the isolated system remains constant during the collision. Before and after the collision, the mechanical energy is solely kinetic energy (although during the collision, there is potential energy as the two objects exert forces on one another, slowing down the object then changing its direction of motion). The law of conservation of mechanical energy can be written as follows:

$$\frac12m_1(v_i)_1^2 +\frac12m_2(v_i)_2^2 = \frac12m_1(v_f)_1^2+\frac12m_2(v_f)_2^2$$

Perfectly inelastic collisions occur when two objects collide with each other and then stick together and move together with the same velocity.

Consider putting some putty and a hockey puck on the floor of an ice rink. If you push the putty so that it moves and collides with the hockey puck, the putty will stick to the hockey puck and they will move together. Inelastic collision.

Inelastic collisions do not conserve mechanical energy. Instead, the mechanical energy is lost from the isolated system and is transformed into thermal energy which is absorbed by the mass or escapes to the environment. However, conservation of momentum still applies, so

$$\overrightarrow{(P_i)_1}+\overrightarrow{(P_i)_2}=\overrightarrow{(P_f)_1}+\overrightarrow{(P_f)_2}$$

When one object collides with another, the energy in the interaction remains constant, so the first object will transfer all of its forward kinetic energy to the second object, and will stop, while the second object continues at the same speed the original object was traveling at.