在這裡，我們將看看如何解決動量問題，在一維和二維使用守恆定律的線性動量。根據這個定律，只要沒有外力作用，粒子系統的總動量就保持不變。因此，解決動量問題需要計算系統在相互作用前後的總動量，並將兩者相等。

如何解決動量問題

一維動量問題

例1

一個質量為0.75 kg、速度為5.8 m s-1的球與另一個質量為0.90 kg、同樣以2.5 m s-1的速度在同一距離內移動的球相撞。碰撞後，較輕的球以3.0 m s-1的速度在同一方向上移動。求大球的速度。

How to Solve Momentum Problems – Example 1

According to the law of c***ervation of momentum,  .

Taking the direction to the right on this digram to be positive, 

Then, 

例2

一個質量為0.32kg的物體以5m s-1的速度與一個質量為0.90kg的靜止物體相撞。碰撞後，兩個粒子粘在一起運動。找出它們的速度。

According to the law of c***ervation of momentum,   .

Then, 

例3

一顆質量為0.015公斤的子彈從一把2公斤重的槍上射出。射擊後，子彈立即以300米s-1的速度移動。假設槍在射擊前是靜止的，求出槍的後坐力速度。

Let the recoil speed of the gun be . We will assume the bullet travels in the “positive” direction. The total momentum before firing the bullet is 0. Then,

.

我們認為子彈的方向是肯定的。所以，負號表示槍在回答中行駛，表示槍在相反方向行駛。

例4：彈道擺

The speed of a bullet from a gun can be found by firing a bullet at a suspended wooden block. The height () that the block rises by can be measured. If the mass of the bullet () and the mass of the wooden block () are known, find an expression to calculate the speed of the bullet.

根據動量守恆，我們得到：

(where is the speed of the bullet+block immediately after collision)

根據能量守恆定律，我們得出：

.

Substituting this expression for in the first equation, we have

二維動量問題

As mentioned in the article on the law of c***ervation of linear momentum, to solve momentum problems in 2 dimensi***, one needs to c***ider momenta in   and   directi***. Momentum will be c***erved along each direction separately.

例5

A ball of mass 0.40 kg, traveling at a speed of  2.40 m s-1 along the  axis collides with another ball of mass 0.22 kg traveling at a speed of  mass 0.18, which is at rest. After the collision, the heavier ball travels with a speed of 1.50 m s-1 with an angle 20o to the  axis, as shown below. Calculate the speed and direction of the other ball.

How to Solve Momentum Problems – Example 5

例6

表明當一個物體與另一個靜止質量相同的物體發生彈性碰撞時，兩個物體之間會以90度的角度移動。

Suppose the initial momentum of the moving body is  . Take the momenta of the two bodies after the collision to be  and  . Since the momentum is c***erved, we can draw up a vector triangle:

How to Solve Momentum Problems – Example 6

since   , we can represent the same vector triangle with vectors  , and . Since  is a common factor to each side of the triangle, we can produce a similar triangle with just the velocities:

How to Solve Momentum Problems – Example 6 Velocity vector Triangle

我們知道碰撞是有彈性的。那麼，

.

排除共同因素，我們得到：

According to Pythagors’ theorem, then,  . Since , so then  . The angle between the two bodies’ velocities is indeed 90o. This type of collision is common when playing billiards.