Impulse and Momentum

一、英文名詞中譯：

Impulse 衝量

Linear momentum 線動量

Impulse–momentum theorem 衝量–動量原理

Isolated system 獨立系統

Conservation of linear momentum 線動量守恆原理

Collision 碰撞

One–dimensional elastic collision 一維彈性碰撞

Elastic head–on collision 彈性正撞

Completely inelastic collision  完全非彈性碰撞

二、重要觀念整理：

  1. 質量m的物體受到合力F（定力）作用，合力在某時段內對物體所施的衝量

          I = F △ t

  2. 變力所施的衝量等於 F ‐ t 圖中函數曲線與 t 軸所圍成的面積。

  3. 合力在某時段內對物體所施的衝量，等於物體在此時段前後的動量變化。

          I = F △ t = m v_f – m v_i

  4. 獨立系統（外力和為零的質點系統）的總動量守恆

          m₁ v_1i + m₂ v_2i = m₁ v_1f + m₂ v_2f

  5. 正向彈性碰撞： a. 動量守恆並且動能守恆

                   b. 碰撞前的相對速度與碰撞後的相對速度大小箱等方向相反

                      （恢復係數e等於1）

                        m₁ v_1i + m₂ v_2i = m₁ v_1f + m₂ v_2f

                        v_1i - v_2i = -（v_1f - v_2f）

6. 完全非彈性碰撞：   m₁ v_1i + m₂ v_2i = （m₁ + m₂）v_f

三、練習題：

1.      A car accelerates from 0 m/s to 8.3 m/s in 6.0 s.  What was the average force in N on a 50 kg passenger in the car?

2.   A 1250 kg car moving with a speed of 28.1 m/s collides head on with a 9260 kg truck moving with a speed of 22.3 m/s in the opposite direction.  If they stick together, with what speed in m/s will they be moving after the collision?

3.    A 12 g bullet is fired into a 3.0 kg ballistic pendulum initially at rest and becomes embedded in it.  The pendulum subsequently rises a vertical distance of 12 cm.  What was the initial speed of the bullet in km/s?

4.   A 2.4 kg ball falling vertically hits the floor with a speed of 2.5 m/s and rebounds with a speed of 1.5 m/s.  What is the magnitude in N×s of the impulse exerted on the floor by the ball?

5.  A 10.0‐g object moving to the right at 20.0 cm/s makes an elastic head ‐ on collision with a 15.0 ‐ g object moving in the opposite direction at 30.0 cm/s. Find the velocity of each object after the collision.