Серпімсіз соқтығысулар

Серпімсіз соқтығысулар

The conservation of kinetic energy law is not applicable in inelastic collisions. The conservation of momentum law is applicable in inelastic collisions if only no external force acts on the two colliding objects. In an inelastic collision, two objects stick together or are attached to each other after the collision.

1-мысал сұрақ.

Two objects are of the same mass, namely 1 kg. Object 1 moves on a flat plane at a speed of 10 m/s and collides with object two which is at rest. After the collision, the two objects stick together. What is the speed of the two objects after the collision?

Белгілі:

m₁ = 1 кг, м₂ = 1 кг, v₁ = 10 м/с, v₂ = 0

Қажет : v’

Шешімі:

m₁ v₁ + м₂ v₂ = (м₁ + м₂) v'

(1 kg)(10 m/s) + 0 = (1 kg + 1 kg) v’

10 kg m/s = (2 kg) v’

v’ = 10 kg m/s : 2 kg = 5 m/s

2-мысал сұрақ.

Three blocks move at 3 m.s^-1 collide another block at rest.

The collision is inelastic. Тәртібі блоктың velocity after the collision, from the largest to the smallest is…

Шешімі:

Figure 1 :

Final momentum = initial momentum

m₁ v₁ + м₂ v₂ = (м₁ + м₂) ішінде

(4m)(3) + (m)(0) = (4m + m) v

12m + 0 = (5m) v

12m = 5m v

v = 12m / 5m = 12/5 = 2.4 m/s

Figure 2 :

Final momentum = Initial momentum

m₁ v₁ + м₂ v₂ = (м₁ + м₂) ішінде

(m)(3) + (3m)(0) = (m + 3m) v

3m + 0 = (4m) v

3m = 4m v

v = 3m / 4m = 3/4 = 0.75 m/s

Figure 3 :

m₁ v₁ + м₂ v₂ = (м₁ + м₂) ішінде

(m)(3) + (m)(0) = (m + m) v

3m + 0 = (2m) v

3m = 2m v

v = 3m / 2m = 3/2 = 1.5 m/s

3-мысал сұрақ.

Two balls with mass of m₁ = 2 кг және м₂ = 1 kg are move in opposite direction with speed of v₁ = 2 мс^-1 және v₂ = 4 мс^-1 as shown in figure below. If a collision is inelastic, what is the speed of both balls after the collision?

Белгілі:

Шардың массасы 1 (м₁) = 2 кг

Шардың массасы 2 (м₂) = 1 кг

1-ші шардың соқтығысқанға дейінгі жылдамдығы (v₁) = 2 м/с

2-ші шардың соқтығысқанға дейінгі жылдамдығы (v₂) = -4 м/с

Plus and minus sign indicates that both balls move in opposite direction.

Қажет : Velocity of balls after collision (v’)

Шешімі:

m₁ v₁ + м₂ v₂ = (м₁ + м₂) v'

(2)(2) + (1)(-4) = (2 + 1) v'

4 – 4 = (3) v'

0 = (3) v'

v' = 0

4-мысал сұрақ.

Two objects, A and B, with a mass of each object, is 1.5-kg approach each other with speed of v_A = 4 мс^-1 және v_B = 5 мс^-1. If the collision is inelastic, what is the speed of both objects after the collision?

Белгілі:

А нысанының массасы (м)_A) = 1.5 кг

B нысанының массасы (м)_B) = 1.5 кг

Соқтығысуға дейінгі А нысанының жылдамдығы (v_A) = 4 m/s (plus sign, to rightward)

Соқтығысуға дейінгі В нысанының жылдамдығы (v_B) = -5 m/s (minus sign, to leftward)

Қажетті: The speed of both objects after collision

Шешімі:

Conservation of linear momentum :

m_A v_A + м_B v_B = (м_A + м_B) v'

(1.5)(4) + (1.5)(-5) = (1.5 +1.5) v’

6 – 7.5 = (3) v'

-1.5 = (3) v’

v' = -1.5 / 3

v' = -0.5 м/с

Minus sign indicates that both objects move to leftward.

20 conceptual questions and answers about inelastic collisions:

1. Сұрақ: What defines an inelastic collision? Жауап: In an inelastic collision, kinetic energy is not conserved, though momentum is. Some of the initial kinetic energy is transformed into other forms of energy.

2. Сұрақ: How does a perfectly inelastic collision differ from a partially inelastic collision? Жауап: In a perfectly inelastic collision, the objects stick together after the collision. In a partially inelastic collision, the objects separate, but there’s still a loss of kinetic energy.

3. Сұрақ: What remains conserved in all types of collisions, including inelastic ones? Жауап: Momentum is always conserved in all collisions, regardless of their elasticity.

4. Сұрақ: Why isn’t kinetic energy conserved in inelastic collisions? Жауап: Some of the kinetic energy gets converted into other forms of energy, such as potential energy, heat, or sound.

5. Сұрақ: How can one identify an inelastic collision just by observing the velocities before and after the collision? Жауап: The total kinetic energy before the collision will be greater than the total kinetic energy after the collision.

6. Сұрақ: Can inelastic collisions occur in one dimension only? Жауап: No, inelastic collisions can occur in one, two, or three dimensions. The principles remain the same, only the vector calculations become more complex.

7. Сұрақ: In the context of particle physics, what’s a common outcome of inelastic collisions? Жауап: In particle physics, inelastic collisions often result in the transformation of the colliding particles into different particles.

8. Сұрақ: How can you determine the amount of energy lost in an inelastic collision? Жауап: By calculating the difference between the total initial kinetic energy and the total final kinetic energy.

9. Сұрақ: Why don’t inelastic collisions violate the law of conservation of energy? Жауап: Energy is still conserved; it’s just converted from one form (kinetic) to others (like heat or sound) rather than remaining purely as kinetic energy.

10. Сұрақ: Are most real-world collisions inelastic? Жауап: Yes, most real-world collisions are inelastic because there’s typically some conversion of kinetic energy to other forms.

11. Сұрақ: In an inelastic collision, if two objects stick together, what can be said about their combined velocity? Жауап: Their combined velocity is determined by the conservation of momentum. The two objects will move with a common velocity after the collision.

12. Сұрақ: How does the coefficient of restitution relate to inelastic collisions? Жауап: The coefficient of restitution, denoted as $e$, measures the “bounciness” of a collision. For perfectly inelastic collisions, $e=0$.

13. Сұрақ: Why might an inelastic collision produce sound? Жауап: The collision can cause vibrations in the colliding objects, which may produce sound waves in the surrounding medium.

14. Сұрақ: Can gravitational potential energy be a factor in inelastic collisions? Жауап: Yes, especially if the collision results in a change in height or position of the objects, converting kinetic energy into gravitational potential energy.

15. Сұрақ: Why do rubber balls not undergo perfectly inelastic collisions, despite being “bouncy”? Жауап: Rubber balls undergo elastic or near-elastic collisions because they tend to retain much of their kinetic energy and bounce back. They don’t stick together, which would be characteristic of a perfectly inelastic collision.

16. Сұрақ: Can two soft clay balls demonstrate a perfectly inelastic collision? Жауап: Yes, because when two soft clay balls collide, they tend to stick together and not bounce back, which is characteristic of a perfectly inelastic collision.

17. Сұрақ: Is it possible for an inelastic collision to occur without any sound or heat generation? Жауап: It’s rare, but possible. The energy could be dissipated in other subtle ways or stored as internal potential energy.

18. Сұрақ: Can inelastic collisions be reversed? Жауап: Generally, inelastic collisions are not reversible because the conversion of kinetic energy to other forms makes it difficult to revert to the initial state.

19. Сұрақ: How does air resistance relate to inelastic collisions? Жауап: Air resistance can make collisions more inelastic by dissipating some of the kinetic energy as heat.

20. Сұрақ: Do inelastic collisions have implications in safety designs, such as car crumple zones? Жауап: Yes, crumple zones in cars are designed to undergo inelastic collisions, absorbing kinetic energy and reducing the forces acting on occupants.

Inelastic collisions play a vital role in understanding the conservation laws of physics and are integral in numerous practical applications and safety designs.