Совршено еластични судири во една димензија – проблеми и решенија

1. A 200-gram ball, A, moving at a speed of 10 m/s strikes a 200-gram ball, B, at rest. What is the speed of ball A and ball B after the судир?

Познато:

Маса of ball A (m_A) = 200 грама = 0.2 кг

Маса на топката Б (м_B) = 200 грама = 0.2 кг

Speed of ball A before collision (v_A) = 10 м/с

Speed of ball B before collision (v_B) = 0

Сакаше: speed of ball A (v_A’) and speed of ball B (v_B’) after a collision

Решение:

v_A' = v_B = 0

v_B' = v_A = 10m/s

2. Two equal-mass objects approach each other, collide and then bounce off. The speed of mass A before the collision is 8 m/s and speed of mass B before the collision is 12 m/s. What is the magnitude and direction of the Брзина на of mass A and mass B after the collision!

Познато:

Mass A (m_A) = м

Маса Б (м_B) = м

Speed of mass A before collision (v_A) = -8 м/с

Speed of mass B before collision (v_B) = 12 м/с

The plus and minus sign indicates that the objects move in opposite direction.

Сакаше: the magnitude and direction of the velocity of mass A (v_A’) and mass B (v_B’) after a collision

Решение:

In a perfectly elastic collision, if the objects of equal mass then the speed of A after the collision (v_A’) = the speed of B before collision (v_B) and the speed of B after the collision (v_B’) = the speed of A before collision (v_A).

If before collision, A moving rightward and B moving leftward, then, after collision, A moving leftward and B moving rightward.

The objects have equal mass and the collision is perfectly elastic so the both objects exchanged speed.

v_A' = -v_B = -12 m/s

v_B' = v_A = 8m/s

The plus and minus sign indicates that the objects move in opposite direction.

3. A 2-kg object, A, moving at a speed of 10 m/s strikes a 4-kg ball, B, moving at a speed of 20 m/s. If the collision is perfectly elastic, what is the speed of object A and object B after the collision?

Познато:

Mass A (m_A) = 2 кг

Маса Б (м_B) = 4 кг

Speed of object A before collision (v_A) = 10 м/с

Speed of object B before collision (v_B) = 20 м/с

Wanted : the speed of object A (v_A’) and the speed of object B (v_B’) after collision

Решение :

In совршено еластичен судир, if the objects have equal mass and approach each other, the speed of the object after collision calculated using this formula :

Speed of object A after collision :

4. A 100-gram moving at 20 m/s strikes a wall perfectly elastic collision. What is the magnitude and direction of object’s velocity after collision.

Познато:

Mass (m_A) = 100 грама = 0.1 кг

Mass of wall (m_B) = infinity

The speed of mass before collision (v_A) = 20 м/с

The speed of mass after collision (v_B) = 0

Wanted : the magnitude and direction of velocity after collision

Решение:

If v_B = 0, м_A very small and m₂ very big then v_A' = -v_A и v₂’ = 0.

Знаците плус и минус означуваат дека предметите се движат во спротивна насока.

5. Two balls, A with a mass of 2 кг and ball B with a mass of 5-kg, before and after the collision are shown in the figure below. If the collision is perfectly elastic, what is the speed of ball A before the collision?

Познато:

Mass of ball A (m_A) = 2 кг

Mass of ball Б (м_B) = 5 кг

Speed of ball B before collision (v_B) = 2 м/с

Speed of ball A after collision (v_A') = 5 м/с

Speed of ball B after collision (v_B') = 4 м/с

Both balls are move to the right so their speed signed positive.

Барани: Speed of ball A before collision (v_A)

Решение:

m_A v_A + м_B v_B = м_A v_A' + м_B v_B"

2(v_A) + (5)(2) = (2)(5) + (5)(4)

2(v_A) + 10 = 10 + 20

2(v_A) + 10 = 30

2(v_A) = 30 - 10

2(v_A) = 20

v_A = 20 / 2

v_A = 10m/s

6. Object A and B travel along horizontal plane, as shown in figure below. If the collision is perfectly elastic and the speed of object B after collision is 15 m / s¹, what is the speed of object A after collision.

Познато:

Mass of object A (m_A) = 5 кг

Mass of object Б (м_B) = 2 кг

Speed of object A before collision (v_A) = 12 м/с

Speed of object B before collision (v_B) = 10 м/с

Speed of object B after collision (v_B') = 15 м/с

Both objects, before and after collision, move to right so their velocity signed positive.

Барани: Speed of object A after collision (v_A')

Решение:

m_A v_A + м_B v_B = м_A v_A' + м_B v_B"

(5)(12) + (2)(10) = (5)v_A' + (2)(15)

60 + 20 = (5)v_A'+ 30

80 = (5)v_A'+ 30

80 – 30 = (5)v_A"

50 = (5)v_A"

v_A' = 50/5

v_A' = 10 м/с

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