פערפעקט עלאַסטישע קאָליזיעס אין איין דימענסיע – פּראָבלעמען און לייזונגען

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 צונויפשטויס?

באַקאַנט:

מאַסע of ball A (m_A) = 200 גראַם = 0.2 ק״ג

מאַסע פון ​​באַל ב (מ_B) = 200 גראַם = 0.2 ק״ג

Speed of ball A before collision (v_A) = 10 מעטער/סעקונדע

Speed of ball B before collision (v_B) = 0

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

לייזונג:

v_A' = ווי_B = קסנומקס

v_B' = ווי_A = 10 עם / 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 גיכקייַט of mass A and mass B after the collision!

באַקאַנט:

מאַסע א (מ_A) = מ

מאַסע ב (מ_B) = מ

Speed of mass A before collision (v_A) = -8 מעטער/סעקונדע

Speed of mass B before collision (v_B) = 12 מעטער/סעקונדע

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

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

לייזונג:

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 מעטער/סעקונדע

v_B' = ווי_A = 8 עם / 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?

באַקאַנט:

מאַסע א (מ_A) = 2 ק"ג

מאַסע ב (מ_B) = 4 ק"ג

גיכקייט פון אביעקט א פארן צוזאמענשטויס (v_A) = 10 מעטער/סעקונדע

גיכקייט פון אביעקט ב פארן צוזאמענשטויס (v_B) = 20 מעטער/סעקונדע

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

באַשייד :

In בישליימעס גומע צונויפשטויס, 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.

באַקאַנט:

Mass (m_A) = 100 גראַם = 0.1 ק״ג

Mass of wall (m_B) = infinity

The speed of mass before collision (v_A) = 20 מעטער/סעקונדע

The speed of mass after collision (v_B) = 0

געוואלט : the magnitude and direction of velocity after collision

לייזונג:

אויב וו_B = 0, מעטער_A very small and m₂ very big then v_A' = -v_A און וו₂’ = 0.

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

5. Two balls, A with a mass of קסנומקס-קג 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?

באַקאַנט:

Mass of ball א (מ_A) = 2 ק"ג

Mass of ball ב (מ_B) = 5 ק"ג

Speed of ball B before collision (v_B) = 2 מעטער/סעקונדע

Speed of ball A after collision (v_A') = 5 מעטער/סעקונדע

Speed of ball B after collision (v_B') = 4 מעטער/סעקונדע

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

געוואָלט: Speed of ball A before collision (v_A)

לייזונג:

m_A v_A + עם_B v_B = עם_A v_A' + מ_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 = 10 עם / 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 ם / s¹, what is the speed of object A after collision.

באַקאַנט:

Mass of object א (מ_A) = 5 ק"ג

Mass of object ב (מ_B) = 2 ק"ג

Speed of object A before collision (v_A) = 12 מעטער/סעקונדע

Speed of object B before collision (v_B) = 10 מעטער/סעקונדע

Speed of object B after collision (v_B') = 15 מעטער/סעקונדע

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

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

לייזונג:

m_A v_A + עם_B v_B = עם_A v_A' + מ_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 מעטער/סעקונדע

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1. לינעאַר מאָמענטום פּראָבלעמען און לייזונגען
2. מאָמענטום און אימפּולס פּראָבלעמען און לייזונגען
3. גאנץ עלאַסטישע קאָליזיעס אין איין דימענסיע פּראָבלעמען און לייזונגען
4. גאנץ נישט-עלאַסטישע קאָליזיעס אין איין-דימענסיע פּראָבלעמען און לייזונגען
5. נישט-עלאַסטישע קאָליזיעס אין איין-דימענסיע פּראָבלעמען און לייזונגען