# Inelastic collisions in one dimension – problems and solutions

1. A 30-gram bullet moving at 30 m/s collide a 1-kg block at rest. Determine the speed of the block if the bullet and the block lock together as a result of the collision.

__Known :__

Mass of bullet (m_{1}) = 30 gram = 0.03 kg

Mass of block (m_{2}) = 1 kg

Initial speed of bullet (v_{1}) = 30 m/s

initial speed of block (v_{2}) = 0 (block at rest)

__Wanted__ : the speed of bullet and block after collision (v’)

Solution :

m_{1 }v_{1} + m_{2} v_{2} = (m_{1} + m_{2}) v’

(0.03)(30) + (1)(0) = (0.03 + 1) v’

0.9 + 0 = 1.03 v’

0.9 = 1,03 v’

v’ = 0.9 / 1,03

v’ = 0.87 m/s

2. Billiard ball A of mass 2 kg moving with speed v_{A} = 6 m.s^{−1 }collides head-on with ball B of equal mass. If the collision is perfectly inelastic, what are the speeds of the two balls after the collision.

__Known :__

Mass A (m_{A}) = 2 kg

Mass B (m_{B}) = 2 kg

Initial speed of ball A (v_{A}) = -6 m/s

Initial speed of ball B (v_{B}) = 4 m/s

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

__Wanted____:__ the speeds of the two balls after the collision. (v’)

__Solution :__

m_{A} v_{A} + m_{B} v_{B} = (m_{A}’ + m_{B}) v’

(2)(-6) + (2)(4) = (2 + 2) v’

-12 + 8 = 4 v’

-4 = 4 v’

v’ = -4 / 4

v’ = -1 m/s

3. m_{1} = 3 kg and m_{2} = 4 kg approach each other in opposite direction with speed of v_{1} = 10 m/s and v_{2} = 12 m/s. If the collision is perfectly inelastic, what are the speeds of the two balls after the collision.

__Known :__

Mass object 1 (m_{1}) = 3 kg

Mass object 2 (m_{2}) = 4 kg

The speed of object 1 (v_{1}) = -10 m/s

The speed of object 2 (v_{2}) = 12 m/s

__Wanted __: the speed after collision (v’)

__Solution :__

m_{1} v_{1} + m_{2} v_{2} = (m_{1}’ + m_{2}) v’

(3)(-10) + (4)(12) = (3 + 4) v’

-30 + 48 = 7 v’

18 = 7 v’

v’ = 18 / 7

v’ = 2.6 m/s

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