Question

1. After being struck by a bowling ball, a 1.5 kg bowling pin moving to the right at +3.0 m/s collides with

another 1.5 kg bowling pin at rest. Find the velocity of the second pin when:
a. The first pin moves to the right after the collision at +0.5 m/s.
b. The first pin stops moving when it hits the second pin.

Answer 1

a) Final velocity of second bowling pin is 2.5m/s.

b) Final velocity of second bowling pin is 3 m/s.

Step-by-step explanation:

Let 'm' be the mass of both the bowling pin -

m = 1.5 kg

Initial velocity of first bowling pin -

`v_(1) = 3 m/s`

In any type of collision between two bodies in horizontal plane , momentum is conserved along the line of impact.

a) Since , initial velocity of second bowling pin is 0 m/s -

Initial momentum ,

`p_(1) = mv_(1)`

Final velocity of first bowling pin ,
`v_(2) = 0.5m/s` [Considering initial direction of motion of the first bowling pin to be positive]

Let
`u_(2)` be the final velocity of the second bowling pin.

∴ Final momentum ,

`p_(2) = mv_(2) + mu_(2)`.

Now ,

`p_(1) = p_(2)`

∴
`mv_(1) = mv_(2) + mu_(2)`

∴
`u_(2)` = 3 - 0.5 = 2.5 m/s

∴ Final velocity of second bowling pin is 2.5 m/s.

b) Since , initial velocity of second bowling pin is 0 m/s -

Initial momentum ,

`p_(1) = mv_(1)`

Final velocity of first bowling pin ,
`v_(2) = 0m/s` [given][Considering initial direction of motion of the first bowling pin to be positive]

Let
`u_(2)` be the final velocity of the second bowling pin.

∴ Final momentum ,

`p_(2) = mv_(2) + mu_(2)`.

Now ,

`p_(1) = p_(2)`

∴
`mv_(1) = mv_(2) + mu_(2)`

∴
`u_(2)` = 3 - 0 = 3 m/s

∴ Final velocity of second bowling pin is 3 m/s.