The elastic collision between two bodies, A and B, can be considered using the following model. A and B are free to move along a common line without friction. When their distance is greater than `d = 1 m`, the interacting force is zero , when their distance is less d, a constant repulsive force `F = 6 N` is present. The mass of body A is `m_(A) = 1 kg` and it is initially at rest, the mass of body B is `m_(B) = 3 kg` and it is approaching body A head-on with a speed `v_(0) = 2 m//s`. Find the minimum distance between A and B :-

Options

A. `0.25 m`
B. `0.50 m`
C. `0.75 m`
D. `1 m`

Answer

C

Explanation

`F_(ext) = 0` on system containing A & B
`vec(P)` is conserved
At minimum seperation both will move with same velocity
`P_(1) = P_(f)`
`2 xx 3 = 3 xx v`
`v = (3)/(2)`
`W_(all) = DeltaKE`
`W_(F) = DeltaKE`
`-6x = (1)/(2) xx 3 xx 2^(2) - (1)/(2) xx 4 xx ((3)/(2))^(2)`
`x = 0.25`
Minimum separation `= d - x = 1 - 0.25 = 0.75`