Question

A 23 kg body is moving through space in the positive direction of an x axis with a speed of 220 m/s when, due to an internal explosion, it breaks into three parts. ?

Answer 1

Question

A 23 kg body is moving through space in the positive direction of an x axis with a speed of 220 m/s when, due to an internal explosion, it breaks into three parts. One part, with a mass of 13 kg, moves away from the point of explosion with a speed of 110 m/s in the positive y direction. A second part, with a mass of 2.8 kg, moves in the negative x direction with a speed of 310 m/s. What are the (a) x-component and (b) y-component of the velocity of the third part? (c) How much energy is released in the explosion? Ignore effects due to the gravitational force.

Answer

Mass of unbroken body `= 23kg`
Its velocity along +ve x-axis `v=220m/s`

Mass of 1st broken part `m_1= 13kg`

Its velocity along +ve y-axis `v_1=110m/s`

Mass of 2nd broken part `m_2= 2.8kg`

Its velocity along -ve x-axis
`v_2=310m/s`

Mass of 3rd broken part `m_3= (23-13-2.8)kg=7.2kg`

Let its velocity along x-axis be `v_x` and along y-axis be `v_y`

Applying conservation of momentum along x direction

`m_1xx0+m_2xx(-310)+m_3xxv_x=23xx220`

`=>-2.8xx310+7.2xxv_x=23xx220`

(a)`=>v_x=(23xx220+2.8xx310)/7.2=823.3m/s`

Applying conservation of momentum along y direction

`m_1xx110+m_2xx0+m_3xxv_y=0`

`=>13xx110+2.8xx0+7.2xxv_y=0`

(b)`=>v_y=(-13*110)/7.2=-198.6m/s`

Energy released or Change in KE

`=(1/2(13*110^2+2.8*310^2+7.2*823.3^2+7.2*198.6^2) -1/2*23*220^2)J`