A 11 kg body is moving through space in the positive direction of an x axis with

Question

A 11 kg body is moving through space in the positive direction of an x axis with a speed of 140 m/s when, due to an internal explosion, it breaks into three parts. One part, with a mass of 6.4 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 1.5 kg, moves in the negative x direction with a speed of 540 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

Explanation / Answer

here,

M = 11 kg , u = 140 i m/s

for m1 = 6.4 kg is at v1 = 110 j m/s

for m2 = 1.5 kg is at v2 = - 540 i m/s

mass of third part , m3 = M - m1 + m2

m3 = 3.1 kg

let the speed of third part be v3

using conservation of momentum

M * v = m1 * v1 + m2 * v2 + m3 * v3

11 * 140 i = 6.4 * 110 j - 1.5 * 540 i + 3.1 * v3

solving for v3

v3 = 758.1 i m/s - 227.1 j m/s

a)

the x-component of third mass is 758.1 m/s

b)

the y-component of third mass is - 227.1 m/s

c)

|v3| = sqrt(227.1^2 + 758.1^2 )

|v3| = 791.4 m/s

the energy released in the collison , E = 0.5 * M * v^2 - 0.5 * m1 * v1^2 - 0.5 * m2 * v2^2 - 0.5 * m3 * v3^2

E = 0.5 * ( 11 * 140^2 -6.4 * 110^2 - 1.5 * 540^2 - 3.1 * 791.4^2) J

E = 2.24 * 10^6 J

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