An object located at the origin and having mass M explodes into three pieces hav

Question

An object located at the origin and having mass M explodes into three pieces having masses M/4, M/3, and 5M/12. The pieces scatter on a horizontal frictionless xy-plane. The piece with mass M/4 flies away with velocity = 5.0 m/s at 18degree above the x-axis. The piece with mass M/3 has velocity 5.0 m/s directed at an angle of 45degree above the -x-axis. What are the velocity components of the third piece? Describe the motion of the center of mass of the system after the explosion. The center of mass of the system remains at the origin after the explosion.

Explanation / Answer

a) Explosion happens due to internal foreces.

hence centre of mass will be at origin .

or velocity of centre of mass will be zero.

Vcm = ( m1v1 + m2v2 + m3v3) / (m1 + m2 + m3) =

m1v1 + m2v2 + m3v3 = 0

(M/4)(5cos18i + 5sin18j) + (M/3)(-5cos45i + 5sin45 j) + (5M/12)v = 0

v = - 0.025 i - 3.76j m/s

( - 0.025, - 3.76 ) m/s

b) centre of mass will be at origin.

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