I'm having trouble figuring out what seems to be a simple problem involving a center of mass collision of two hard spheres. Sphere #1 has mass M, and Sphere #2 has a mass of M/2. Sphere 1 is moving at velocity V, while Sphere 2 is stationary. What are their speeds after the collision? My problem is, that to conserve both momentum and kinetic energy, it seems that Sphere 2 must have a resulting speed equal to 4V/3 (and Sphere 1 a speed of V/3), which seems impossible. How could the impact from an object moving at only speed V lead an object initially at rest to recoil at an even greater speed (1.333V)?(adsbygoogle = window.adsbygoogle || []).push({});

For Momentum, this yields:

MV = (M/2)(4V/3) + MV/3 = 4/6 MV + 1/3 MV = 2/3 MV+ 1/3 MV

For Kinetic Energy:

1/2 MV^{2}= 1/2 (M/2) (4V/3)^{2}+ 1/2 M(V/3)^{2}

=M/4 (16/9) V^{2}+ 1/18 MV^{2}= 4/9 MV^{2}+ 1/18 MV^{2}= 9/18 MV^{2}= 1/2 MV^{2}

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# Homework Help: A simple collision problem

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