A 27.5-g object moving to the right at 19.5 cm/s overtakes and collides elastica

Question

A 27.5-g object moving to the right at 19.5 cm/s overtakes and collides elastically with a 10.5g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision. (Take the positive direction to be to the right. Indicate the direction with the sigh of your answere.) 27.5-g object Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. cm/s. 10.5-g Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. cm/s.

Explanation / Answer

Apply conservation of linear momentum along right,

27.5*(19.5)-10.5(15)=27.5(v1)+10.5(v2)

27.5(v1)+10.5(v2) =378.75---(1)

Apply conservation of mechanical energy

27.5(19.5)2/2 + 10.5(15)2/2=27.5(v1)2/2 + 10.5(v2)2/2

Solve the equations (1) and (2)

27.5(v1)2/2 + 10.5(v2)2=12819.375---(2)

v1=1.677cms-1

v2=31.677 cms-1

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