A 10.0-g marble slides to the left with a velocity of magnitude0.400 m/s on the

Question

A 10.0-g marble slides to the left with a velocity of magnitude0.400 m/s on the frictionless, horizontalsurface of an icy, New York sidewalk and has a head-on, elasticcollision with a larger 35.0-g marblesliding to the right with a velocity of magnitude 0.250 m/s. J (larger marble) J (smaller marble) 6 m/s (larger marble) (c) Calculate the change in kinetic energy (that is, thekinetic energy after the collision minus the kinetic energy beforethe collision) for each marble. 5 m/s (smaller marble) 2 (a) Find the velocity of each marble (magnitude and direction)after the collision. (Since the collision is head-on, all themotion is along a line. Take right as the positive xdirection.) 1

Explanation / Answer

Calculation of change in Kinetic Energy: Small marble: Initial KE = 1/2 x m1 x v^2 m = 10 x 10^-3 Kg = .01 Kg v = 0.4 m/s Initial KE = 0.5 x .01 x .4^2 =0.0008 J Final KE = 0.5 x .01 x .61^2 = .0018605 J Change in KE = .0018605-.0008 = .0010605 J Big marble: Initial KE = 0.5 x .035 x .25^2 = .00109375 Final KE = 0.5 x .035 x .039^2 = .0000266175 Change in KE = .0000266175-.00109375 = -0.0010671325 J ( -vesign indicates it lost Energy)

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