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A 10.0-g marble slides to the left with a velocity of magnitude 0.300 m/s on the

ID: 1261569 • Letter: A

Question

A 10.0-g marble slides to the left with a velocity of magnitude 0.300 m/s on the frictionless, horizontal surface of an icy, New York sidewalk and has a head-on, elastic collision with a larger 35.0-g marble sliding to the right with a velocity of magnitude 0.200 m/s.

(a) Find the velocity of each marble (magnitude and direction) after the collision. (Since the collision is head-on, all the motion is along a line. Take right as the positive x direction.)
m/s (smaller marble)
m/s (larger marble)

(b) Calculate the change in momentum (that is, the momentum after the collision minus the momentum before the collision) for each marble.
kg?m/s (smaller marble)
kg?m/s (larger marble)

(c) Calculate the change in kinetic energy (that is, the kinetic energy after the collision minus the kinetic energy before the collision) for each marble.
J (smaller marble)
J (larger marble)

A 10.0-g marble slides to the left with a velocity of magnitude 0.300 m/s on the frictionless, horizontal surface of an icy, New York sidewalk and has a head-on, elastic collision with a larger 35.0-g marble sliding to the right with a velocity of magnitude 0.200 m/s. (a) Find the velocity of each marble (magnitude and direction) after the collision. (Since the collision is head-on, all the motion is along a line. Take right as the positive x direction.) m/s (smaller marble) m/s (larger marble) (b) Calculate the change in momentum (that is, the momentum after the collision minus the momentum before the collision) for each marble. kgAm/s (smaller marble) kgAm/s (larger marble) (c) Calculate the change in kinetic energy (that is, the kinetic energy after the collision minus the kinetic energy before the collision) for each marble. J (smaller marble) J (larger marble)

Explanation / Answer

Momentum conservation

35*0.2 - 10*0.3 = 10 Vb - 35 Va

Elastic collision

Vb + Va = 0.5

Vb = 21.5/45 = 0.4777 m/sec (Smaller marble) (ans)

Va = 0.0222 m/sec (Larger marble) (ans)

b) Change in momentum = 0.035 ( 0.2+ 0.0222) = 0.00777 Kg m/sec (ans) (Larger marble)

Chaneg in momntum of smaller marble = 0.00777 Kg m/sec (ans) (smaller marble)

c) Change in kinetic energy = 1/2*35*(0.2^2 - 0.0222^2) = 0.00069 J (ans)

Change in kinetic energy of smaller marble = 0.00069 J (ans)