A 10.0-g marble slides to the left with a velocity of magnitude 0.400 m/s on the

Question

A 10.0-g marble slides to the left with a velocity of magnitude 0.400 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 0.150 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)

Explanation / Answer

Here ,

let the final velocity of smaller marble is v1

final velocity of larger marble is v2

a)

using conservation of momentum

-10 * 0.40 + 35 * 0.15 = 10*v1 + 35 v2 ----(1)

as the collision is elastic , coeffcient of restitution = 1

v1 - v2 = 0.40 + 0.15 ----(2)

solving 1 and 2

v1 = 0.46 m/s

v2 = -0.0944 m/s

velocity of smaller marble is 0.46 m/s

velocity of larger marble is -0.0944 m/s

b)

change in momentum of small marble = m*(vf - vi)

change in momentum of small marble = 0.010 *(0.46 + 0.40)

change in momentum of small marble = 8.6 *10^-3 kg.m/s

change in momentum of small marble is 8.6 *10^-3 kg.m/s

change in momentum of larger marble = 0.35 (-0.0944 - 0.15)

change in momentum of larger marble = - 8.6 *10^-3 kg.m/s

the change in momentum of larger marble is - 8.6 *10^-3 kg.m/s

c)

change in kientic energy for smaller marble = 0.5* 0.010 *(0.46^2 - 0.40^2 )

change in kientic energy for smaller marble = 2.58 *10^-4 J

the change in kientic energy for smaller marble is 2.58 *10^-4 J

change in kientic energy for larger marble = 0.5 * 0.035 *(0.0944^2 - 0.15^2)

change in kientic energy for larger marble = -2.58 *10^-4 J

change in kientic energy for larger marble is -2.58 *10^-4 J

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