(a) Find the velocity of each marble (magnitude and direction)after the collisio
ID: 1667314 • Letter: #
Question
(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 thepositive 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 thecollision) for each marble.
kg·m/s(smaller marble)
kg·m/s(larger marble)
(c) Calculate the change in kinetic energy (thatis, the kinetic energy after the collision minus the kinetic energybefore the collision) for each marble.
J(smaller marble)
J(larger marble)
Explanation / Answer
masses m = 10 g
M =25 g
Initial speed u = -0.5 m / s
U = 0.2 m / s
From law of conservation of momentum , mu + MU = mv + MV
10 v + 25 V = ( 10 * -0.5 ) + ( 25 * 0.2 )
= 0
10 v = -25 V
v = -2.5 V ---( 1)
For eleastic collision coefficient of restitution e = 1
( V – v ) / ( u–U ) = 1
(V +2.5 V ) / (-0.5-0.2 ) = 1
From this V = -0.2 m / s
v = 0.5 m / s
(a). velocity of the smaller marble v = -0.2 m /s i.e., left direction
Velocity of the larger marble V = 0.5 m / s right
(b). change in momentum of smaller marble = m ( v – u)
= 10 g * 1 m / s
= 0.01 kg * 1 m / s
= 0.01 kg m / s
Change in momentum of the larger marble = M ( V – U)
c). Change in kinetic energy of thesmaller marble = ( 1/ 2)m [ v ^ 2- u^2 ]
Change in kinetic energy of the larger marble = ( 1/ 2) M [ V ^2- U^2]
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