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(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]