Question

A cart with mass 330 g moving on a frictionless linear air track at an initial speed of 2.1 m/s undergoes an elastic collision with an initially stationary cart of unknown mass. After the collision, the first cart continues in its original direction at 1.05 m/s. 1.) What is the mass of the second cart? 2.)What is its (second cart) speed after impact? 3.)What is the speed of the two-cart center of mass?

Answer 1

masses m = 330 g

            M = ?

Initial speed of 1 st cart u = 2.1 m / s

initial speed of 2 nd cart U = 0

final speed of 1 st cart v = 1.05 m / s

for eleastic collision ,coeffcient of restitution e= 1

       e = ( V - v ) / ( u - U )

      1 = ( V - 1.05) / ( 2.1-0)

V-1.05 = 2.1

      V = 3.15 m / s

(a). from law of conservation of momentum ,

mu + MU = mv + MV

m( u -v) = M ( V - U )

               = MV

from this mass of 2nd cart M = [ m(u-v) ] / V

                                             = 110 g

(b). speed of cart2 after impact V = 3.15 m / s

(c). speed of the two cart center of mass V ' = [mv + MV ] / ( m + M )

                V ' = 1.575 m / s