a 2.0 kg mass is sliding on a horizontal, frictionless trackwith speed of 3.0 m/

Question

a 2.0 kg mass is sliding on a horizontal, frictionless trackwith speed of 3.0 m/s when it hits and sticks to a 1.3 kg massinitally at rest on the track. The 1.3 kg mass is connectedto one end of a masseless spring which has a spring constant of 100N/m. Other end of spring is fixed Determine the linear momentum of the .2 kg mass immediatelybefore impact Kinetic energy of .2 kg mass immediately before impact Determine the linear momentum for combined masses immediatelyafter impact The Kinetic energy of combined masses immediately afterimpact How far does spring compress after the collision? a 2.0 kg mass is sliding on a horizontal, frictionless trackwith speed of 3.0 m/s when it hits and sticks to a 1.3 kg massinitally at rest on the track. The 1.3 kg mass is connectedto one end of a masseless spring which has a spring constant of 100N/m. Other end of spring is fixed Determine the linear momentum of the .2 kg mass immediatelybefore impact Kinetic energy of .2 kg mass immediately before impact Determine the linear momentum for combined masses immediatelyafter impact The Kinetic energy of combined masses immediately afterimpact How far does spring compress after the collision?

Explanation / Answer

mass m = 2 kg Initial speed u = 3 m / s mass M = 1.3 kg initial speed U = 0 spring constant k = 100 N / m (a). the linear momentum of the 2 kg mass immediately beforeimpact = m u = 6 kg m / s (b). kinitic energy K = ( 1/ 2) m u ^ 2                               = 9 J (c). from law of conservation of momentum , mu + MU = ( m +M )v                                                                           6 + 0 = 3.3 v from this speed ater colliison v = 1.8181 m / s linear momentum = ( m + M) v                           = 6 (d). kinetic energy = ( 1/ 2) ( m + M ) v ^ 2                           K = 5.4545 J (e) . we know K = ( 1/ 2) k x ^ 2 from this compression x = [ 2K / k ]                                       = 0.33 m

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