A block of mass m = 6.0 kg, moving on a frictionless surface with a speed v_i =

Question

A block of mass m = 6.0 kg, moving on a frictionless surface with a speed v_i = 5.8 m/s makes a perfectly elastic collision with a block of mass M at rest. After the collision, the 6.0 kg block recoils with a speed of V_f = 3.0 m/s Iam asking you to calculate speed of V and mass M V = ____ M = _____ A carousel in initially at rest, the radius from center to edge 3.5 m, at t = 0 it is given a constant angular acceleration alpha = 0.050 rad/s^2, which increase its angular velocity for 8.0 s. At t = 8.0 s, determine the following quantities: the liner velocity of a child located 3.15 m from the center. the angular velocity of the child; the tangential (linear) acceleration of that child: the centripetal acceleration of the edge: and the total linear acceleration of the child (magnitude and direction). v = ________ w = ________ a_t = ________ a_c = ________ a = ________:9=____

Explanation / Answer

momentum conservation

m*vi + M*0 = m*vf + M*V

=> 6*5.8 = 6*3 + M*V

=> M*V = 16.8   ---------------- (1)

energy conservation

0.5*m*vi2 + 0.5*M*0 = 0.5*m*vf2 + 0.5*M*V2

=> 0.5*6*5.82 = 0.5*6*9 + 0.5*MV2

=> MV2 = 147.84     -------------- (2)

from eq (1) and eq(2)

V = 8.8 m/s

M = 1.909 kg

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