Question

V = ? 2M An object of mass 3M, moving in the +x direction at speed vo, breaks into two pieces of mass M and 2M as shown in the figure. If 01 = 67.0° and 02 = 24.0°, determine the final velocities Vj and v2 of the resulting pieces in terms of vo. 3M 0, M = ? U1 = 1.14 VO Incorrect U2 = 1.4 VO

Answer 1

According to conservation of momentum along x axis, 3Mv = My, cosą +2 Mv, cos, 3v, = y; cos 67° + 2v, cos 24° 3v0 = 0.39v, +1.827v, ---(1) The momentum along y axis is, 0= Mv, sin , +2 Mv, sin , 2v, sin 02 vi sin 2v, sin 24° sin 67° = 0.88v2 Solve equation (1) and (2) 3v = 0.39v, +1.827v2 3V0 = 0.39(0.88v2)+1.827v2 3v0 = 0.34465v, +1.827v2 3v= 2.17v, 3 2.17 =1.38v vi = 0.88v2 = 0.88(1.38v.) =1.22v. 12 Vo

The strain is, strain= dl 1 0.05 II u = 0.01 The elastic limit is, W E = 1p2 8000 4x108 = (3.14)r2 r = 0.0025 m =0.25 cm