An object of mass 3M, moving in the +x direction at speed vo, breaks into two pi
ID: 1445200 • Letter: A
Question
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 below. theta_1 = 49.0 degree and theta_2 = 34.0 degree, determine the final velocities of the resulting pieces in terms of vo. v_0. Determine the x component of the velosity of the smaller piece v1_x in terms of v_0. (Express your answer to three significant figures.) Determine the y component of the velosity of the smaller piece v1_y in terms of v_0 (Express your answer to three significant figures.) Determine the x component of the velosity of the larger piece V_2x in terms of v_0 (Express your answer to three significant figures.) Determine the y component of the velosity of the larger piece V_2y,n terms of v_0 (Express your answer to three significant figures.)Explanation / Answer
x direction:
(3M) v0 = M v1 cos(B1) + (2M) v2 cos(B2)
cancel M:
3 v0 = v1 cos(B1) + 2 v2 cos(B2)
Solve for v2:
v2 = (2 cos(B2)) (3 v0 - v1 cos(B1))
v2 = (2 cos(34)) (3 v0 - v1 cos(49))
v2 = (1.6581) (3 v0 - (0.65606) v1)
y direction:
v1 sin(B1) = v2 sin(B2)
v1 sin(49) = v2 sin(34)
v1 (0.75471) = v2 (0.55919)
v1 = (0.74094) v2
v1 = (0.74094) ((1.6581) (3 v0 - (0.65606) v1))
v1 = (0.74094) ((1.6581) (3 v0 - (0.65606) v1))
v1 = (3.6857) v0 - (0.8060) v1
==> v1 = (3.6857)/(1.8060) v0
==> v1 = 2.0408 v0
x component:
v1x = v1 cos(B1) = (2.0408 v0) cos(49) = 1.34 v0
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b)
y component:
v1y = v1 sin(B1) = (2.0408 v0) sin(49) = 1.54 v0
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c)
v2 = (1.6581) (3 v0 - (0.65606) v1)
v2 = (1.6581) (3 v0 - (0.65606) (2.0408 v0))
v2 = 2.7543 v0
x direction:
v2x = v2 cos(B2) = (2.7543 v0) cos(34) = 2.28 v0
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d)
v2y = v2 sin(B2) = (2.7543 v0) sin(34) = 1.54 v0
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