The momentum and direction of the third piece with respect to the 100 g piece is 0.11 kgm/s at 11 degrees.
Conservation of linear momentum
The momentum and direction of the third piece with respect to the 100 g mass is determined by applying the principle of conservation of linear momentum.
Pi = Pf
where;
- Pi is initial momentum
- Pf is final momentum
0 = P₁ + P₂ + P₃
where;
- P₁ is final momentum of the first piece
- P₂ is final momentum of the second piece
- P₃ is final momentum of the third piece
-P₃ = P₁ + P₂
-P₃x = P₁cosθ + P₂Cosθ --(1)
-P₃y = P₁sinθ + P₂sinθ --(2)
-P₃x = (0.1 x 1.2 x cos0) + (0.03 x 0.8 x cos120)
-P₃x = 0.12 - 0.012
-P₃x = 0.108 kgm/s
P₃x = -0.108 kgm/s
-P₃y = (0.1 x 1.2 x sin0) + (0.03 x 0.8 x sin120)
-P₃y = 0.0208 kgm/s
P₃y = -0.0208 kgm/s
Resultant momentum of third piece
[tex]P_3 = \sqrt{P_3x^2 + P_3y^2} \\\\P_3 = \sqrt{(-0.108)^2 + (-0.0208)^2} \\\\P_3 = 0.11 \ kgm/s[/tex]
Direction of third piece
[tex]tan \ \theta = \frac{P_3y}{P_3x} \\\\\theta = tan^{-1} (\frac{P_3y}{P_3x} )\\\\\theta = tan^{-1} (\frac{-0.0208}{-0.108} )\\\\\theta = 11\ ^0[/tex]
with respect to 100 g, direction of third piece is 11⁰
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