Respuesta :
The velocity v₁ of object 1 followed by the velocity v₂ of object 2 as coordinates gives; (v₁, v₂) = [(¹/₃v, ⁴/₃v)]
How to solve inelastic collision?
Momentum of object 1 before collision = (2m)v = 2mv
Momentum of object 2 before collision = (m)(0) = 0
Momentum of object 1 after collision = (2m)(v₁) = 2mv₁
Momentum of object 2 after collision = (m)(v₂) = mv₂
Thus, we now have;
2mv = 2mv₁ + mv₂
2v = 2v₁ + v₂
v₂ = 2v - 2v₁ -----(eq 1)
Kinetic energy of object 1 before collision = (¹/₂)(2m)(v²) = mv²
Kinetic energy of object 2 before collision = (¹/₂)(m)(0²) = 0
Kinetic energy of object 1 after collision = (¹/₂)(2m)(v₁²) = mv₁²
Kinetic energy of object 2 after collision = (¹/₂)(m)(v₁²) = (¹/₂mv₂²)
Thus, we now have;
mv² = mv₁² + (¹/₂mv₂²)
v² = v₁² + (¹/₂v₂²)
2v² = 2v₁² + v₂² ---- (eq 2)
Substitute 2v - 2v₁ for v₂ in eq 2 to get;
2v² = 2v₁² + (2v - 2v₁)²
2v² = 2v₁² + 4v² - 8vv₁ + 4v₁²
6v₁² - 8vv₁ + 2v² = 0
6v₁² - 6vv₁ - 2vv₁ + 2v² = 0
6v₁(v₁ - v) - 2v(v₁ - v) = 0
(6v₁ - 2v)(v₁ - v) = 0
6v₁ = 2v or v₁ = v
v₁ = (¹/₃v) or v₁ = v
If v₁ = (¹/₃v), then eq 1 becomes;
v₂ = 2v - 2(¹/₃v)
v₂ = 2v - (²/₃v)
v₂ = (⁴/₃v)
If v₁ = v, then eq 1 becomes;
v₂ = 2v - 2v = 0
(v₁, v₂) = [(¹/₃v), (⁴/₃v)] or (v₁, v₂) = (v, 0)
Complete question is;
Let two objects of equal mass m collide. Object 1 has initial velocity v, directed to the right, and object 2 is initially stationary.
Now assume that the mass of object 1 is 2m, while the mass of object 2 remains m. If the collision is elastic, what are the final velocities v1 and v2 of objects 1 and 2? Give the velocity v1 of object 1 followed by the velocity v2 of object 2, separated by a comma. Express the velocities in terms of v.
Read more about Inelastic Collision at; https://brainly.com/question/18432099
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