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Two spheres A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction.
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Two spheres A and B of masses m1 and m2 respectively collide. A is at ...
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Two spheres A and B of masses m1 and m2 respectively collide. A is at ...
Collision between Spheres A and B
Initial Conditions:
- Sphere A is at rest initially.
- Sphere B is moving with velocity v along the x-axis.
Collision Process:
- The collision between the two spheres can be considered as a two-dimensional collision.
- The collision is assumed to be perfectly elastic, meaning there is no loss of kinetic energy during the collision.
- The spheres can be assumed to be rigid bodies.
Momentum Conservation:
- In the absence of external forces, the total momentum of the system is conserved.
- Before the collision, the momentum of Sphere B is given by:
- P₁ = m₂ * v (initial momentum)
- After the collision, Sphere B changes its direction and has a velocity of v/2 perpendicular to the original direction.
- The change in momentum of Sphere B is given by:
- ΔP = m₂ * (v/2) - m₂ * v = -m₂ * (3v/2)
- The negative sign indicates a change in direction.
- According to the principle of momentum conservation, the total momentum before the collision must be equal to the total momentum after the collision.
- Since Sphere A is initially at rest, its momentum before and after the collision is zero.
- Therefore, the change in momentum of Sphere B must be equal to the momentum of Sphere A after the collision.
- The momentum of Sphere A after the collision is given by:
- P₂ = ΔP = -m₂ * (3v/2)
Motion of Sphere A after Collision:
- The momentum of Sphere A after the collision is in the direction opposite to the initial motion of Sphere B.
- Therefore, Sphere A moves in the direction opposite to the initial motion of Sphere B.
- The magnitude of its velocity can be determined by dividing the momentum by the mass of Sphere A:
- v₂ = P₂ / m₁ = -m₂ * (3v/2) / m₁
Conclusion:
- After the collision between the spheres A and B, Sphere A moves in the direction opposite to the initial motion of Sphere B.
- The magnitude of its velocity is given by v₂ = -m₂ * (3v/2) / m₁.
Initial Conditions:
- Sphere A is at rest initially.
- Sphere B is moving with velocity v along the x-axis.
Collision Process:
- The collision between the two spheres can be considered as a two-dimensional collision.
- The collision is assumed to be perfectly elastic, meaning there is no loss of kinetic energy during the collision.
- The spheres can be assumed to be rigid bodies.
Momentum Conservation:
- In the absence of external forces, the total momentum of the system is conserved.
- Before the collision, the momentum of Sphere B is given by:
- P₁ = m₂ * v (initial momentum)
- After the collision, Sphere B changes its direction and has a velocity of v/2 perpendicular to the original direction.
- The change in momentum of Sphere B is given by:
- ΔP = m₂ * (v/2) - m₂ * v = -m₂ * (3v/2)
- The negative sign indicates a change in direction.
- According to the principle of momentum conservation, the total momentum before the collision must be equal to the total momentum after the collision.
- Since Sphere A is initially at rest, its momentum before and after the collision is zero.
- Therefore, the change in momentum of Sphere B must be equal to the momentum of Sphere A after the collision.
- The momentum of Sphere A after the collision is given by:
- P₂ = ΔP = -m₂ * (3v/2)
Motion of Sphere A after Collision:
- The momentum of Sphere A after the collision is in the direction opposite to the initial motion of Sphere B.
- Therefore, Sphere A moves in the direction opposite to the initial motion of Sphere B.
- The magnitude of its velocity can be determined by dividing the momentum by the mass of Sphere A:
- v₂ = P₂ / m₁ = -m₂ * (3v/2) / m₁
Conclusion:
- After the collision between the spheres A and B, Sphere A moves in the direction opposite to the initial motion of Sphere B.
- The magnitude of its velocity is given by v₂ = -m₂ * (3v/2) / m₁.
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Two spheres A and B of masses m1 and m2 respectively collide. A is at rest initially and B is moving with velocity v along x-axis. After collision B has a velocity v/2 in a direction perpendicular to the original direction. The mass A moves after collision in the direction.
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