Calculate Velocity of Cars in Elastic Collision

Explanation:

Given:

  • Cart 1 speed is twice that of Cart 2
  • Cart 2 inertia is twice that of Cart 1
  • Initial speed of Cart 2 is v

To calculate the velocity of cart 1 after an elastic collision on a low-friction track, we need to apply the principles of momentum and kinetic energy conservation.

Equations for Elastic Collision:

Velocity of cart 1 after collision (v1) = [(m1 - m2) / (m1 + m2)] * u1 + [(2m2) / (m1 + m2)] * u2

Velocity of cart 2 after collision (v2) = [(2m1) / (m1 + m2)] * u1 - [(m1 - m2) / (m1 + m2)] * u2

Given:

m1 = m, m2 = 2m (mass of cart 1 and cart 2 respectively)

u1 = 2u, u2 = u (initial velocities of cart 1 and cart 2 respectively)

Solving for v1:

v1 = [(m - 2m) / (3m)] * 2u + 2 * [(2m) / (3m)] * u

v1 = (2u / 3)

Solving for v2:

v2 = [(2m) / (3m)] * (2u) - [(m - 2m) / (3m)] * u

v2 = (5u / 3)

Therefore, the speed of cart 1 right after the collision in an elastic collision scenario is 2u/3.

Final Answer:

To find the velocity of cart 1 after an elastic collision on a low-friction track, we use the principles of momentum and kinetic energy conservation to create two equations and solve them to determine the final velocities of both carts.

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