Two air-track carts move toward one another on an air track. Cart 1 has a mass of 0.34 kg and a speed of 1.1 m/s . Cart 2 has a mass of 0.68 kg and a speed of 0.55 m/s .
answered in "fixed" post above
To find the final velocities of the two carts after collision, we can use the principles of conservation of momentum and conservation of kinetic energy.
1. Conservation of momentum: The total momentum before the collision should be equal to the total momentum after the collision.
The initial momentum of Cart 1 (Pi1) is given by the product of its mass (m1) and its initial velocity (v1):
Pi1 = m1 * v1 = 0.34 kg * 1.1 m/s
The initial momentum of Cart 2 (Pi2) is given by the product of its mass (m2) and its initial velocity (v2):
Pi2 = m2 * v2 = 0.68 kg * 0.55 m/s
The total initial momentum (Pi) is the sum of the individual momenta of the two carts:
Pi = Pi1 + Pi2
2. Conservation of kinetic energy: The total kinetic energy before the collision should be equal to the total kinetic energy after the collision if there are no external forces acting on the system.
The initial kinetic energy of Cart 1 (Ki1) is given by one-half the product of its mass (m1) and the square of its initial velocity (v1):
Ki1 = 0.5 * m1 * v1^2
The initial kinetic energy of Cart 2 (Ki2) is given by one-half the product of its mass (m2) and the square of its initial velocity (v2):
Ki2 = 0.5 * m2 * v2^2
The total initial kinetic energy (Ki) is the sum of the individual kinetic energies of the two carts:
Ki = Ki1 + Ki2
After the collision, the final velocities of the two carts (v1f and v2f) can be calculated using the equations:
v1f = (Pi - Pi2) / m1
v2f = (Pi - Pi1) / m2
It is important to note that these equations assume an elastic collision, where kinetic energy is conserved. If the collision is not perfectly elastic, some kinetic energy may be lost as heat or sound, and the final velocities will be different.