Final answer:
To find the total kinetic energy post-collision of a two-mass system after an elastic collision, we rely on the principles of conservation of momentum and kinetic energy, calculating the kinetic energy for each object individually and then adding them together.
Step-by-step explanation:
To calculate the total kinetic energy of a two-mass system after an elastic collision, we first need to understand the principles of conservation of momentum and conservation of kinetic energy.
Conservation of Momentum
In an elastic collision, the total momentum before the collision is equal to the total momentum after the collision. The formula for momentum is ℝp = m × v, where m is mass and v is velocity.
Conservation of Kinetic Energy
Similarly, in an elastic collision, the total kinetic energy before the collision is equal to the total kinetic energy after the collision. Kinetic energy is given by ℝKE = 0.5 × m × v2.
Given the masses and velocities for the two objects in the collision, we can find the total kinetic energy post-collision by calculating the kinetic energy for each mass with their final velocities and then summing them. For the 16.0-kg object, the kinetic energy after collision is KE1 = 0.5 × 16.0 kg × (4.0 m/s)2 = 128 Joules, and for the 4.0-kg object, assume a final velocity v2. For the system, it would be KEtotal = KE1 + 0.5 × 4.0 kg × v22.