Final answer:
In an inelastic collision like the one in this problem, there will be a loss of kinetic energy. The amount will be determined by the initial and final speeds of the carts, but without those specifics, we can't calculate the exact fraction lost. The larger cart's kinetic energy will be shared with the smaller cart post collision, leading to less kinetic energy overall.
Step-by-step explanation:
To solve this problem, we must consider the principles of conservation of momentum and kinetic energy.
Momentum is conserved during the collision because no external force is acting on the system. However, kinetic energy is not always conserved in a collision. In this case, the collision is inelastic because the carts stick together after collision which results in a loss of kinetic energy.
The fraction of kinetic energy lost will depend on the initial movements of the carts and the final combined movement. The initial kinetic energy is entirely associated with the 400-g cart while the 200-g cart is initially at rest. After collision, the kinetic energy is shared between both carts.
Without knowing the specifics of the initial and final speeds, we can't calculate the exact fraction of kinetic energy lost. But we can say that there will be a loss, giving less final kinetic energy than initial.
Learn more about Inelastic Collision