Final answer:
The physics problem is about analyzing a collision between carts on a track, where one cart is moving and the other is initially at rest. By applying conservation of momentum, the final velocity of the combined mass can be determined.
Step-by-step explanation:
Understanding Momentum in Collisions
When dealing with collisions between carts in a physics context, momentum is a key concept to explore. As an example, two carts on a track demonstrate the conservation of momentum. With one cart of mass mA moving and the other cart initially at rest, the system's total momentum prior to collision must equal the momentum after the carts have collided and stuck together.
In a case where two carts of masses mA and 2m collide and stick together, we can analyze the velocity change and apply the principle of conservation of momentum. For a cart with mass 2m, moving with velocity v, the momentum before the collision and the joint momentum of both carts after the collision must be equal, assuming no external forces apply.
The formula for kinetic energy can be used to compare the initial and final energy states of the system. It's important to note that if the carts stick together and the collision is not elastic, some of the system's kinetic energy will be transformed into other forms of energy, such as internal energy or sound.