A large mass collides with a stationary, smaller mass. How will the masses behave if the collision is inelastic?
The bigger mass will stop and the smaller mass will start moving.
Is this still true with a frictionless surface?
In an inelastic collision between a large mass and a stationary, smaller mass, the masses will stick together after the collision and move as a single entity. This means that they will have a common final velocity.
To understand why this happens, it is important to know that in an inelastic collision, the total kinetic energy of the system is not conserved. Some of the initial kinetic energy is transformed into other forms of energy, such as heat or deformation.
To calculate the final velocity after an inelastic collision, we can use the principle of conservation of momentum, which states that the total momentum of a system remains constant before and after the collision.
The momentum, denoted by p, is calculated by multiplying the mass of an object by its velocity. Since the smaller mass is initially stationary, its initial momentum is zero.
The total momentum before the collision is equal to the momentum after the collision. So, the equation becomes:
(mass of the large mass * velocity of the large mass) = (mass of the combined masses * final velocity)
Since the masses stick together after the collision, the mass of the combined masses is the sum of the individual masses.
Thus, we have:
(mass of the large mass * velocity of the large mass) = (mass of the large mass + mass of the smaller mass) * final velocity
Simplifying this equation, we find:
final velocity = (mass of the large mass * velocity of the large mass) / (mass of the large mass + mass of the smaller mass)
This equation gives us the final velocity of the masses after the inelastic collision. Keep in mind that the final velocity will be less than the initial velocity of the large mass, as some of its kinetic energy is transferred to the smaller mass during the collision.