91Ó°ÊÓ

Inelastic collisions are a type of collision where two objects collide and move together after the impact. This means their kinetic energy is not conserved as some of it is transformed into other forms of energy, such as heat or sound. However, the total momentum of the system remains the same before and after the collision. This principle is known as the conservation of momentum. In the given problem, the two skaters collide and stick together, making it a perfect example of an inelastic collision.
The moment they grab onto each other, their individual velocities change to become a shared velocity, resulting in a combined mass system moving in a single direction.

The momentum equation is crucial for understanding how the motion of objects changes in collisions. Momentum (\(p\)) is calculated as the product of mass (\(m\)) and velocity (\(v\)). The equation for momentum is:

• \(p = m \cdot v\)

To solve the collision problem, we calculate the momentum of each skater before they collide.
The first skater's momentum is \((70.0 \, \text{kg} \times 2.00 \, \text{m/s})\) and the second skater's momentum is \((65.0 \, \text{kg} \times (-2.50) \, \text{m/s})\). Notice we use a negative velocity for the second skater as they move in the opposite direction.
The total initial momentum is then calculated by summing these values, which provides the total momentum before the collision.

Frictionless surfaces are idealized surfaces where no force opposes the movement of objects. This assumption simplifies our calculations, as no external forces like friction alter the momentum of the objects involved.
In our problem, the skaters are on an ice rink, approximating a frictionless surface, allowing us to use the conservation of momentum without adjustment for friction.
This means the total momentum before the collision is the same as the total momentum afterwards, as no energy is lost due to friction. This makes frictionless environments perfect for examining momentum conservation principles.