91Ó°ÊÓ

In an inelastic collision, two objects collide and do not bounce apart. The main characteristic of this type of collision is that kinetic energy is not conserved, though the momentum is. Typically, the objects stick together post-collision, moving as a single mass.

• Imagine a 90 g ball moving towards a 10 g stationary ball.
• They crash and cling together, forming a 100 g mass.
• In this scenario, only momentum is conserved.

For our example, we calculate their shared velocity using the conservation of momentum formula: \[ m_1v_1 + m_2v_2 = (m_1 + m_2)v_f \]The initial momentum of the system is solely due to the moving 90 g ball. Thus, after substitution and solving, the combined velocity of both balls is found to be \(0.9\, \text{m/s}\). This reduced speed indicates kinetic energy was lost, typically transformed into heat or deformation energy.

An elastic collision is one where both momentum and kinetic energy are conserved. In this type of collision, after impact, the objects do not stick together but continue moving separately.

• Picture again our 90 g moving ball colliding with the 10 g ball.
• After the hit, they part ways without any energy loss.
• Both momentum and energy equations must be satisfied.

When doing the math:

• Use the momentum conservation: \(m_1v_1 + m_2v_2 = m_1v_{1f} + m_2v_{2f}\)
• And kinetic energy: \(\frac{1}{2}m_1v_1^2 = \frac{1}{2}m_1v_{1f}^2 + \frac{1}{2}m_2v_{2f}^2\)

Solving these equations for the given scenario, one finds the 90 g ball stops (\(v_{1f} = 0\, \text{m/s}\)), and the 10 g ball moves ahead with the previous speed of \(1\, \text{m/s}\). No kinetic energy is lost.

Momentum conservation is a key principle in mechanics. It states that within an isolated system, the total momentum remains constant before and after an event, such as a collision.

• Momentum, represented as \(p\), is calculated by the formula \(p = mv\).
• In a closed system (no external forces), the sum of all momenta of the involved bodies remains the same.

For example:

• A 90 g and a 10 g ball interact.
• Regardless of whether they stick or bounce apart, the initial and final total momentum will equalize.

While momentum dictates the movement of mass, remember it does not account for energy changes directly. Hence each collision type - elastic or inelastic - involves its distinct energy focus.

Kinetic energy conservation refers to the idea that, in certain types of collisions, the total kinetic energy of the system remains unchanged pre- and post-collision. This is not universal for all collisions and primarily applies to elastic collisions.

• Kinetic energy \(KE\) is given by \(\frac{1}{2}mv^2\).
• Unlike elastic collisions, inelastic collisions do not return all kinetic energy in the same form post-impact.

In the scenario with our balls:

• During a perfectly elastic collision, the kinetic energy remains consistent before and after collision.
• In the inelastic example, energy conservation does not hold, evidenced by the reduced velocity of the combined mass.

Thus, acknowledging the collision type helps anticipate potential energy transformations - exterior forces like friction often alter kinetic pathways even when momentum is conserved.