91Ó°ÊÓ

The conservation of momentum is a fundamental principle in physics that states that in a closed system with no external forces, the total momentum remains constant before and after a collision. This principle is extremely useful in analyzing collisions, such as the one between the two hockey pucks in our exercise.

In our problem, we have two pucks colliding head-on. The first puck, with a mass of 0.450 kg, moves at a velocity of 4.80 m/s. The second puck is initially at rest, with a mass of 0.900 kg. The law of conservation of momentum is represented mathematically as:

• \[ m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2 \]

This equation allows us to relate the initial momenta of the pucks to their final momenta. By inputting the known values from our exercise, we solve for the unknown final velocities, \( v_1 \) and \( v_2 \). Using this principle, we preserve the total momentum of the system, ensuring we can accurately predict the pucks' final states post-collision.

In a perfectly elastic collision, not only is momentum conserved, but kinetic energy is also preserved. This means that the total kinetic energy of both objects before the collision is equal to the total kinetic energy after the collision.

The formula for conservation of kinetic energy in our problem is:

• \[ \frac{1}{2}m_1 u_1^2 + \frac{1}{2}m_2 u_2^2 = \frac{1}{2}m_1 v_1^2 + \frac{1}{2}m_2 v_2^2 \]

Applying this to our exercise, we calculate the kinetic energy of each puck. Initially, only the first puck possesses kinetic energy because the second puck is at rest. Solving this equation alongside our momentum conservation equation helps us find the final velocities, \( v_1 \) and \( v_2 \).

The calculated final velocities must satisfy both the momentum and energy equations simultaneously, as these are the hallmark conditions of an elastic collision.

Tackling physics problems like this one involves a structured approach, often starting with identifying known and unknown quantities. In our case, we began by noting the masses and initial velocities of the two hockey pucks.

A systematic method includes:

• Identifying the physical principles at play, such as the conservation laws involved in the collision.
• Setting up the appropriate equations to represent these physical principles, as shown with our momentum and kinetic energy equations.
• Solving the system of equations by substitution or elimination to find unknown variables, such as the final velocities here.

This process is critical in physics problem-solving. It allows students to translate real-world scenarios into mathematical formulations that can be solved to derive meaningful results.

By practicing this method, students build the analytical skills necessary to tackle more complex problems, providing a strong foundation for understanding physics.