91Ó°ÊÓ

Kinetic energy is the energy of motion. When an object is moving, it possesses kinetic energy, which depends on its mass and speed. For the clay in our exercise, its kinetic energy is determined at the moment it is thrown downward. We use the formula:

• \( KE_i = \frac{1}{2}mv_i^2 \)

Here, \( m \) is the mass of the clay (5.00 kg), and \( v_i \) is its initial speed (5.00 m/s).
Substitute these values into the formula to calculate the initial kinetic energy.
The concept of kinetic energy is crucial because it tells us how energy is transitioning from motion into another form—in this case, the clay uses kinetic energy to compress the spring.

Spring compression occurs when a spring is pushed together, storing potential energy. This energy is known as elastic potential energy, and it can be calculated using Hooke's Law. We express this stored energy using:

• \( PE_s = \frac{1}{2}kx^2 \)

Here, \( k \) is the spring constant (1600 N/m), which measures the spring's stiffness, and \( x \) is the amount of compression.
When the clay hits the spring, the initial potential and kinetic energy transform into the elastic potential energy of the spring as it compresses.
Understanding spring compression is pivotal as it showcases how mechanical energy transitions into stored energy and accounts for energy conservation principles.

Energy conservation is a fundamental principle in physics that states that the total energy in a closed system remains constant. In this problem, all initial energies are converted without loss.
Initially, the clay has potential energy from its height and kinetic energy from its motion.
At the moment the spring is fully compressed, these energies are transformed into elastic potential energy.The energy conservation equation for this process is:

• \( PE_i + KE_i = PE_s \)

This means the sum of initial potential and kinetic energy is equal to the spring's stored energy.
Energy conservation helps us understand how different types of energy interact and balance within a system, demonstrating that energy doesn't vanish but rather morphs into different forms.