91Ó°ÊÓ

When you compress or stretch a spring, you store energy in the form of elastic potential energy. This energy can do work, like pushing or pulling an object, when the spring returns to its original shape. Elastic potential energy is calculated using the formula:

• \( PE_{spring} = \frac{1}{2}kx^2 \)

Where \( k \) is the spring constant (a measure of the spring's stiffness) and \( x \) is the compression or extension distance from its natural length.
This equation tells us how much energy is "stored" in a spring by either compressing or stretching it. In the exercise, the spring was initially compressed 0.045 meters contributing energy to launch the block of ice across the table.

Kinetic energy is the energy of motion. If an object is moving, it has kinetic energy. It is given by the equation:

• \( KE = \frac{1}{2}mv^2 \)

Here, \( m \) is the mass of the object, and \( v \) is its velocity. This equation emphasizes how kinetic energy depends on both the mass of the object and its speed.
The faster something moves, the more kinetic energy it has, and the same goes if the object's mass increases. This concept was crucial in our exercise to determine how fast the ice block was moving once it reached the floor after falling off the table.

Gravitational potential energy is energy an object possesses because of its position relative to the Earth. The higher an object is, the more gravitational potential energy it has. It is calculated as:

• \( PE_{gravity} = mgh \)

where \( m \) is the mass, \( g \) is the acceleration due to gravity \( (9.8 \ \text{m/s}^2) \), and \( h \) is the height above the ground.
In our problem, the block of ice initially starts with gravitational potential energy due to its height on the tabletop. This energy shifts into kinetic energy as it falls, with the energy transformations ensuring total mechanical energy conservation. This part of the solution helped us determine how the initial height affected the speed of the block upon reaching the ground.