91Ó°ÊÓ

Potential energy is the energy an object possesses due to its position or state. It is stored energy that has the potential to do work. When an object is lifted against a gravitational field, it gains potential energy.
In our exercise, the child at the top of the slide represents an example of gravitational potential energy. This energy is calculated using the formula \[ PE = mgh \]Where:

• \( m \) is the mass of the object (child in this case), which is \( 16.0 \text{ kg} \)
• \( g \) is the acceleration due to gravity, approximately \( 9.8 \text{ m/s}^2 \)
• \( h \) is the height from which the object is elevated, \( 2.20 \text{ m} \)

The potential energy of the child at the top is calculated as \( 344.96 \text{ J} \). As the child descends the slide, this potential energy is transformed into other forms of energy, including kinetic and thermal energy.

Kinetic energy is the energy of motion. When an object is in motion, it possesses kinetic energy, which depends on two key factors: mass and velocity. In our scenario, once the child reaches the bottom of the slide, they are moving, and hence they have kinetic energy.
The formula to calculate kinetic energy is: \[ KE = \frac{1}{2} mv^2 \]Where:

• \( m \) is the mass of the object, which is \( 16.0 \text{ kg} \)
• \( v \) is the velocity of the object at the bottom, \( 1.25 \text{ m/s} \)

Substituting these values gives the kinetic energy as \( 12.5 \text{ J} \).
This energy is much less than the initial potential energy because some energy has been transformed into other forms, primarily thermal energy due to friction.

Thermal energy refers to the energy that comes from heat. In mechanical processes, like a child sliding down a slide, energy is often partly converted to thermal energy, demonstrating the concept of energy dissipation.
In our exercise, as the child descends the slide, friction between the slide and the child generates heat, transforming some of the energy into thermal energy. This is considered energy loss since it is not available to do mechanical work.
The amount of thermal energy generated can be calculated by finding the difference between the potential energy at the top and the kinetic energy at the bottom:

• \( 344.96 \text{ J} \) (initial potential energy) minus \( 12.5 \text{ J} \) (kinetic energy at the bottom) results in \( 332.46 \text{ J} \) of thermal energy generated due to friction.

Understanding these transformations and calculations highlights how energy changes forms yet is conserved in total, adhering to the principle of conservation of energy in physics.