91Ó°ÊÓ

Kinetic energy is a fundamental concept in physics that describes the energy an object has due to its motion. It is directly proportional to the mass of the object and the square of its velocity.
When the purse in the exercise reaches the ground, we calculate its kinetic energy using the formula:

• \( KE = \frac{1}{2}mv^2 \)

In this equation:

• \( m \) is the mass of the object, 2.0 kg for the purse.
• \( v \) is the velocity, which is 27 m/s when it hits the ground.

Inserting these values:

• \( KE = \frac{1}{2} \times 2.0 \times 27^2 = 729 \, \text{Joules} \)

This energy represents how much work would be needed to bring the purse to a stop if there were no other forces, like air resistance. Kinetic energy illustrates the energy transformation as the purse falls from rest to maximum motion.

Potential energy is the energy stored in an object due to its position relative to other objects. For instances like this exercise, we consider gravitational potential energy, which depends on the height of the object above the ground.
We calculate potential energy using the formula:

• \( PE = mgh \)

Where:

• \( m \) is the mass of the purse, 2.0 kg.
• \( g \) is the gravitational acceleration, approximately 9.8 m/s² on Earth.
• \( h \) is the height, which is 55 m in this case.

Substituting these values gives:

• \( PE = 2.0 \times 9.8 \times 55 = 1078 \, \text{Joules} \)

This potential energy represents the energy stored due to the purse’s elevated position on the tower. Upon release, this energy is transformed into kinetic energy as the purse falls. The decrease in height leads to a decrease in potential energy, ultimately reaching zero at ground level.

Gravitational acceleration is a crucial factor influencing the motion of falling objects. On Earth's surface, it is approximately 9.8 meters per second squared (m/s²), indicating that an object's velocity increases by 9.8 m/s for every second it falls.
In this exercise, gravitational acceleration is central to both potential and kinetic energy calculations. Initially, it contributes to the potential energy of the purse due to its height:

• \( PE = mgh \)

The gravitational force also influences the conversion of potential energy to kinetic energy as the object falls while no additional force acts on it, except for air resistance.
Even if the concept seems simple, gravitational acceleration is foundational to understanding motion. It affects how objects speed up when dropped and influences the time it takes for them to reach the ground. All objects, regardless of mass, will experience the same acceleration due to gravity in the absence of air resistance.