91Ó°ÊÓ

When we talk about potential energy in the context of physics, we're referring to the stored energy that an object has due to its position relative to other objects. In this scenario, when the purse is at the top of the Leaning Tower of Pisa, it has a certain amount of potential energy because of its height above the Earth.
The formula to determine this is given by:

• \( PE = mgh \)

where:

• \( m \) is the mass of the object
• \( g \) is the acceleration due to gravity (approximately 9.8 m/s² on the surface of the Earth)
• \( h \) is the height from which the object is dropped

In the exercise, the purse with a mass of 2.0 kg is dropped from 58 meters, so its potential energy is calculated using:

• \( PE = 2.0 \times 9.8 \times 58 \)
• \( PE = 1136.4 \text{ J} \)

As the purse falls, this stored energy is gradually converted into kinetic energy.

Kinetic energy refers to the energy that an object possesses because of its motion. Once the purse begins to fall, its potential energy starts transforming into kinetic energy due to the Earth's gravitational pull.
To calculate the kinetic energy at the point just before the purse hits the ground, we use the formula:

• \( KE = \frac{1}{2}mv^2 \)

Here:

• \( m \) is the mass again (2.0 kg)
• \( v \) is the velocity of the object at impact (given as 27 m/s in the exercise)

Substituting these values into the equation gives us:

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

So, by the time the purse reaches the ground, it has a kinetic energy of 729 J.

The work-energy principle is a crucial concept that helps us understand the relationship between work and energy. This principle states that the work done on an object by various forces results in a change in the kinetic energy of the object.
In our exercise, the purse encounters air resistance as it falls, which does work on the purse and results in a loss of energy.
The energy lost due to air resistance can be calculated as the difference between the initial potential energy and the kinetic energy when it hits the ground:

• \( \text{Energy lost} = 1136.4 \text{ J} - 729 \text{ J} \)
• \( \text{Energy lost} = 407.4 \text{ J} \)

The work done by the air resistance is equal to this energy loss. We utilize the work-energy principle to relate this energy loss to the force of air resistance:

• \( \text{Work} = \text{Force} \times \text{Distance} \)
• \( 407.4 = F \times 55 \)
• \( F = \frac{407.4}{55} \)
• \( F \approx 7.41 \text{ N} \)

This calculated force represents the average force of air resistance acting on the purse during its descent.