A 1.60-m-tall person lifts a 1.65-kg book off the ground so it is 2.20 m above the ground. What is the potential energy of the book relative to How is the work done by the person related to the answers in parts (a) and (b)?

Verified step by step guidance

1. Step 1: Understand the problem. The potential energy of an object is given by the formula: $U=mgh$, where $m$ is the mass of the object, $g$ is the acceleration due to gravity (approximately 9.8 m/s²), and $h$ is the height above the reference point. Here, the mass of the book is 1.65 kg, and the height above the ground is 2.20 m.
2. Step 2: Calculate the potential energy of the book relative to the ground. Substitute the given values into the formula: $U=mgh$. Use $m=1.65$, $g=9.8$, and $h=2.20$. This will give the potential energy relative to the ground.
3. Step 3: Relate the work done by the person to the change in potential energy. Work done is defined as the energy transferred to or from an object via a force acting over a distance. In this case, the work done by the person to lift the book is equal to the increase in the book's gravitational potential energy, assuming no energy is lost to other factors like friction or air resistance.
4. Step 4: Recognize that the work done by the person is equal to the change in potential energy. Since the book starts at ground level (0 m) and is lifted to 2.20 m, the work done by the person is equal to the potential energy of the book at 2.20 m above the ground.
5. Step 5: Summarize the relationship. The work done by the person is directly related to the potential energy of the book. Specifically, the work done is equal to the increase in the book's potential energy, which can be calculated using the formula $W=U$, where $U$ is the potential energy calculated in Step 2.

Key Concepts

Potential Energy

Potential energy is the energy stored in an object due to its position in a gravitational field. It is calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.81 m/s²), and h is the height above a reference point. In this scenario, the book's potential energy can be determined by its height above the ground.

Work Done

Work done is defined as the energy transferred when a force is applied to an object over a distance. It is calculated using the formula W = Fd, where F is the force applied and d is the distance moved in the direction of the force. In lifting the book, the work done by the person is equal to the change in potential energy of the book, illustrating the relationship between work and energy.

Conservation of Energy

The conservation of energy principle states that energy cannot be created or destroyed, only transformed from one form to another. In this context, the work done by the person in lifting the book is converted into potential energy. This principle helps to understand how the energy expended in lifting the book corresponds to the increase in its potential energy as it is raised to a higher position.