INTRODUCTION

Relevance of the Theme

Work: Weight is one of the first topics that delve into the concept of energy and forces in Physics. It covers fundamental concepts that permeate many other areas of physics, including thermodynamics, fluid mechanics, and electromagnetism. Additionally, it is a concept with important practical applications, such as calculating energy expenditure in physical activities and the operation of machines.

Contextualization

By understanding the concept of Work: Weight, we enter into an intertwining of the two most fundamental physical quantities: force and displacement. Previous material on vectors, scalars, force (especially weight), and the concept of work as a scalar product is the basis for the in-depth study of this topic. With an understanding of Work: Weight, we advance to the comprehension of other types of work and forms of energy, being a crucial step in the student's journey in the study of physics.

THEORETICAL DEVELOPMENT

Components

• Weight: It is the force acting on a body in a gravitational field. The standard unit for weight is the newton (N), which is the force required to accelerate 1 kg at 1 m/s^2. It can be calculated by the formula W = m * g, where m is the mass of the body and g is the acceleration due to gravity.

• Gravitational Potential Energy (GPE): The potential energy associated with the position of an object in a gravitational field. It is calculated by the formula GPE = m * g * h, where h is the height of the object relative to a reference level. Its concept is directly related to Work: Weight, as the variation of GPE in a vertical displacement is equal to Work: Weight.

• Work: Weight (Ww): It is the work done by the weight force in a displacement. It is calculated by the formula Ww = W * d * cosθ, where W is the weight, d is the distance of the displacement, and θ is the angle formed between the directions of the weight and the displacement. If the displacement is in the opposite direction to the weight force, the work is negative, indicating energy transfer to the system.

Key Terms

• Work: In Physics, work is the transfer of energy to or from the system as a result of the application of a force. It is a scalar quantity given by the scalar product of the force by the distance over which the force acts.

• Energy: Capacity to do work. In Physics, energy is a quantity that can be transferred through the performance of work.

• Force: Action capable of modifying the state of rest or motion of an object. In Physics, force is a vector quantity defined by its magnitude, direction, and sense.

Examples and Cases

• Example 1: Suppose a student lifts a backpack weighing 5 kg to a height of 2 meters from the ground. The Work: Weight performed is given by Ww = W * d * cosθ = (5 kg * 9.8 m/s²) * 2 m * cos180° = -98 J, where the negativity indicates work done against the weight force.

• Example 2: Consider an elevator moving vertically at a constant speed. The tension force of the elevator performs Work: Weight, as the direction of the displacement and the force are the same. If an 80 kg passenger goes from the ground floor to the fourth floor (12 meters), the Work: Weight will be equal to Ww = W * d * cosθ = (80 kg * 9.8 m/s²) * 12 m * cos0° = 9417.6 J.

DETAILED SUMMARY

Key Points

• Definition and Calculation of Weight: Weight is the force acting on a body in a gravitational field. This force is given by the product of the body's mass by the acceleration due to gravity. The direction of weight is always downward, opposite to the vertical axis.

• Gravitational Potential Energy (GPE): Gravitational potential energy is a form of energy that depends on the position of an object in a gravitational field. It is directly proportional to the object's mass, the acceleration due to gravity, and its height relative to a reference level.

• Calculation of Work: Weight (Ww): Work: Weight is the energy transferred or performed due to the weight acting on a vertically moving body. It is calculated as the product of weight by the distance of displacement and by the cosine of the angle formed between the direction of displacement and the direction of weight.

• Relationship between Work: Weight and GPE: The variation of GPE in a vertical displacement is equal to Work: Weight. If the displacement is made in the opposite direction to the weight, the work is negative, indicating energy transfer to the system.

Conclusions

• The weight force, which is the resultant force of the gravitational field on an object, performs work when the object is vertically displaced. This work, called Work: Weight, can be positive or negative, depending on the direction of displacement.

• The gravitational potential energy of an object in a gravitational field is also directly related to Work: Weight. The variation of this energy in a vertical displacement is exactly the Work: Weight.

• Understanding the concept of Work: Weight is fundamental not only for the study of physics but also for the comprehension of natural phenomena and for the application of physical concepts in practical situations, such as calculating energy expenditure in physical activities.

Suggested Exercises

1. Exercise 1: An object weighing 6 kg is lifted vertically by a string. If the object is initially kept at rest at a height of 3 meters from the ground and then lowered back to the initial position, what is the energy transferred by Work: Weight during this process?

2. Exercise 2: A man weighing 80 kg climbs a 20-meter-high staircase. How much Work: Weight does he perform on this journey?

3. Exercise 3: If the weight of an object is 50 N and it is horizontally displaced by 10 m, what is the value of the Work: Weight performed?