Work: Weight | Traditional Summary
Contextualization
In Physics, the concept of work is closely linked to the application of a force that causes a displacement. Unlike the everyday use of the term, where work generally refers to any type of activity performed, in Physics, work is a measure of the energy transferred by a force. For example, when we push a box along the floor, we are doing work because we apply a force that causes a displacement in the direction of the applied force.
The weight force, which is the force with which gravity pulls an object toward the center of the Earth, also does work. When we lift an object from the ground to a certain height, the work done by the weight force can be calculated by the formula τ = mgh, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.81 m/s² at the Earth's surface), and h is the change in height. This concept is fundamental for understanding various physical phenomena and their practical application, such as the functioning of elevators and the free fall of objects.
Concept of Work in Physics
In Physics, the concept of work is related to the application of a force that causes a displacement. Work is a measure of the energy transferred by a force over a displacement. The general formula for calculating work is τ = F * d * cos(θ), where F is the force, d is the displacement, and θ is the angle between the force and the displacement. It is important to emphasize that work is only done when there is displacement in the direction of the applied force.
Work can be positive or negative. Work is positive when the force and the displacement are in the same direction, as when pushing an object forward. Work is negative when the force and the displacement are in opposite directions, as when braking a car. Additionally, if the force is perpendicular to the displacement, as in the case of an object moving in a circle under the action of a centripetal force, the work done is zero.
Unlike the everyday use of the term, where work generally refers to any type of activity performed, in Physics, work is a specific measure of the energy transferred by a force. For example, when we push a box along the floor, we are doing work because we apply a force that causes a displacement in the direction of the applied force. This concept is fundamental to understanding how energy is transferred and transformed in different physical systems.
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Work is the energy transferred by a force over a displacement.
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The general formula is τ = F * d * cos(θ).
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Work can be positive, negative, or zero, depending on the direction of the force relative to the displacement.
Work of the Weight Force
The weight force is a conservative force that acts on objects due to gravity. The work done by the weight force is given by the formula τ = mgh, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.81 m/s² at the Earth's surface), and h is the change in height. This formula is specific to situations where the weight force is the only force doing work and the object moves vertically.
When we lift an object from the ground to a certain height, we are doing work against the weight force. In this case, the work done by the weight force is negative, as the force of gravity acts in the opposite direction to the displacement. On the other hand, when an object is dropped, the work done by the weight force is positive, because the force of gravity and the displacement are in the same direction.
Understanding the work of the weight force is essential for understanding various natural and technological phenomena. For example, the work done by the weight force is an important consideration in the operation of elevators, in the free fall of objects, and in many other systems where gravity plays a crucial role.
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The weight force is a conservative force due to gravity.
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The formula for the work of the weight force is τ = mgh.
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Work can be positive or negative, depending on the direction of the displacement relative to the weight force.
Practical Examples
To illustrate the concept of work of the weight force, let's consider some practical examples. First, imagine that you lift a 1 kg book from the ground to a table that is 1 meter high. In this case, the mass of the book (m) is 1 kg, the acceleration due to gravity (g) is 9.81 m/s², and the height (h) is 1 meter. Applying the formula τ = mgh, we get τ = 1 kg * 9.81 m/s² * 1 m = 9.81 Joules. Therefore, the work done against the weight force is 9.81 J.
Another example is when a 2 kg object is dropped from a height of 3 meters. In this case, the mass (m) is 2 kg, the acceleration due to gravity (g) is 9.81 m/s², and the height (h) is 3 meters. Applying the formula τ = mgh, we get τ = 2 kg * 9.81 m/s² * 3 m = 58.86 Joules. The work done by the weight force is 58.86 J, and it is positive because the displacement is in the same direction as the force.
These examples demonstrate how the formula τ = mgh can be applied to calculate the work of the weight force in different contexts. It is important to practice with various examples to reinforce the understanding of the concept and its application in real situations.
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Example of lifting a 1 kg book from the ground to a table that is 1 meter high.
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Example of dropping a 2 kg object from a height of 3 meters.
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Practicing with various examples helps reinforce the understanding of the concept.
Guided Problem Solving
To apply the formula for the work of the weight force in different scenarios, it is useful to solve problems step by step. Let's consider some typical problems and how to solve them. First, a 5 kg object is lifted to a height of 2 meters. We apply the formula τ = mgh, where m = 5 kg, g = 9.81 m/s², and h = 2 meters. Substituting the values, we have τ = 5 kg * 9.81 m/s² * 2 m = 98.1 Joules. The work done against the weight force is 98.1 J.
Another problem involves calculating the work done by the weight force when a 10 kg object descends from a height of 3 meters. Here, m = 10 kg, g = 9.81 m/s², and h = 3 meters. Applying the formula, we have τ = 10 kg * 9.81 m/s² * 3 m = 294.3 Joules. The work done is 294.3 J, considering that the displacement is negative (descent).
Finally, consider a 7 kg object thrown upwards that reaches a maximum height of 4 meters. Here, m = 7 kg, g = 9.81 m/s², and h = 4 meters. Applying the formula, we have τ = 7 kg * 9.81 m/s² * 4 m = 274.68 Joules. The work done during the ascent is -274.68 J (negative work), as the weight force acts in the opposite direction to the displacement.
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Example of a 5 kg object lifted to a height of 2 meters.
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Example of a 10 kg object descending from a height of 3 meters.
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Example of a 7 kg object thrown upwards reaching a height of 4 meters.
To Remember
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Work: Measure of the energy transferred by a force over a displacement.
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Weight Force: The force with which gravity pulls an object toward the center of the Earth.
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Formula τ = mgh: Formula to calculate the work of the weight force, where m is the mass, g is the acceleration due to gravity, and h is the change in height.
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Positive Work: When the force and the displacement are in the same direction.
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Negative Work: When the force and the displacement are in opposite directions.
Conclusion
In this lesson, we discussed the concept of work in Physics, with a special focus on the weight force. We learned that work is a measure of the energy transferred by a force over a displacement and that the formula for the work of the weight force is τ = mgh. We explored how work can be positive or negative, depending on the direction of the displacement relative to the gravitational force.
Through practical examples and guided problem-solving, we saw how to apply the formula τ = mgh to calculate the work done by the weight force in different situations, such as lifting an object or letting it fall. These examples help connect theory with practical applications in daily life, such as the functioning of elevators and the free fall of objects.
Understanding the work of the weight force is fundamental for Physics, as it allows for a better understanding of natural and technological phenomena. This knowledge is applicable in many contexts, from engineering to meteorology, highlighting the importance of Physics in our everyday lives.
Study Tips
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Revisit the practical examples discussed in class and try to solve additional problems to reinforce your understanding of the concept of work of the weight force.
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Use online Physics simulators to visualize how the weight force does work in different scenarios and variations in height.
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Form study groups to discuss and solve problems together, helping to clarify doubts and strengthen collaborative learning.
