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Question about Work: Graphics

Subject Physics

Physics

Source Originais Teachy

Originais Teachy

Topic Work: Graphics

Work: Graphics

Difficulty Medium

Medium

(Originais Teachy 2024) - Question Medium of Physics

During a Physics class, a group of 1st-year High School students is challenged to analyze the work done by a constant force acting on a body in rectilinear motion. The motion occurs along a horizontal axis and is represented by the graph of force as a function of displacement, which shows a region where the force is represented by a decreasing linear function. Considering the hypothetical situation in which the body moves 4 meters under the exclusive action of this force and the graph provides the dimensions of the rectangles representing the infinitesimal variations of force and displacement, the students are challenged to determine the total work done by the force. Additionally, the teacher asks the students to reflect on how variations in the static friction coefficient between the body and the surface would affect the total calculated work. Drawing on the interdisciplinary knowledge of Physics and Mathematics, how could the students use the concept of area under the graph curve to solve the proposed problem?

The total work done by the force is calculated by multiplying the average value of the force by the total displacement of the body, disregarding the infinitesimal variations of force and displacement provided by the graph.

The total work done by the force is calculated by integrating the function describing the force as a function of displacement, using Hooke's Law to consider the force variation with the body's position.

The total work done by the force is calculated by summing the areas of all triangles formed by the variations of force and displacement, instead of rectangles, and considering the variation of the dynamic friction coefficient in the calculation.

The total work done by the force is calculated by summing the areas of all the rectangles provided by the graph, where the area of each rectangle is given by F * dx, and reflecting on how variations in the static friction coefficient can affect the calculation of the total work.

The total work done by the force is calculated by dividing the area under the force graph by the total displacement of the body, considering the variation of the angle between the force and the displacement.

Answer sheet:

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