(Originais Teachy 2024) - Question Medium of Mathematics

In a physics experiment, an object of unknown mass is placed on a spring and the elongation of the spring is measured as a function of the object's mass. The generated graph shows a straight line passing through the origin, indicating that the force exerted by the spring (F) is directly proportional to the elongation (x), assuming the spring follows Hooke's law. However, the spring's elastic constant (k) is unknown and needs to be determined. For this purpose, a second experiment is conducted: a block of known mass is placed on the same spring, resulting in an elongation of 5 cm. Based on this data, you must estimate the mass of the unknown object. Step 1: Determine the mathematical relationship between the elastic constant (k), the force exerted by the spring (F), and the elongation (x) from Hooke's law. Step 2: Calculate the force exerted by the block of known mass on the spring. Step 3: With the calculated force, determine the elastic constant (k) of the spring. Step 4: Use the elastic constant (k) to calculate the mass of the unknown object from its elongation in the spring, which is also known.