A student is investigating how the force applied to two different springs affects their extension. She plots an extension-force graph for spring A (with extension on the y-axis and force on the x-axis) and obtains a straight line. On the same axes, she plots a second straight line using the data which she obtained for spring B. The gradient (slope) of the line for spring B is lower than that for spring A. What does this tell us about the spring constants of these springs?The spring constant of spring A is equal to that of spring BThe spring constant of spring A is lower than that of spring BNothingThe spring constant of spring A is greater than that of spring B
Question
A student is investigating how the force applied to two different springs affects their extension. She plots an extension-force graph for spring A (with extension on the y-axis and force on the x-axis) and obtains a straight line. On the same axes, she plots a second straight line using the data which she obtained for spring B. The gradient (slope) of the line for spring B is lower than that for spring A. What does this tell us about the spring constants of these springs?The spring constant of spring A is equal to that of spring BThe spring constant of spring A is lower than that of spring BNothingThe spring constant of spring A is greater than that of spring B
Solution
The spring constant of spring A is greater than that of spring B.
Here's why: The spring constant (k) is a measure of the stiffness of a spring. It is defined as the force (F) needed to extend or compress a spring by some distance (x), according to Hooke's Law (F = kx). In the extension-force graph, the spring constant is represented by the gradient or slope of the line. A higher gradient means a larger spring constant, indicating a stiffer spring. Therefore, since the gradient of the line for spring A is higher than that for spring B, the spring constant of spring A is greater than that of spring B.
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