The relationship between the length of a spring and the force required to stretch the spring is shown below. What is the work done when the spring length is increased from 20 cm to 30 cm?

Question

The relationship between the length of a spring and the force required to stretch the spring is shown below.  What is the work done when the spring length is increased from 20 cm to 30 cm?

Quizplus · Accepted Answer

11ecba2d_131d_6217_a3bf_5195d0ee8e59_MD0008_00 Mechanical work refers to the transfer of energy in or out of a system that occurs as the result of the application of a force (F) over some distance (d): 11ecba2d_131d_6218_a3bf_87c5461d43ad_MD0008_00 The SI unit for work is the joule (J), where 1 J is equal to 1 newton (N) of force exerted over 1 meter (m) of distance (1 J = 1 N∙m). In a graph of force versus distance, the area under the curve is equal to work associated with the displacement because the F ∙ d component of the above equation is equal to a y-axis value (a force) multiplied by an x-axis value (a distance). In this question, the graph shows a variable force being applied to the end of a spring to stretch it from a length of 15 cm to a length of 35 cm. When stretching the spring from 20 cm to 30 cm long, the variable force acts over a distance of 10 cm. Converting this distance to standard units results in: 11ecba2d_131d_8929_a3bf_899f746f487d_MD0008_00 In the graph of force versus distance, the area under the curve can be calculated by visualizing the total area as the sum of the areas (A) of two geometric shapes (one triangle and one rectangle) that both have a base 0.10 m in length. The combined area of these two shapes yields the work: 11ecba2d_131d_892a_a3bf_6172f6aa129f_MD0008_00 11ecba2d_131d_892b_a3bf_7778bb141dd7_MD0008_00 11ecba2d_131d_892c_a3bf_fdd3db785014_MD0008_00 11ecba2d_131d_892d_a3bf_9768a42686c3_MD0008_00 Therefore, stretching the spring from a length of 20 cm to 30 cm through the application of a variable force is associated with mechanical work equal to 25 J in magnitude (Choice A). Educational objective: Work describes the energy transfer into or out of a system that takes place as the result of a force acting through a distance. In a graph of force versus distance, the work associated with a given displacement can be derived from the graph by evaluating the total area under the curve.

The Relationship Between the Length of a Spring and the Force