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Suppose that 4 J of work is needed to stretch a spring from its natural length of 28 cm to a length of 42 cm. What is the spring constant of the spring?

User Katenoox
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Final answer:

The spring constant of the spring is 57.14 N/m.

Step-by-step explanation:

To find the spring constant, we can use Hooke's law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position. So, F = kx, where F is the force, k is the spring constant, and x is the displacement. In this case, we are given the work done to stretch the spring, which is equal to the area under the force-displacement graph.

The work done is equal to the product of force and displacement, which can be calculated as the area of the triangle formed by the force-displacement graph. Since the graph is a straight line, the area can be calculated as half the base times the height.

Using the given values, we have a displacement of 0.14 m (42 cm - 28 cm) and a work done of 4 J. Plugging these values into the equation for work done, we have 4 J = 0.5k(0.14 m). Solving for k, we get k = 57.14 N/m.

User Nicolasthenoz
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