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A block of mass M = 2 kg slides back and forth on a one-dimensional frictionless surface between...

Question:

A block of mass M = 2 kg slides back and forth on a one-dimensional frictionless surface between two springs, of spring constant {eq}\rm k_{left} = 30 \ N/m {/eq} and {eq}\rm k_{right} = 54 \ N/m {/eq}. When the block hits the left spring it compresses a maximum distance of {eq}\rm d_{left, \ max} = 0.7 \ m {/eq}. Suppose instead that there is friction between the block and the surface and that the distance between the relaxed springs is d = 2.8 m. The block is initially placed against the left spring which is compressed by 0.7 m and then released. The first time the block hits the right spring, it is compressed by 0.41 m. Find the coefficient of kinetic friction between the block and the table.

Hooke's Law:

Hooke's law says that the force needed to compress or extend a spring by a distance x from its equilibrium position is given by the expression

$$F \ = \ k \ x $$

where k is the spring constant.

Answer and Explanation:

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We should first note that the direction of the restoring force {eq}F_{L} {/eq} on the left spring after being compressed by the block acts in the...

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Hooke's Law & the Spring Constant: Definition & Equation

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Chapter 4 / Lesson 19
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After watching this video, you will be able to explain what Hooke's Law is and use the equation for Hooke's Law to solve problems. A short quiz will follow.


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