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A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring 14...

Question:

A hollow steel ball weighing 4 pounds is suspended from a spring. This stretches the spring 14 feet. The ball is started in motion from the equilibrium position with a downward velocity of 9 feet per second. The air resistance (in pounds) of the moving ball numerically equals 4 times its velocity (in feet per second). Suppose that after t seconds the ball is y feet below its rest position. Find y in terms of t. (Note that the positive direction is down.) Take as the gravitational acceleration 32 feet per second.

Spring

The spring absorbs the mechanical energy, so the springs are also referred to as the shock absorber, energy reservoir. The spring force depends on the spring constant (stiffness of spring) and the expansion or compression of the spring.

Answer and Explanation: 1

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Given data

  • The weight of the ball is: {eq}w = 4\;{\rm{lb}} {/eq}
  • The stretching in the spring is: {eq}x = 14\;{\rm{ft}} {/eq}
  • The initial...

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Practice Applying Spring Constant Formulas

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Chapter 17 / Lesson 11
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In this lesson, you'll have the chance to practice using the spring constant formula. The lesson includes four problems of medium difficulty involving a variety of real-life applications.


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