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A small glider is placed against a compressed spring at the bottom of an air track that slopes...

Question:

A small glider is placed against a compressed spring at the bottom of an air track that slopes upward at an angle of {eq}\displaystyle{ 42.0^\circ }{/eq} above the horizontal. The glider has mass {eq}8.00 \times 10^{-2} {/eq}kg. The spring has 640 N/m and negligible mass. When the spring is released, the glider travels a maximum distance of 1.40 m along the air track before sliding back down. Before reaching this maximum distance, the glider loses contact with the spring.

Part A: What distance was the spring originally compressed? x =

Part B: When the glider has traveled along the air track 0.400 m from its initial position against the compressed spring, is it still in contact with the spring? Yes/No

Part C: What is the kinetic energy of the glider at this point? k =

Law of Conservation of Energy:

When a spring of constant k is compressed by an amount x from its equilibrium position, it has elastic potential energy {eq}PE_{spring} =\dfrac{1}{2} k x^2 {/eq}

When a mass is against the spring, as the spring is released this potential energy will be converted to kinetic energy of the mass.

As the mass passes the equilibrium position of the spring it will lose contact with the spring and it will be launched with the maximum kinetic energy possible. As the mass moves along an incline, this kinetic energy will be converted into gravitational potential energy at the maximum point the mass will reach where the mass will be momentarily at rest and then return back along the incline.

Answer and Explanation: 1

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{eq}\textbf {Given data:} {/eq}

  • Slope of an air track {eq}\phi = 42^\circ {/eq}
  • Mass of the glider {eq}m = 0.08\ kg {/eq}.
  • Spring constant {eq}k =...

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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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