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A horizontal spring attached to a wall has a force constant of 850 N/m. A block of mass 1.00 kg...

Question:

A horizontal spring attached to a wall has a force constant of 850 N/m. A block of mass 1.00 kg is attached to the spring and oscillates freely on a horizontal, frictionless surface. The initial goal of this problem is to find the velocity at the equilibrium point after the block is released.

(a) What objects constitute the system, and through what forces do they interact?

(b) What are the two points of interest?

(c) Find the energy stored in the spring when the mass is stretched 6.00 cm from equilibrium and again when the mass passes through equilibrium after being released from rest.

(d) Write the conservation of energy equation for this situation and solve it for the speed of the mass as it passes equilibrium. Substitute to obtain a numerical value.

(e) What is the speed at the halfway point? Why isn't it half the speed at equilibrium?

Spring:

Spring is coiled, hardened steel usually nonferrous material which is used to store elastic potential energy, dampened vibrations, or to exert force. One of the example of a spring used to store energy are the spring in watches.

Answer and Explanation:

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Given:

  • {eq}k = 850 \frac{\text{ N}}{\text{ m}} {/eq}
  • {eq}m = 1 \text{ kg} {/eq}

(a)

The motion of the spring determines the motion of the block....

See full answer below.


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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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