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A 1.18 kg block is attached to a horizontal spring with spring constant 3750 N/m. The block is at...

Question:

A 1.18 kg block is attached to a horizontal spring with spring constant 3750 N/m. The block is at rest on a frictionless surface. A 7.70 g bullet is fired into the block, in the face opposite the spring, and sticks. The subsequent oscillations have an amplitude of 13.4 cm.

Part A) Find the total energy of the oscillator.

Part B) Find the speed of the bullet and block immediately after the collision.

Part C) Find the speed of the bullet just before it hits the block.

Spring Potential Energy:

Consider an object attached to the end of a spring that is oscillating back and forth. This object's speed (and kinetic energy) will constantly change, increasing and decreasing. When the object is moving at a low speed or is momentarily stopped, what has happened to its previous kinetic energy? It must be stored somewhere as potential energy, which is then converted back into kinetic energy when the block speeds up again.

This is spring potential energy {eq}U {/eq}, given by the formula:

{eq}U = \frac{1}{2}kx^2 {/eq}

Here {eq}k {/eq} is the spring constant and {eq}x {/eq} is the current displacement from equilibrium.

Answer and Explanation: 1

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A) The total energy of the oscillator is the sum of its potential energy and kinetic energy at any given moment.

{eq}E = U + K {/eq}

To simplify...

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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