A 5.00 kg block is moving at v0 = 6.00 m/s along a frictionless, horizontal surface toward a...

Question:

A 5.00 kg block is moving at v0 = 6.00 m/s along a frictionless, horizontal surface toward a spring with force constant k = 500 N/m that attached to a wall. The spring has negligible mass. Find the maximum distance the spring will be compressed. If the spring is to compress by no more than 0.150 m, what should be the maximum velocity of v0?

Spring Potential Energy:

Consider an object attached to a compressed spring. When the object is allowed to move, it will shoot forward and then oscillate back and forth, as the spring stretches and compresses. This movement requires energy, which must have come from somewhere. There must have been potential energy stored in the initial configuration of the object and spring.

The potential energy of a stretched or compressed spring is called spring potential energy. Its formula is:

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

Here, k is the spring constant and x is the spring's displacement from its unstretched (equilibrium) position.

Answer and Explanation: 1

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The answers are (a) 60 cm and (b) 1.5 m/s.

(a) First, we want to find the spring's compression distance. We can do this with conservation of energy.

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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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