Question
Asked Feb 18, 2020
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A spring with a force constant of 20 newtons per meter is known to obey Hooke's Law. The spring is attached to a mass of 5 kilograms and placed on a horizontal, frictionless surface. The mass is displaced 3 meters from its equilibrium position and released. What is the kinetic energy of the mass as it passes through its equilibrium position?

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Expert Answer

Step 1

Introduction- The principle of the conservation of mechanical energy states that the total mechanical energy in a system (i.e., the sum of the potential plus kinetic energies) remains constant as long as the only forces acting are conservative forces (i.e., spring force, gravitational force).

given- Force constant of a spring,

Physics homework question answer, step 1, image 1

 Mass,

Physics homework question answer, step 1, image 2

 Displacement,

Physics homework question answer, step 1, image 3

Determine the kinetic energy of the mass at the equilibrium position of a spring 

 

 

 

Step 2

 From the conservation of mechanical energy 

Physics homework question answer, step 2, image 1

When the mass displaced 3 meters from its equilibrium position initial kinetic energy

Physics homework question answer, step 2, image 2

And initial potential energy

Physics homework question answer, step 2, image 3

When the mass passes through the equilibrium position of spring final kinetic energy Physics homework question answer, step 2, image 4

And final potential energy 

Physics homework question answer, step 2, image 5

Step 3

From the conservation of mechanical energy

Physics homework question answer, step 3, image 1

...

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