You push a 2.0 kg block against a horizontal spring,...

You push a $2.0 \mathrm{~kg}$ block against a horizontal spring, compressing the spring by $15 \mathrm{~cm}$. Then you release the block, and the spring sends it sliding across a tabletop. It stops $75 \mathrm{~cm}$ from where you released it. The spring constant is $200 \mathrm{~N} / \mathrm{m}$. What is the block-table coefficient of kinetic friction?

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Key Concepts

Hooke's Law

Hooke's Law describes how the force exerted by a spring is proportional to its displacement from equilibrium, expressed as F = -kx. This principle is crucial for understanding how springs store and release energy when compressed or extended.

Spring Potential Energy

When a spring is compressed or stretched, it stores energy in the form of potential energy, which is calculated using the formula U = 1/2 k x^2. This concept is key to analyzing situations where the energy stored in the spring is converted into kinetic energy or work done against other forces.

Work-Energy Principle

The work-energy principle states that the work done by all forces acting on an object equals the change in its kinetic energy. In problems involving friction, the energy initially stored in a spring or the initial kinetic energy is partly dissipated as work done against friction while the object moves.

Friction and Coefficient of Kinetic Friction

The friction force that opposes the motion of an object sliding on a surface is given by F_friction = ?k N, where ?k is the coefficient of kinetic friction and N is the normal force. This concept is vital for determining how much energy is lost due to friction as an object moves across a surface.

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