It is weigh-in time for the local under-

It is weigh-in time for the local under- - 85 -kg rugby team. The bathroom scale used to assess eligibility can be described by Hooke's law and is depressed 0.75 $\mathrm{cm}$ by its maximum load of 120 $\mathrm{kg}$ . (a) What is the spring's effective spring constant? (b) A player stands on the scales and depresses it by 0.48 $\mathrm{cm} .$ Is he eligible to play on this under-85 kg team?

It is weigh-in time for the local under- - 85 -kg rugby team. The bathroom scale used to assess eligibility can be described by Hooke's law and is depressed 0.75 $\mathrm{cm}$ by its maximum load of 120 $\mathrm{kg}$ . (a) What is the spring's effective spring constant? (b) A player stands on the scales and
depresses it by 0.48 $\mathrm{cm} .$ Is he eligible to play on this under-85
kg team?

Key Concepts

Equilibrium in Mechanical Systems

Equilibrium in a mechanical system is achieved when all forces acting on the system balance each other out. In the case of a weighing scale, equilibrium occurs when the upward restoring force from the spring equals the downward gravitational force acting on the mass.

Gravitational Force

Gravitational force is the force with which the Earth attracts objects, and it is calculated using the equation F = mg, where m is mass and g is the gravitational acceleration. This force is essential in converting a physical mass into the force that causes a spring to compress or extend.

Application of Elasticity in Measurement Devices

Elastic systems, such as the spring in a bathroom scale, use the principles of elasticity and Hooke’s law to convert a physical deformation into a measurable quantity. This application is crucial for devices that determine weight based on the amount of displacement caused by an applied force.

Hooke's Law

Hooke’s law states that the force exerted by a spring is directly proportional to its displacement from equilibrium (F = kx). This fundamental principle is used to analyze systems where elastic behavior is prominent, such as in measuring devices that rely on spring deformation.

Spring Constant

The spring constant, denoted as k, quantifies the stiffness of a spring by describing how much force is needed to produce a unit displacement. It is a critical parameter for understanding and predicting the behavior of elastic systems under various loads.

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