A light spring of constant k=90.0 N / m is attached vertically to a table (Fig. Pl4.59a). A 2.00

step 1 spring constant K is 90 Newton per meter mass of the balloon is 2 grams density of helium is 0 .

A light spring of constant k=90.0 N / m is attached...

A light spring of constant $k=90.0 \mathrm{N} / \mathrm{m}$ is attached vertically to a table (Fig. Pl4.59a). A $2.00-\mathrm{g}$ balloon is filled with helium (density $=0.180 \mathrm{kg} / \mathrm{m}^{3} )$ to a volume of 5.00 $\mathrm{m}^{3}$ and is then connected to the spring, causing it to stretch as in Figure $\mathrm{P} 14.59 \mathrm{b}$ . Determine the extension distance $L$ when the balloon is in equilibrium.

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Key Concepts

Hooke's Law

Hooke's Law states that the force exerted by an elastic object, such as a spring, is directly proportional to its displacement from equilibrium. This relationship, typically expressed as F = -kx where k is the spring constant and x is the displacement, is fundamental in analyzing systems where elastic restoring forces come into play.

Archimedes' Principle

Archimedes' Principle explains that any object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. This principle is essential for understanding flotation and determining the net upward force acting on objects in a fluid medium.

Equilibrium Condition

The equilibrium condition in mechanics requires that the sum of all forces acting on a system is zero, resulting in no net acceleration. This concept is central when analyzing systems at rest or moving with constant velocity, ensuring that forces such as buoyant force, gravitational force, and elastic force balance each other.

Gravitational Force

Gravitational force, often calculated as the product of mass and the acceleration due to gravity (F = mg), is the force that attracts objects toward the Earth's center. It plays a key role in systems where weight and buoyancy must be balanced, particularly in problems involving vertical equilibrium.

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