A light spring of constant k=90.0 N / m is attached vertically to a table (Fig. Pl4.55 a). A 2.0

step 1 Question number 55. The spring constant is K equal to 90 Newton per meter. The mass of balloon i

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. Pl4.55 a). A 2.00 -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 the spring to stretch as shown in Figure $\mathrm{P} 14.55 \mathrm{b}$ . Determine the extension distance $L$ when the balloon is in equilibrium.

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Key Concepts

Gravitational Force

Gravitational force is the force with which the earth attracts an object towards its center, calculated as the product of the object's mass and the acceleration due to gravity. This force is a crucial downward component that must be balanced by upward forces in equilibrium problems.

Force Equilibrium

Force equilibrium occurs when the sum of all forces acting on an object equals zero, meaning there is no net acceleration. In vertical systems, the upward buoyant force and the downward forces such as gravitational weight and the restoring spring force must balance to determine the equilibrium position.

Buoyant Force (Archimedes’ Principle)

Archimedes’ Principle explains that any body fully or partially immersed in a fluid experiences an upward force equal to the weight of the fluid displaced by the body. In problems involving balloons or objects in a fluid, this force plays a key role in determining the net upward force acting against gravity.

Hooke's Law

Hooke's Law states that the force exerted by a spring is proportional to its displacement from equilibrium, with the constant of proportionality being the spring constant. This concept is crucial in understanding how the restoring force of the spring balances other forces acting on the system when it is displaced.

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