Λcubical block of wood of edge 3 cm floats in water. 'The lower surface of the cube just touche

step 1 so let's solve this question when block just touches the spring it floats really on water that w

Λcubical block of wood of edge 3 cm floats in water. 'The...

$\Lambda$ cubical block of wood of edge $3 \mathrm{~cm}$ floats in water. 'The lower surface of the cube just touches the free end of a vertical spring fixed at the bottom of the pot. Find the maximum weight that can be put on the block without wetting it. Density of wood $=800 \mathrm{~kg} / \mathrm{m}^{3}$ and spring constant of spring $=50 \mathrm{~N} / \mathrm{m}$. Take $g=10 \mathrm{~m} / \mathrm{s}^{2}$

Key Concepts

Equilibrium of Forces

Equilibrium conditions require that the sum of all forces acting on a system be zero for the system to be at rest. In problems involving floating objects with additional weights and elastic supports, setting up an equation equating gravitational force, buoyant force, and spring force is key to solving for unknown quantities like the maximum additional weight.

Archimedes' Principle

This principle states that a body immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid displaced by it. It is essential for understanding floating objects and determining how much of an object remains submerged when floating.

Density and Buoyancy

Density is a measure of mass per unit volume and plays a critical role in determining whether an object sinks or floats. In problems involving floating objects, the density of the object relative to that of the fluid dictates the volume of fluid displaced, which directly affects the buoyant force acting on the object.

Hooke's Law

Hooke's Law relates the force exerted by a spring (or any elastic medium) to the displacement it experiences from its equilibrium position. The law is expressed as F = kx, where k is the spring constant and x is the displacement. This concept is vital when analyzing systems where elastic forces interact with gravitational and buoyant forces.

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