A 170-kg granite rock ( ρ=2700 kg / m^3 ) is dropped into a lake. A man dives in and tries to l

step 1 This question covers the concept of buoyancy and from the concept of buoyancy the weight of the

A 170-kg granite rock ( ρ=2700 kg / m^3 ) is dropped into a...

A $170-\mathrm{kg}$ granite rock ( $\rho=2700 \mathrm{~kg} / \mathrm{m}^3$ ) is dropped into a lake. A man dives in and tries to lift the rock. Determine how much force the man needs to apply to lift it from the bottom of the lake. Do you think he can do it?

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Key Concepts

Apparent Weight

Apparent weight is the weight of an object as measured when it is submerged in a fluid, resulting from the subtraction of the buoyant force from the object's actual weight. This concept is important when calculating the net force required to lift an object underwater.

Buoyant Force

The buoyant force is the net upward force exerted by a fluid on an immersed object. It is calculated by multiplying the volume of the displaced fluid by the fluid's density and the acceleration due to gravity, effectively reducing the effective weight of the object in the fluid.

Archimedes' Principle

Archimedes' Principle states that any object immersed in a fluid experiences an upward buoyant force equal to the weight of the fluid that the object displaces. This principle is the foundation for understanding how and why objects appear lighter in fluids.

Density and Volume Relationship

Density is defined as mass per unit volume. This concept is used to find the volume of an object when its mass and density are known, which is critical for determining the amount of fluid the object displaces when submerged.

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