# Newton's Second Law / Archimedes Principle

• nxn
In summary, the density of the wood is 722 kg/m^3 and the density of the oil is 1000 kg/m^3. The block of wood floats because it is less dense than water, and its density is determined by the fraction of its volume that is submerged in the fluid.
nxn

## Homework Statement

A block of wood floats in fresh water with 0.722 of its volume V submerged and in oil with 0.895 V submerged. Find the density of (a) the wood and (b) the oil.

## Homework Equations

mass = density x volume

f = ma

conservation of mass

$F_{weight} - F_{buoyancy} = 0$ when an object floats on the surface of a fluid.

density of water = $1000 \frac{kg}{m^3}$

## The Attempt at a Solution

$ρ_{wood}(V)g - ρ_{water}(.722V)g = m\cdot0$ when the block floats

so

$ρ_{wood}(V)g = ρ_{water}(.722V)g$

and

$ρ_{wood} = ρ_{water}\frac{(.722V)g}{(V)g}$

we know density of water = $1000 \frac{kg}{m^3}$ so

$ρ_{wood} = 1000(.722) = 722 \frac{kg}{m^3}$

Can you confirm that this looks correct? I've been waiting for a chance to practice with LaTeX and decided to jump in with this problem. I appreciate your time.

Welcome to PF nxn,
nxn said:

## Homework Statement

A block of wood floats in fresh water with 0.722 of its volume V submerged and in oil with 0.895 V submerged. Find the density of (a) the wood and (b) the oil.

## Homework Equations

mass = density x volume

f = ma

conservation of mass

$F_{weight} - F_{buoyancy} = 0$ when an object floats on the surface of a fluid.

density of water = $1000 \frac{kg}{m^3}$

## The Attempt at a Solution

$ρ_{wood}(V)g - ρ_{water}(.722V)g = m\cdot0$ when the block floats

so

$ρ_{wood}(V)g = ρ_{water}(.722V)g$

and

$ρ_{wood} = ρ_{water}\frac{(.722V)g}{(V)g}$

we know density of water = $1000 \frac{kg}{m^3}$ so

$ρ_{wood} = 1000(.722) = 722 \frac{kg}{m^3}$

Can you confirm that this looks correct? I've been waiting for a chance to practice with LaTeX and decided to jump in with this problem. I appreciate your time.

Yes, this looks correct. If the wood floats, it must be less dense than water, and it makes perfect sense that it would be less dense than water by a factor of 0.722, the fraction of the wood volume that had to be displaced.

Thanks! This ended up working out just fine.

## What is Newton's Second Law?

Newton's Second Law, also known as the Law of Force and Acceleration, states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The formula for this law is F=ma, where F is the net force, m is the mass, and a is the acceleration.

## How is Newton's Second Law applied in real life?

Newton's Second Law is applied in many real life situations, such as when a car accelerates or decelerates, when a pitcher throws a ball, or when a rocket launches into space. It helps us understand the relationship between force, mass, and acceleration, and allows us to predict and control the motion of objects.

## What is Archimedes Principle?

Archimedes Principle states that the buoyant force acting on an object immersed in a fluid is equal to the weight of the fluid displaced by the object. This principle explains why objects float or sink in a fluid, and is also used to calculate the density of an object.

## How is Archimedes Principle applied in real life?

Archimedes Principle is applied in many real life situations, such as when a ship floats on water, when a hot air balloon rises, or when a submarine sinks. It also plays a crucial role in the design and functionality of various watercrafts and underwater structures.

## What is the difference between Newton's Second Law and Archimedes Principle?

Newton's Second Law and Archimedes Principle are two different laws that govern different aspects of motion. Newton's Second Law deals with the relationship between force, mass, and acceleration, while Archimedes Principle deals with the buoyant force acting on an object immersed in a fluid. While Newton's Second Law applies to all types of motion, Archimedes Principle only applies to objects in fluids.

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