Can wooden block float on freon?
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Answered by
1
Answer:
If it floats, the buoyancy has to be greater than the weight. The weigh is easy to compute from the mass (3.5 kg). However, to compute the buoyancy, you need to know the volume of the wood block in addition to the mass (given) and the density of water, which we know is about 998.2071 kg/m^3 at STP.
The weight formula uses Newton's second law (F = m•a) in the form:
w = m • g
where:
w is the weight (force of gravity on a mass)
m is the mass
g is the acceleration due to gravity.
The formula for buoyancy is:
F = V•ρ•g
where
F = buoyant force
V = body volume
ρ = density of fluid
g = acceleration of gravity
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Answered by
0
The buoyant force acting on an immersed body is equal to the weight of the fluid displaced by it, if the fluid is in rest. In this case, the fluid is accelerating upwards so the buoyant force must also provide the displaced fluid force to accelerate. Therefore, buoyant force will be fVρg
eff
where V = volume of body and f = fraction of volume of body immersed in fluid and g
eff
=g+a=1.5g.
When fluid is at rest: f=1−0.4=0.6, so 0.6Vρg=Vρ
b
g where ρ
b
is the density of the block.
⇒ρ
b
=0.6ρ.
In the second case: 1.5fVρg=Vρ
b
g+Vρ
b
a=1.5Vρ
b
g⇒fρ=ρ
b
⇒f=0.6.
Thus, the fraction of immersed volume remains the same.
Body will float with 40% of the volume above water surface.
eff
where V = volume of body and f = fraction of volume of body immersed in fluid and g
eff
=g+a=1.5g.
When fluid is at rest: f=1−0.4=0.6, so 0.6Vρg=Vρ
b
g where ρ
b
is the density of the block.
⇒ρ
b
=0.6ρ.
In the second case: 1.5fVρg=Vρ
b
g+Vρ
b
a=1.5Vρ
b
g⇒fρ=ρ
b
⇒f=0.6.
Thus, the fraction of immersed volume remains the same.
Body will float with 40% of the volume above water surface.
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