A Soap Film on a Slider

solved SurfaceTension

Q. A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire and the light slider supports a weight of 1.5 × 10⁻² N $F_{S} = 1.5 \times 10^{−2}$ N (which includes the small weight of the slider). The length of the slider is 30 cm $l = 30$ cm. What is the surface tension of the film, in N/m?

Inputs

weight

F_{S}

0.015 N

length

l

30 cm

Outputs

tension

S

How it's solved

Solved with SurfaceTension

Given

$F_{S} = 1.5 \times 10^{−2}$ N
$l = 30$ cm

Find $S$ .

Working

$l = 30$ cm $= 0.3$ m
a film pulls with both its faces(slider) $F_{S} = 2 \cdot S \cdot l$
$0.015 = 2 \cdot S \cdot 0.3$
$S = 0.025$ N/m
$S \approx 0.025$ N/mto 2 significant figures

Conclusion

The film has two faces, and each pulls along the whole slider; together they hold up the weight, so the surface tension is the weight over twice the slider's length.

The web of concepts

given read from the words equation asked

The Ruby that solves it

The question and its solution are small Ruby files. The engine runs them.

question.rb

1require_relative "../physics"23question :a_soap_film_on_a_slider do4  kind :numerical5  describes "A U-shaped wire is dipped in a soap solution, and removed. The thin soap film formed between the wire " \6            "and the light slider supports a weight of %{weight} (which includes the small weight of the slider). " \7            "The length of the slider is %{length}. %{tension}, in N/m?"8  given weight: "1.5e-2 N"9  given length: "30 cm"10  asks tension: "What is the surface tension of the film"11end

solution.rb

1require_relative "../questions/a_soap_film_on_a_slider"2require_relative "../science/mechanical_properties_of_fluids/surface_tension"34solve :a_soap_film_on_a_slider, using: SurfaceTension do5  objects :slider67  take weight: slider.pull_of_the_film8  take length: slider.slider_length910  tension = S11  answer tension:, in: "N/m", figures: 21213  conclusion "The film has two faces, and each pulls along the whole slider; together they hold up the " \14             "weight, so the surface tension is the weight over twice the slider's length."15end

playground.rb

1require_relative "../solutions/a_soap_film_on_a_slider"23play_with :a_soap_film_on_a_slider do4  title "A Soap Film on a Slider"5end

The laws it drew on

quantity	written	units	within	from
mass	$m$	kg	0 … ∞	Pressure
gravity	$g$	m/s²	—	Pressure
thrust	$F$	N	—	Pressure
area	$A$	m²	—	Pressure
pressure	$P$	Pa	0 … ∞	Pressure
pressure at the surface	$P_{a}$	Pa	—	PressureAtDepth
density	$ρ$	kg/m³	0 … ∞	PressureAtDepth
depth	$h$	m	—	PressureAtDepth
gauge pressure	$P_{g}$	Pa	—	PressureAtDepth
surface tension	$S$	N/m	—	SurfaceTension
radius	$r$	m	—	SurfaceTension
excess pressure	$Δ P$	Pa	—	SurfaceTension
excess pressure in a soap bubble	$Δ P_s$	Pa	—	SurfaceTension
pressure inside	$P_{i}$	Pa	—	SurfaceTension
slider length	$l$	m	—	SurfaceTension
pull of the film	$F_{S}$	N	—	SurfaceTension
pressure of ground	$P_{g}$	Pa	0 … ∞
thrust on ground	$F_{g}$	N	—
area of ground	$A_{g}$	m²	—
pressure of slider	$P$	Pa	0 … ∞
thrust on slider	$F$	N	—
area of slider	$A$	m²	—
gauge pressure on ground	$P_{g,g}$	Pa	—
depth of ground	$h_{g}$	m	—
gauge pressure on slider	$P_{g}$	Pa	—
depth of slider	$h$	m	—
excess pressure of ground	$Δ P_{g}$	Pa	—
radius of ground	$r_{g}$	m	—
excess pressure of slider	$Δ P$	Pa	—
radius of slider	$r$	m	—
excess pressure in a soap bubble of ground	$Δ {P_s}_{g}$	Pa	—
excess pressure in a soap bubble of slider	$Δ P_s$	Pa	—
pressure inside of ground	$P_{i,g}$	Pa	—
pressure inside of slider	$P_{i}$	Pa	—
pull of the film on ground	$F_{S,g}$	N	—
slider length of ground	$l_{g}$	m	—
pull of the film on slider	$F_{S}$	N	—
slider length of slider	$l$	m	—
mass of slider	$m$	kg	0 … ∞

P_{s} = \frac{F_{s}}{A_{s}}

pressure is force over area

P_{g,p} = ρ \cdot g \cdot h_{p}

pressure of the fluid above

P_{p} = P_{a} + P_{g,p}

pressure adds the surface s

Δ P_{b} = \frac{2 \cdot S}{r_{b}}

excess pressure in a bubble in liquid

Δ {P_s}_{b} = \frac{4 \cdot S}{r_{b}}

excess pressure in a soap bubble with two surfaces

P_{i,b} = P_{b} + Δ P_{b}

pressure inside a bubble

F_{S,s} = 2 \cdot S \cdot l_{s}

a film pulls with both its faces

P_{g} = \frac{F_{g}}{A_{g}}

pressure is force over area(ground)

P = \frac{F}{A}

pressure is force over area(slider)

P_{g,g} = ρ \cdot g \cdot h_{g}

pressure of the fluid above(ground)

P_{g} = ρ \cdot g \cdot h

pressure of the fluid above(slider)

P_{g} = P_{a} + P_{g,g}

pressure adds the surface s(ground)

P = P_{a} + P_{g}

pressure adds the surface s(slider)

Δ P_{g} = \frac{2 \cdot S}{r_{g}}

excess pressure in a bubble in liquid(ground)

Δ P = \frac{2 \cdot S}{r}

excess pressure in a bubble in liquid(slider)

Δ {P_s}_{g} = \frac{4 \cdot S}{r_{g}}

excess pressure in a soap bubble with two surfaces(ground)

Δ P_s = \frac{4 \cdot S}{r}

excess pressure in a soap bubble with two surfaces(slider)

P_{i,g} = P_{g} + Δ P_{g}

pressure inside a bubble(ground)

P_{i} = P + Δ P

pressure inside a bubble(slider)

F_{S,g} = 2 \cdot S \cdot l_{g}

a film pulls with both its faces(ground)

F_{S} = 2 \cdot S \cdot l

a film pulls with both its faces(slider)