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Question: Calculate the force required to take away a flat circular plate of radius \(0.01\;{\text{m}}\) from ...

Calculate the force required to take away a flat circular plate of radius 0.01  m0.01\;{\text{m}} from the surface of water when the surface tension of water is 0.075  N/m0.075\;{\text{N/m}}.

Explanation

Solution

Here, the interface between the water, plate and air is a circle of given radius. To determine the length of the plate circumference of the circle is required.
Formula Used: Here we will be using the formulaT=FLT = \dfrac{F}{L}, where TT is the surface tension of water, FF is the force required to take away a circular plate and LL is the length of the surface.

Complete step by step solution
The surface tension of water is T=0.075  N/mT = 0.075\;{\text{N/m}}.
Radius of the flat circular plate is R=0.01  mR = 0.01\;{\text{m}}.
As the interface between the water, plate and air is a circle of given radius, then the length of the circular plate will be equal to the circumference of the circle.
The formula for circumference of a circle is L=2πRL = 2\pi R.
From the above, the radius of the flat circular plate is RR.
Now, substitute the value of radius in the above formula of circumference.
⇒L=2π×0.01  m\Rightarrow L = 2\pi \times 0.01\;{\text{m}}
The formula for surface tension of water is T=FLT = \dfrac{F}{L}.
Now write force in terms of tension and length from the above formula.
⇒F=T×L\Rightarrow F = T \times L
Substitute the given value of surface tension and length of the circular plate in the above formula.
⇒F=0.075  N/m×2π×0.01  m\Rightarrow F = 0.075\;{\text{N/m}} \times 2\pi \times 0.01\;{\text{m}}
Substitute 3.143.14 for π\pi and multiply the terms to solve the above expression.
⇒F=0.004717  N\Rightarrow F = 0.004717\;{\text{N}}
So, the force required to take away a flat circular plate from the surface of water is 0.004717  N0.004717\;{\text{N}}.

Additional information surface tension is the property of a liquid or fluid surface to contract into the possible minimum surface area. Surface tension in terms of force is defined as the force per unit length. Its SI unit is Newton per metre or dyne per centimetre.

Note The length of the surface depends on the type of the surface given. Knowledge of the standard unit of the force, tension and length is required.