Question

What force is required to produce a pressure of 25000 N/m^2 when the surface area is 0.50 cm^2

Answer 1

Question:

• What force is required to produce a pressure of 25000 N/m² when the surface area is 0.50 cm²

Answer:

• 1.25 newton ( N ) force is required to gain the following pressure

Explanation:

Given that:

• The pressure produced is 25000 N/m²
• The surface area of the object is 0.50 cm²

To Find:

• The amount of force applied of the body

Formula Used:

$\bigstar \; {\underline{\boxed{\bf{ P = \dfrac{F}{A} }}}}$

Where,

• P denotes the pressure
• F denotes the force
• A denotes the area

Here we know that ,

• Pressure produced is 25000 N/m²
• Area of the object is 0.50 cm²

Required Knowledge,

→ S. I unit of force is Newton

→ S.I unit of area is Meter²

→ S.I unit of pressure is newton / meter²

Converting area into SI system,

⇨ 1 cm = 0.01 metre

⇨ 1 cm² = 0.0001 metre²

⇨ 0.50 cm² = 0.0001 × 0.5 metre²

⇨ 0.50 cm² =  0.00005

Calculations:

→ P = F/A

→ F = P × A

→ F = 25000 × 0.00005 N

→ F = 25000 × 5 / 100000 N

→ F = 0.25 × 5 N

→ F = 1.25 N

Therefore:

• The force to be applied on the object is 1.25 N

Answer 2

1.25 N of force is required to produce a pressure of 25,000 Pa on an area of 0.5 cm²

Explanation

In the question, we've been asked to calculate the amount force which can produce a pressure of 25000 N/m² (25000 Pa) on an area of 0.5 m².

Simply on having a look at the S.I. unit of pressure, i.e., newtons per metre square, the formula for finding the force required is very clear.

$\qquad \: { \sf{ \bigg[Pressure = \dfrac{N}{m^2}\xrightarrow{S.I. \: unit} \dfrac{Force}{Area} \bigg]}}$

$\qquad \qquad \: \: \: \boxed{ \sf {Pressure = \dfrac{Force}{Area}}}$

By using this formula, the amount of force required can be determined.

• Pressure (P) = 25000 Pa
• Area (A) = 0.5 cm²
• Force (F) = ?

The value of area has to be converted to m² beforehand, since it's been given in the unit of cm².

Dividing the area value by 10000:

$\twoheadrightarrow \quad{ \sf{ \dfrac{0.5}{10000} }}$

$\twoheadrightarrow \quad{ \sf{ \dfrac{{}^{5} / {}_{10}}{10000} }}$

$\twoheadrightarrow \quad{ \sf{ \dfrac{5}{10} \times \dfrac{1}{10000} }}$

$\twoheadrightarrow \quad{ \sf{ \dfrac{5 \times 1 }{100000} }}$

$\twoheadrightarrow \quad{ \sf{ \dfrac{5 }{100000} }}$

$\twoheadrightarrow \quad{ \sf{0.00005 \: {m}^{2} } }$

Since the values are applicable now, substituting them in the formula:

$\twoheadrightarrow \quad\sf {Pressure = \dfrac{Force}{Area}}$

$\twoheadrightarrow \quad\sf {25000 = \dfrac{F}{0.00005}}$

$\twoheadrightarrow \quad\sf {25000 \times 0.00005 = F}$

$\twoheadrightarrow \quad{ \sf{25 \cancel{000} \times \dfrac{5}{100 \cancel{000}} =F}}$

$\twoheadrightarrow \quad{ \sf{25 \times \dfrac{5}{100} =F}}$

$\twoheadrightarrow \quad{ \sf{ \dfrac{25 \times 5}{100}=F}}$

$\twoheadrightarrow \quad{ \sf{ \dfrac{125}{100}=F}}$

$\twoheadrightarrow \quad \underline{ \boxed{ \bf \red{ 1.25\:N =Force}}}$

∴ 1.25 N of force is required to create the given amount of pressure.