Question

a hammer hits a nail with a force of 200N the piont of the nail has an area of 0.5mm2 touching a piece of wood. calculate the pressure of wood

Answer 1

Solution :-

Given ,

• Force acted on nail by the hammer = 200N
• Area of nail on the wood piece = 0.5 mm²

We need to find ,

• Pressure acted by the nail on wood = ?

As we know that ,

• Pressure = Force ÷ Area

Substituting ,

• Force = 200 N
• Area = 0.5 mm² = 5 × 10⁻⁷ m²

Substituting the values we have ,

⇒ Pressure = $\sf\dfrac{200}{5\times 10^{-7}}$

⇒ Pressure = $\sf\dfrac{200}{5\times\frac{1}{10^7}}$

⇒ Pressure = $\sf\dfrac{2\times 10^2}{\frac{5}{10^7}}$

⇒ Pressure = $\sf 2\times {10^2}\times\dfrac{10^7}{5}$

⇒ Pressure = $\sf \dfrac{2\times 10^9}{5}$

⇒ Pressure = $\bf 4\times 10^8$ pa

Hence, pressure = 4 × 10⁸ pascal

Answer 2

Answer:

$\huge{\fcolorbox{black} {black}{\color{yellow}{ANSWER}}}$

GIVEN :

• Force exerted on the nail by the hammer = 200 N
• Area of nail on the wooden piece = 0.5 mm²

TO FIND :

• Pressure exerted by the nail on the wood

SOLUTION :

$\boxed{\large\red{Pressure = \frac{force}{area}}}$

Substituting the values .

$Area = 0.5 \: mm² = 5 \times {10}^{ - 7} \: {m}^{2}$

Since we know 1 mm² = 10-⁸ m²

Force = 200 N

$\implies Pressure = \frac{200}{5 \times {10}^{ - 7} }$

$\implies Pressure = \frac{40}{ {10}^{ - 7} }$

Since 5 × 40 = 200

$\implies Pressure = 40 \times {10}^{7}$

Since we know

${a}^{x} = \frac{1}{ {a}^{ - x} }$

$</strong><strong>\</strong><strong>green</strong><strong>{</strong><strong>\</strong><strong>boxed</strong><strong>{</strong><strong>\</strong><strong>blue</strong><strong>{</strong><strong>\</strong><strong>boxed</strong><strong>{</strong><strong>So \: \: pressure = 4 \times {10}^{8} \: pascal</strong><strong>}</strong><strong>}</strong><strong>}</strong><strong>}</strong><strong>$

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Knowledge EXPRESS:

SI Unit of pressure is Pascal (Pa).

Where

1 Pascal is the pressure exerted by a force of 1 N on 1m² area.

Force = ma (m is mass and a is acceleration).

So pressure formula may also take the form of

$</strong><strong>\</strong><strong>large</strong><strong>\</strong><strong>red</strong><strong>{</strong><strong>p ressure = \frac{ma}{area} </strong><strong>}</strong><strong>$

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Hope it helps

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