Question

Agirl standing upright exerts a pressure of 13600n/m.Given that the total area the shoe and the floor is 0.0368m , Determine the mass of the girl

Answer 1

Appropriate Question:

A girl standing upright exerts a pressure of 13600 N/m² .Given that the total area the shoe and the floor is 0.0368 m² , Determine the mass of the girl.

Answer:

50.048 kg

Explanation:

As per the provided information in the given question, we have :

• Pressure exerted by girl (P) = 13600 N/m²
• Total area of the shoe (A) = 0.0368 m²

We have been asked to calculate the mass of the girl.

In order to calculate the mass of the girl, firstly we'll calculate force applied by her. As it is known to us that, pressure is defined as force per unit area.So,

$\longrightarrow\boxed{\sf{\red{P = \dfrac{F}{A} }}}$

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

Now, substitute the values, we have

$\longrightarrow\sf{13600 \dfrac{N}{m^2}= \dfrac{F}{0.0368 \; m^2} }$

$\longrightarrow\sf{13600 \dfrac{N}{m^2} \times 0.0368 \; m^2= F }$

$\longrightarrow\sf{13600 \times 0.0368 \; N= F }$

$\longrightarrow\sf{13600 \times \dfrac{368}{10000} \; N= F }$

$\longrightarrow\sf{136 \times \dfrac{368}{100} \; N= F }$

$\longrightarrow\sf{ \dfrac{136 \times 368}{100} \; N= F }$

$\longrightarrow\sf{ \dfrac{50048}{100} \; N= F }$

$\longrightarrow\boxed{\sf{ 500.48\; N= F }}$

Now, as we know that Force is the product of mass and acceleration.

$\longrightarrow\boxed{\sf{\red{F = ma}}}$

• F denotes force
• m denotes mass
• a denotes acceleration

Here, acceleration due to gravity is acting on the body that is 10 m/s². Now substitute the values.

$\longrightarrow\sf{500.48 \; N= m \times 10 \; ms^{-2}}$

Newton = 1 kg.m/s². So,

$\longrightarrow\sf{500.48 \; kg.m/s^2= m \times 10 \; ms^{-2}}$

$\longrightarrow\sf{ \dfrac{500.48 \; kg.m/s^2}{10 \; ms^{-2}} = m}$

$\longrightarrow\boxed{\sf{ \red{50.048\; kg= m }}}$

Therefore, mass of the girl is 50.048 kg.

$\rule{200}2$