Question

A bird of mass 400g, falls into a chimney of height 10m. If it lands at the bottom with a speed of 4ms/. During the fall how much work was done on the bird by air resistance?

Answer 1

36 Joules

Step-by-step explanation

the work done is the amount of energy transmited ( the change of energy)

Step 1

find the potential energy at the moment before the birds falls

the potential energy is given by :

`\begin{gathered} E_p=mgh \\ \text{where} \\ m\text{ is the mass } \\ g\text{ is the acceleration due to gravity} \\ \text{and h is the height, so} \end{gathered}`

let

m= 400g=0.4 kg

replace

`\begin{gathered} E_p=mgh \\ E_p=0.4\text{ Kg}\cdot9.8m(m)/(s^2)\cdot10m \\ E_p=39.2\text{ Joules} \end{gathered}`

Step 2

now, the energy at the bottom

when the bird is the bottom it has kinetic energy, it is given by the expression

`\begin{gathered} E_k=(1)/(2)mv^2 \\ \text{where m is the mass} \\ \text{and v is the velocity of the object} \end{gathered}`

then,

let

m=0.4 kg

v=4 m/s

replace.

`\begin{gathered} E_k=(1)/(2)mv^2 \\ E_k=(1)/(2)(0.4kg)(4(m)/(s))^2 \\ E_k=(1)/(2)(0.4kg)(16(m^2)/(s^2)) \\ E_k=3.2\text{ Joules} \end{gathered}`

Step 3

finally, the work done by the air resitance, is the difference of the energy ,so

`\begin{gathered} \text{Work done(w)=E}_f-E_i \\ \text{replace} \\ W=3.2\text{ J-}39.2 \\ W=-36\text{ Joules} \end{gathered}`

the negative sign indicates that the work done by the air was against the movement of the bird

therefore, the answer is

36 Joules

I hope this helps you