Question

0.24. A bird weighing 2 kg strikes an airplane diving at 900 km/h. With what force does the bird strike the
plane if the collision lasts for 0.001 s? What is the pressure on the glass surface on which it collides
if the contact area is 1000 cm?​

Answer 1

Given :

• Mass of bird = 2 kg

• Velocity = 900 km/h

• Time of collision = 0.001 s

• Area of contact = 1000 cm

To Find :

• Force exerted by the bird on plane during collision .

• Pressure exerted by the bird on the surface of contact.

Solution :

⠀⠀⠀⠀To Find the Force exerted :

Formula for Force : $\underline{\bf{F = ma}}$

Where :

• F = Force Exerted

• a = Acceleration Produced

According to the formula , Force is the product of mass and acceleration , so to find force we need both the mass and acceleration.

To find the acceleration produced , we can use the first Equation of Motion .

First Equation of Motion :

⠀⠀⠀⠀⠀⠀$\underline{\bf{v = u + at}}$

Where :

• v = Final Velocity
• u = Initial Velocity
• a = Acceleration
• t = time taken

Here , the velocity given is in km/h , so need to find the velocity in m/s.

To convert the unit in m/s from km/h , multiply it by 5/18.

⠀⠀⠀⠀⠀⠀⠀⠀⠀v = 900 km/h

⠀⠀⠀⠀⠀⠀⠀⠀⠀v = (900 × 5/18) m/s

⠀⠀⠀⠀⠀⠀⠀⠀⠀v = (50 × 5) m/s

⠀⠀⠀⠀⠀⠀⠀⠀⠀v = 250 m/s

Hence, the velocity of bird in m/s is 250 m/s.

Now , using the first Equation of Motion and substituting the values in it , we get :

$:\implies \bf{v = u + at}$

$:\implies \bf{250 = 0 + a \times 0.001}$

$:\implies \bf{250 = \dfrac{1}{1000}a}$

$:\implies \bf{250 \times 1000 = a}$

$:\implies \bf{250000 = a}$

$\therefore \bf{Acceleration = 250000\:ms^{-2}}$

Hence, the acceleration produced is 250000 m/s².

Since , we know the acceleration produced and the mass of the bird , we can find the force exerted.

Using the formula for force exerted and substituting the values in it , we get :

$:\implies \bf{F = ma}$

$:\implies \bf{F = 2 \times 250000}$

$:\implies \bf{F = 500000}$

$\therefore \bf{Force = 5 \times 10^{5}\:N}$

Hence, the acceleration produced is 5 × 10⁵ N.

⠀⠀⠀⠀⠀⠀To find the Pressure :

Formula : $\boxed{\bf{P= \dfrac{F}{A}}}$

Where :

• P = Pressure
• F = Force
• A = Area of contact

Here , the area of contact is in cm, so we need to convert it in m.

We know that , 1 m = 100 cm.

So ,1000 cm = 10 m.

Hence, the area of contact in m is 10 m.

Now , using the formula and substituting the values in it, we get :

$:\implies \bf{P = \dfrac{F}{A}}$

$:\implies \bf{P = \dfrac{500000}{10}}$

$:\implies \bf{P = 50000}$

$:\implies \bf{Pressure = 5 \times 10^{4}\:Pa}$

Hence, the pressure exerted is 5 × 10⁴ Pa.