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Peregrine falcons frequently grab prey birds from the air, as BI0 in Example 9.10. Sometimes they strike at high enough speeds that the force of the impact disables prey birds. A 480 g per- egrine falcon high in the sky spies a 240 g pigeon some dis- tance below. The falcon slows to a near stop, then goes into ve-called a stoop-and picks up speed as she falls. The n reaches a vertical speed of 45 m/s before striking the pigeon, which we can assume is stationary. The falcon strikes the pigeon and grabs it in her talons. The collision between the falco birds lasts 0.015 s. a. What is the final speed of the falcon and pigeon? b. What is the average force on the pigeon during the impact?

Respuesta :

skyluke89

A) 30 m/s

The problem can be solved by using the law of conservation of momentum. In fact, the total momentum falcon+pigeon before the collision must be equal to the total momentum falcon+pigeon after the collision:

[tex]p_i = p_f[/tex]

[tex]m_f u_f + m_p u_p = (m_f + m_p) v[/tex]

where

mf = 0.480 g is the mass of the falcon

uf = 45 m/s is the initial velocity of the falcon

mp = 0.240 g is the mass of the pigeon

up = 0 is the initial velocity of the pigeon

v is the final combined velocity of pigeon+falcon

Solving the equation for v, we find

[tex]p=\frac{m_f u_f}{m_f +m_p}=\frac{(0.480 kg)(45 m/s)}{0.480 kg+0.240 kg}=30 m/s[/tex]

B) 480 N

The average force on the pigeon during the impact is given by

[tex]F=\frac{\Delta p}{\Delta t}[/tex]

where

[tex]\Delta p[/tex] is the change in momentum of the pigeon

[tex]\Delta t[/tex] is the duration of the collision

here we have:

- Change in momentum of the pigeon:

[tex]\Delta p = m (v-u)=(0.240 kg)(30 m/s-0)=7.2 kg m/s[/tex]

- Duration of the collision:

[tex]\Delta t=0.015 s[/tex]

So the average force is

[tex]F=\frac{7.2 kg m/s}{0.015 s}=480 N[/tex]

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