Final answer:
To calculate the average force on the pigeon during the collision with the peregrine falcon, we use the impulse-momentum theorem. The average force is found by dividing the change in momentum by the time interval of the collision. The result is an average force of 2560 N on the pigeon.
Step-by-step explanation:
To calculate the average force exerted on a pigeon during a collision with a peregrine falcon, we need to use the impulse-momentum theorem. The theorem states that the impulse on an object is equal to the change in momentum of the object. The impulse can also be described as the average force applied during the time interval of the collision multiplied by the duration of the collision.
The formula for impulse (I) is I = F_avg * Δt = Δp, where F_avg is the average force, Δt is the change in time, and Δp is the change in momentum. The change in momentum (Δp) is the mass (m) times the change in velocity (Δv).
The pigeon has a mass of 0.240 kg and an initial velocity of 0 m/s (since it's assumed to be stationary). The falcon, with a mass of 0.480 kg and a velocity of 80 m/s, grabs the pigeon. After the collision, the falcon and the pigeon move together with the same velocity, but we need only the force during the collision, not their final velocity. The duration of the collision is given as 15 ms (0.015 s).
To find the average force on the pigeon during the impact, we first find the change in momentum of the pigeon, which is equal to the final momentum minus the initial momentum. It can be assumed that the final momentum of the pigeon is approximately equal to the momentum of the falcon right before the impact because they stick together after the collision. Therefore:
Δp = m_falcon * v_falcon = 0.480 kg * 80 m/s = 38.4 kg*m/s
Now, using the impulse-momentum theorem:
F_avg = Δp / Δt = 38.4 kg*m/s / 0.015 s = 2560 N
So, the average force on the pigeon during the collision is 2560 N.