A.The displacement in the graph is measured from the surface of the wood. From t

Question

A.The displacement in the graph is measured from the surface of the wood. From the data in the graph, estimate the speed with which the beak tip hits the wood and the acceleration that turns its motion around. (This all occurs in the first millisecond.)

Woodpeckers' skulls are adapted to be able to deliver a large force to a wood surface in order to drill a hole to get at insects under the bark of the tree. In order to get an idea of the scale of the forces involved we will consider a model from a 2011 paper by Yoon and Park.* A photo from their paper is shown at the right to set a scale. A. In the figure below is shown Yoon & Parks model of the beak displacement. 0.004 0,002 0 0.000 -0.002 0.000 0.005 0.010 0.015 0.020 0.025 5 cm Time (sec) Yoon &Park; From the displacement curve of the tip of the beak, we can infer the force that the woodpecker's head and beak feel and therefore the forces they exert on the tree. This curve has been smoothed somewhat, especially in the initial ms when the woodpecker feels a high frequency vibration. Although this has important consequences for the woodpecker's brain mounting structure, we will ignore it here.)

Explanation / Answer

The beak goes from 0.000 m to about -0.001 m (about 1 mm) in a time which looks to be about 0.001 s and back in about the same time.
So the initial velocity going into the wood is about
v = x/t
= (-0.001 m)/(0.001 s)
= -1 m/s

Going back out it goes about the same distance in the same time so the final velocity coming out of the wood is +1 m/s.

This makes the change in the velocity equal to
vf - vi = (1 m/s) - (-1 m/s)
= 2 m/s

This take place in about 1/5 of the time to go down, so perhaps 0.0002 s.

This makes the acceleration equal to

a = v/t
= (2 m/s)/(2 x 10 -4 s)
= 10 4 m/s 2 or about 10,000 m/s2

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