What is the stopping time of the skull?

Question

A woodpecker's brain is specially protected from large decelerations by tendon-like attachments inside the skull. While pecking on a tree, the woodpecker's skull comes to a stop from an initial speed of 0.52m/s0.52m/s in a distance of only 2.00mm2.00mm. Treat the initial direction of motion to be the positive direction. Include units as appropriate.

In part (a) we found the skull's acceleration, and the g-force (magnitude of the number of 𝑔g's of acceleration) of the woodpecker's skull.

(b) What is the stopping time of the skull?

Answer 1

Part a]

Using the formula and substituting the given values,

a = (0 m/s)² - (0.52 m/s)² / 2 (2.00 x 10^-3 m) = -67.6 m/s²

So the deceleration is - 67.6 m/s²

To get the deceleration in multiples of g, we divide a by g,

67.6 m/s² / 9.8 m/s² = 6.896

a = 13.26 g

Part b]

The words “Calculate the stopping time” mean find t

Using x-x₀ = 1/2(v₀+v)t

t = 2 (2.00 x 10^-3 m) / (0.52 m/s) + (0 m/s) = 7.7 x 10^-3 s

Hence, the stopping time of the skull is 0.0077 s