What is the brain's acceleration, and the "g-force" (the unitless number of 𝑔g's of acceleration, where 𝑔g is given on the formula sheet) of the woodpecker's brain?

Question

This question is a continuation from the previous 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 on the woodpecker's skull. In part (b) we found the stopping time of the skull.

(c) The tendons cradling the brain in fact stretch, ensuring a greater stopping distance of 4.50mm4.50mm. What is the brain's acceleration, and the "g-force" (the unitless number of 𝑔g's of acceleration, where 𝑔g is given on the formula sheet) of the woodpecker's brain ?

Answer 1

Part c]

To calculate the deceleration of the brain, we will use

x - x₀ = 4.50 mm = 4.5 x 10^-3 m

a = v² - v₀² / 2 (x - x₀) = (0 m/s)² - (0.52 m/s)² / 2 (4.50 x 10^-3 m)

a = - 30.04 m/s²

And expressed in multiples of g gives: 30.04 m/s² / 9.8 m/s² = 3.06

a = 3.06 g