Problem 9.33 The human head can be considered as a 3.3kg cranium protecting a 1,

Question

Problem 9.33 The human head can be considered as a 3.3kg cranium protecting a 1,5 kg brain, with a small amount of Derebrospinal fuid that allows the brain to move a inte bi inside the cranium. Suppose a cranium at rest is subjected to a force of 2800 N for 5.5 msin the forward direction Part A What is the final speed of the cranium? Express your answer to two significant figures and include appropriate units. Value Units Submit My Answers Glye Up The back of the cranium then collides with the back of the brain, which is still at rest, and the two move together whatis heirsna speed? Express your answer to two significant figures and appropriate units. include Part B Value Units

Explanation / Answer

here,

mass of cranium , m1 = 3.3 kg

mass of brain , m2 = 1.5 kg

A)

force , f = 2800 N and t = 55 ms = 0.055 s

let the final speed be v

the impulse delivered , I = F * t

m1 * v = 2800 * 0.055

3.3 * v = 2800 * 0.055

v = 46.7 m/s

the final speed of cranium is 46.7 m/s

B)

let the final speed after the collison be v1

as the collison is inelastic

using conservation of momentum

m1 * v = (m1 + m2) * v1

3.3 * 46.7 = ( 3.3 + 1.5) * v1

v1 = 32.1 m/s

C)

time taken to stop , t = 15 ms = 0.015 s

the average force on brain , F' = I/t

F' = m2 * v1 /t = 1.5 * 32.1 /0.015 N

F' = 3208.3 N

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