Question

. A 5.03 g nickel is dropped from the top of the Shanghai Tower in Lujiazui, Pudong, Shanghai and lands on the head of a person that is a distance of 632 m below. Just before the nickel hits the person's head, it is falling at a speed of 48.19 distance of 3.61 mm. The nickel comes to a complete stop in the person's head after penetrating a A) Determine the acceleration of the nickel after it strikes the head (i.e. this will be a deceleration as the nickel will stop upon hitting the head). B) Calculate the average force of the quarter on the head using Newton's 2nd Law. C) Recalculate the average force of the quarter on the head using momentum techniques D) Parts of the skull bone will be fractured by forces of about 900 N or more. Is there a chance of this person's skull being fractured by the nickel? Explain.

Answer 1

1. (A) vf^2 - vi^2 = 2 a d

0^2 - 48.19^2 = 2(-a)(3.61 x 10^-3)

a = 3.22 x 10^5 m/s^2  

(B) F_avg = m a = (5.03 x 10^-3)(3.22 x 10^5)

F_avg = 1618 N

(C) change in momnetum = F t

{ vf = vi + a t , t = 48.19/(3.22 x 10^5) = 1.50 x 10^-4 s}

(5.03 x 10^-3)(48.19 - 0) = F (1.50 x 10^-4)

F = 1618 N  

(D) average force is more than 900 N .

so skull will get fractured.