Question

-/10 points SerCP11 2.4.P.049. My Notes Ask Your Teacher Traumatic brain injury such as concussion results when the head undergoes a very large acceleration Generally, an acceleration less than 300 m/slasting for any length of time will not cause injury, whereas an acceleration greater than 1,000 m/s lasting for at least 1 ms will cause injury. Suppose a small child rolls off a bed that is 0.5 m above the foor. If the floor is hardwood, the child's head is brought to rest in approximately 2.1 mm If the floor is carpeted, this stopping distance is increased to about 14cm. Calculate the magnitude and duration of the deceleration in both cases, to determine the risk of injury. Assume the child remains horizontal during the fall to the floor. Note that a more compecated fall could result in a head velocity greater or less than the speed you calculate hardwood floor magnitude hardwood floor duration carpeted for magnitude carpeted for duration Need Help?

Answer 1

. he 0.53 m . h = 7.1 min = 2.1716? m he' = 1.4cm = 1.4 xiom ₃. The velocity of the child's head just before import (After falling a distance o. som ustating fromvert). = vyp + 20 (ay) 4y=-=-0.53m -' mesme falling do 0726g) 1–] 249.81 X 0.53 Yezgh' y= Vägh = J8x9.81 % 0.83 V= 3.225 mls down toer of lecceleration 4= -3.225 m1,4 → If, upon impact, child's head undergoes an acklitonal displacement Ly =-h before Corming to rest, V olgt 2a (Ay) ujao final

. -= - Qah. acceleration as 11 h - 0 * The duration impcut is, forme kinematic equation V = Yptat Yp- Vprat 1. t= f - Vf - - // Tab terme + t = -9h » Hardwood floor (n= 9.141om). - acceleration magnitudo . a = . L ast 3.995) 24 (214162) a = 24-76.34 mls?

- Duration to t -2(914163) - (-3.925) = 1.30 4163 sec It= 1.30ms) >> Carpeted floor Che = 1.47102m). u gh = 2(1.47102) a = 371.45 m/s2 t= -2h duration vf =-21144816?) - 3.225 = 8.68 x16 3 sec t= 8.68 ms