Falls resulting in hip fractures are a major cause of injury and even death to t

Question

Falls resulting in hip fractures are a major cause of injury and even death to the elderly.Typically, the hip’s speed at impact is about 2.0 m/s. If this can be reduced to 1.3 m/s or less, the hip will usually not fracture. One way to do this is by wearing elastic hip pads. Part A.If a typical pad is 5.0 cm thick and compresses by 2.0 cm during the impact of a fall, what acceleration (in m/s^2 ) does the hip undergo to reduce its speed to 1.3 m/s? Part B. What acceleration (in g's ) does the hip undergo to reduce its speed to 1.3 m/s? Part C. The acceleration you found in part A may seem like a rather large acceleration, but to fully assess its effects on the hip, calculate how long it lasts in seconds.

Explanation / Answer

s = v0t + (1/2)at^2

v = v0 + at and t = (v - v0)/a

s = v0(v - v0)/a + (1/2)a (v - v0)^2/a^2

2as = 2vv0 - 2v0^2 + (v^2 - 2vv0 + v0^2)

2as = v^2 - v0^2

v^2 = v0^2 + 2as

v0 = 2

v = 1.3

s = 2 cm = .02 m

1.3^2 = 2^2 + 2a(.02)

(A) a = -57.75 m/s^2 = 5.893 g's

(B) a = -57.75 m/s^2 = 5.893 g's

v = v0 + at = 2 - 57.75t = 1.3

(C) t = 0.01212 seconds

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