Traumatic brain injury such as concussion results when the head undergoes a very

Question

Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s2 lasting for any length of time will not cause injury, whereas an acceleration greater than 1000 m/s2 lasting for at least 1 ms will cause injury. Suppose a small child rolls off a bed that is 0.42 m above the floor. If the floor is hardwood, the child's head is brought to rest in approximately 2.2 mm. If the floor is carpeted, this stopping distance is increased to about 1.2 cm. 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 complicated fall could result in a head velocity greater or less than the speed you calculate.

hardwood floor magnitude                                                  
Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. m/s2 hardwood floor duration                                                  
Your response differs from the correct answer by more than 10%. Double check your calculations. ms carpeted floor magnitude          m/s2 carpeted floor duration          ms Traumatic brain injury such as concussion results when the head undergoes a very large acceleration. Generally, an acceleration less than 800 m/s2 lasting for any length of time will not cause injury, whereas an acceleration greater than 1000 m/s2 lasting for at least 1 ms will cause injury. Suppose a small child rolls off a bed that is 0.42 m above the floor. If the floor is hardwood, the child's head is brought to rest in approximately 2.2 mm. If the floor is carpeted, this stopping distance is increased to about 1.2 cm. 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 complicated fall could result in a head velocity greater or less than the speed you calculate.

Explanation / Answer

velocity of child reaching at the surface of floor =sqrt(2*9.8*.42)=2.869146214468688m/sec

a)hardwood floor

deacceleration=(2.869146214468688^2)/[2*.0022)=1870.813747570606 m/sec^2 will cause injury

time t= 2.869/1870.813747570606

=1.5335 millisecond

b)carpet floor

deacceleration=(2.869^2)/[2*.011]=374.1436818181818 m/sec^2 will not cause injury

time t=2.869/374.1436818181818

=7.66819 millisecond

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