Traumatic brain injury such as concussion results when thehead undergoes a very

Question

Traumatic brain injury such as concussion results when thehead undergoes a very large acceleration. Generally, anacceleration less than 800 m/s2 lasting for any lengthof time will not cause injury, whereas an acceleration greater than1000 m/s2 lasting for at least 1 ms will cause injury.Suppose a small child rolls off a bed that is 0.37 m above the floor. If the floor is hardwood,the child's head is brought to rest in approximately 1.8 mm. If the floor is carpeted, this stoppingdistance is increased to about 1.0 cm.Calculate the magnitude and duration of the deceleration in bothcases, to determine the risk of injury. Assume that the childremains horizontal during the fall to the floor. Note that a morecomplicated fall could result in a head velocity greater or lessthan the speed you calculate.
a.Hardwood Floor Magnitude and duration b.Carpet Floor Magnitude and duration Traumatic brain injury such as concussion results when thehead undergoes a very large acceleration. Generally, anacceleration less than 800 m/s2 lasting for any lengthof time will not cause injury, whereas an acceleration greater than1000 m/s2 lasting for at least 1 ms will cause injury.Suppose a small child rolls off a bed that is 0.37 m above the floor. If the floor is hardwood,the child's head is brought to rest in approximately 1.8 mm. If the floor is carpeted, this stoppingdistance is increased to about 1.0 cm.Calculate the magnitude and duration of the deceleration in bothcases, to determine the risk of injury. Assume that the childremains horizontal during the fall to the floor. Note that a morecomplicated fall could result in a head velocity greater or lessthan the speed you calculate.
a.Hardwood Floor Magnitude and duration b.Carpet Floor Magnitude and duration

Explanation / Answer

Determine the velocity of the child just as it hits thefloor: -- v(i) = 0 v(f) = ?? d = 0.37 m a = 9.8 m/s^2 -- v(f)^2 = v(i)^2 + 2ad v(f)^2 = 0 + (2)(9.8)(0.37) ---> initial velocity iszero v(f) = 2.7 m/s -- Now, determine the acceleration upon impact with the floorunder both hardwood and carpet, knowing that the final velocitywill be zero: -- Hardwood: v(f)^2 = v(i)^2 + 2ad 0 = 2.7^2 + (2)(a)(0.0018) --> 1.8mm =.0018m a = -2.7^2 / 0.0036 a = - 2025 m/s^2 = - 2 x 10^3 m/s^2 (negativeacceleration for slowing) -- Carpet: v(f)^2 = v(i)^2 + 2ad 0 = 2.7^2 + (2)(a)(0.01) --> 1cm =.01m a = -2.7^2 / 0.02 a = -364.5 m/s^2 = - 3.6 x 10^1 m/s^2(negative acceleration for slowing) -- -- Hope this helps. v(f)^2 = v(i)^2 + 2ad 0 = 2.7^2 + (2)(a)(0.0018) --> 1.8mm =.0018m a = -2.7^2 / 0.0036 a = - 2025 m/s^2 = - 2 x 10^3 m/s^2 (negativeacceleration for slowing) -- Carpet: v(f)^2 = v(i)^2 + 2ad 0 = 2.7^2 + (2)(a)(0.01) --> 1cm =.01m a = -2.7^2 / 0.02 a = -364.5 m/s^2 = - 3.6 x 10^1 m/s^2(negative acceleration for slowing) -- -- Hope this helps. 0 = 2.7^2 + (2)(a)(0.01) --> 1cm =.01m a = -2.7^2 / 0.02 a = -364.5 m/s^2 = - 3.6 x 10^1 m/s^2(negative acceleration for slowing) -- -- Hope this helps.

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