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ID: 1880910 • Letter: I
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iPad 11:08 AM a webassign.net 90%- Show My Work olonan 12. 0/1 points | Previous Answers SerEssen1 2.P036. 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 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 0.40 m above the floor. If the floor is hardwood, the child's head is brought to rest in approximately 1.9 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 that 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. 2063.158x Your response differs from the correct answer by more than 1.36 Hardwood floor Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error, ms duration magnitude 10%. Double check your calculations. m/s2 116.7 2.39 Carpeted floor Your response differs from the correct answer by more than 10%. Double check your calculations. m/s2 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. ms duration magnitude O Show My Work (optional) Viewing Saved Work Revert to Last Response
Explanation / Answer
Velocity at floor : v 2 = 2gs, g=9.8066, s= 0.4
v = 2.8008 m/s
First case: hardwood floor
u 2 = 2as, s= 1.9 mm, u = 2.8008 m/sec
a= deceleration= 2064.421 m/sec 2
u= at, a= 2064.421, u =2.8008
t =1.356 msec
Second case : Carpet floor
u 2 = 2as, s= 1.2 cm, u= 2.8008 m/sec
a= deceleration= 326.866 m/sec 2
u= at, a = 326.866, u = 2.8008
t= 8.568 msec
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