978-0128012420 Chapter 16 Part 1

Solution Manual Chapter 16: Bioengineering

Problems 1 and 2 concern the following situation: A car is traveling 30. mph hits a wall.

The car has a crumple zone of zero and the passenger is not wearing a seat belt. The

passenger’s head hits the windshield, and is stopped in the distance of 0.10 m. The skull

mass is 5.0 kg. The area of contact of the head and the windshield is 0.010 m2. Assume

direct contact (that is, ignore whiplash) and ignore the time it takes the passenger to reach

the windshield.

16-1) Provide a graph of v – t graph of the collision of the skull and the windshield, and

then graph the force experienced by the skull as a function of time.

Need: v – t graph of the collision and F = _____ N (as fn. of time)

Know: v = 30. mph = 13. m/s; Ds = 0.10 m and A(contact) = 0.010 m2.

Skull mass = 5.0 kg.

16-2) If the compressive strength of bone is 3.0  106 N/m2, will the collision in the

previous exercise break the skull?

Need: Max allowable stress on skull exceeded = _____ (yes/no)

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Problems 3 and 4 concern an experiment in the 1950s when Air Force Colonel John

Paul Stapp volunteered to ride a rocket sled to test the resistance of the human body to “g

forces”. The sled accelerated from 0 to 625 miles per hour in 5.0 seconds. Then the sled

hit a water brake and decelerated in 3.0 seconds to a standstill. Assume that Stapp was

rigidly strapped into the sled, and he had a mass of 75 kg.

16-3) Prepare v – vs.- t and F – vs.- t graphs of Stapp’s trip, and compute the “g forces”

he experienced in the course of acceleration and deceleration.

Need: v – vs.- t and F – vs.- t graphs and g = ____ [0].

Know: vmax = 625 mph = 279 m/s. Constant acceleration for 5.0 s and

constant deceleration for 3.0 s.

Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition

16-4) Using the force vs. time graph (Figure 16.6) for human resistance to “g forces”,

predict whether Stapp suffered serious injury in the course of his record-breaking trip in

the worse case.

Need: Was Stapp’s maximum g force that was experienced for a duration

of 3.0 second in the “serious injury or death” region = ______ yes/no?)

16-5) A tall person sits down onto a sofa to watch TV. Assume that the center of gravity

of the person falls 1.0 m with constant gravitational acceleration in the course of sitting

down. The sofa compresses by 0 .05 m. Assume constant deceleration. Determine the g

forces experienced by the person in the course of this sitting down.

Need: g forces on a tall couch potato = ____ g

7

Problems 16.6 and 16.7 concern an infant’s rear–facing safety seat as illustrated below.

16-6) A ear facing child safety seat holds a child of mass 12. kg rigidly within the interior

of a car. The area of contact between the seat and the child is 0.10 m2. The car undergoes

a 30. mph collision. The car’s crumple zone causes the distance traveled by the rigid

interior to be 1.0 m. Give the stress experienced by the child’s body in terms of a fraction

of the breaking strength of bone assuming an infant’s bone breaks at a stress of 10.

MN/m2.

Need: Stress experienced by child’s body = ____ compared to breaking

stress of bone.

0,0

v

tft s

1.0 m

0,0

v

tft s

1.0 m

Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition

8

16-7) A rear facing child safety seat holds a child of mass 25. kg rigidly within the rigid

interior of a car. The area of contact between the seat and the child is 0.10 m2. The car

undergoes a 30. mph collision. The car has no crumple zone, but a harness attached to the

car seat stops it uniformly within a distance of 0.30 m. According to the Gadd severity

index, will the child sustain serious injury or death?

Need: Child ___ (will/will not) suffer serious injury or death.

16-8) Consider a parachute as a safety device. When parachute opens the previously

freely falling person has typically reached a speed of about 50. m/s. The parachute slows

to a terminal speed of about 10. m/s in 1.3 s. Approximating this set of motions by a

constant deceleration, what is the maximum g experienced by the parachutist?

Need: maximum acceleration = ___ g

16-9) In the previous problem, the force exerted by the parachute is spread by a harness

in contact with 0.50 m2 of the parachutist, and the parachutist has a mass of 75. kg, what

is the force per unit area (stress) experienced by the person during the deceleration?

Need: Stress = ____ N/m2

16-10) The parachutist in the previous two exercises hits the ground (still wearing the

parachute!) and is stopped in a distance of 0.10 m. If this final deceleration is constant,

calculate the Gadd Severity Impact of the landing.

Need: GSI = ____ (a number)

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16-11) A 75. kg person jumping from a 1.00  103 m cliff will reach a terminal speed of

50. m/s and uses a 1.00  102 m bungee cord to slow the descent. The bungee cord exerts

a force F proportional to its extension, where F (in newtons) = (5.0 N/m)  (extension in

m) and is designed to extend by 5.00  101 m in the course of bringing the user to a stop

just above the ground. Is the maximum deceleration in g experienced by the falling

person more or less than the maximum deceleration experienced by a parachutist

undertaking the same leap (excluding landing forces)?

Need: Maximum deceleration for bungee is ____ (greater/equal/less) than

for parachute.

from 50. to 10. m/s (Exercise 16-10). The parachutist’s maximum g = 3.1

Kosky, Balmer, Keat and Wise: Exploring Engineering, Fourth Edition

16-12) An airbag is designed to inflate very quickly and to subsequently yield if the

driver hits it. A collision uniformly stops a car from 30. mph to 0.0 and then triggers the

air bag. The driver is not seat belted and so hits the inflated airbag. This acts as a local

“crumple zone” and consequently compresses by 0.20 meters as his head is brought to

rest.

According to the Gadd Severity Index, will the driver suffer serious injury? Assume

constant deceleration of the driver’s head after hitting the air bag.

Need: Driver ____ (will/will not) suffer serious injury.