7.89. Set Up:
For part (a), apply
with
which results in
For
parts (b) through (d), the maximum force
F
exerted by the air bag is expressed as
Solve: (a)
Solving
for the spring constant gives
(b)
Use the expression in part (a) to replace
k
in the relation
(c)
(d)
The expression in part (b) gives
(e) Reflect:
A safer design requires a larger distance
This could be accomplished by extending the gas, brake
and clutch pedals so that the driver could sit further away from the steering wheel or by decreasing the stiffness
k
of
the airbag. A stiffer air bag would increase
k
and
and thus make the system less safe.
7.90. Set Up:
To find the maximum speed, start with
Let
the initial
displacement from equilibrium, and
then
and
Substituting and solving for the
maximum speed, we obtain
For the maximum acceleration, noting that
we have
The instrument has
Solve: (a)
Maximum speed:
Maximum acceleration:
(b) Reflect:
No. The maximum speed occurs at
when the object passes through the equilibrium position. The
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This note was uploaded on 03/06/2009 for the course PHYS 114 taught by Professor Shoberg during the Spring '07 term at Pittsburg State Uiversity.
 Spring '07
 Shoberg
 Force

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