________________________________________________________________________
PROBLEM (12.88) A car of weight W = 15 kips is stopped by means of spring bumper which it
will hit at a speed of v = 25 mph (Fig. P12.87). The largest allowable horizontal force is P = 180 kips.
Calculate:
(a) The maximum deflection of the spring.
(b) The required spring constant k.
SOLUTION
25(5280 12) 440
3600
vi
×
==
ps
2
15,000 38.82 .
32.2(12)
W
ml
g
== = bins
(a) Energy absorbed by the spring is
2
max
11
22
Pm
δ
=v
or
22
max 3
38.82(440)
180 10
mv
P
δ
== ×41.8 .in
=
(b) Spring rate is
3
max
180(10 ) 4.31 .
41.8
P
k kip in
δ
== =
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