Runaway Car Using Hooke’s Law, we can show that thework done in compressing a spring a distance of x feetfrom its at-rest position is W = 12 kx2, where k is a stiffnessconstant depending on the spring. It can also be shown thatthe work done by a body in motion before it comes to restis given by W∼ = w2g v2, where w = weight of the object (lb),g = acceleration due to gravity (32.2 ft/sec2), andv = object’s velocity (in ft/sec). A parking garage has aspring shock absorber at the end of a ramp to stop runawaycars. The spring has a stiffness constant k = 9450 lb/ft andmust be able to stop a 4000-lb car traveling at 25 mph. Whatis the least compression required of the spring? Expressyour answer using feet to the nearest tenth.[Hint: Solve W 7 W∼, x Ú 0].

Runaway Car Using Hooke’s Law, we can show that the
work done in compressing a spring a distance of x feet
from its at-rest position is W = 1
2 kx2
, where k is a stiffness
constant depending on the spring. It can also be shown that
the work done by a body in motion before it comes to rest
is given by W
∼ = w
2g v2
, where w = weight of the object (lb),
g = acceleration due to gravity (32.2 ft/sec2
), and
v = object’s velocity (in ft/sec). A parking garage has a
spring shock absorber at the end of a ramp to stop runaway
cars. The spring has a stiffness constant k = 9450 lb/ft and
must be able to stop a 4000-lb car traveling at 25 mph. What
is the least compression required of the spring? Express
your answer using feet to the nearest tenth.
[Hint: Solve W 7 W
∼, x Ú 0].