446 Solutions Manual
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 447
Problem 3.29
A scale is to be used on a wood countertop made from some very nice Brazilian
cherry. To protect the countertop, the owner attaches self-sticking felt pads to the feet of
the scale. When the weight was placed on the scale before the felt pads were applied, the scale read a
certain value. Will the value be higher, lower, or the same when the same weight is placed on the scale but
with the felt pads between the scale and the countertop? Ignore the transient dynamic effects that occur
immediately after the weight is placed on the scale.
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
448 Solutions Manual
Problem 3.30
Car bumpers are designed to limit the extent of damage to the
car in the case of low-velocity collisions. Consider a
3300 lb
passenger car impacting a concrete barrier while traveling at a
speed of
4:0 mph
. Model the car as a particle, and consider two
types of bumpers: (1) a simple linear spring with constant
k
and
(2) a linear spring of constant
k
in parallel with a shock-absorbing
unit generating a nearly constant force of 700 lb over 0:25 ft.
If the bumper is of type 1 and if
kD6500 lb=ft
, find the
spring compression necessary to stop the car.
Solution
Dynamics 2e 449
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
450 Solutions Manual
Problem 3.31
Car bumpers are designed to limit the extent of damage to the
car in the case of low-velocity collisions. Consider a
3300 lb
passenger car impacting a concrete barrier while traveling at a
speed of
4:0 mph
. Model the car as a particle, and consider two
types of bumpers: (1) a simple linear spring with constant
k
and
(2) a linear spring of constant
k
in parallel with a shock-absorbing
unit generating a nearly constant force of 700 lb over 0:25 ft.
If the bumper is of type 1, find the value of
k
necessary to
stop the car when the bumper is compressed 0:25 ft.
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 451
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
452 Solutions Manual
Problem 3.32
Car bumpers are designed to limit the extent of damage to the
car in the case of low-velocity collisions. Consider a
3300 lb
passenger car impacting a concrete barrier while traveling at a
speed of
4:0 mph
. Model the car as a particle, and consider two
types of bumpers: (1) a simple linear spring with constant
k
and
(2) a linear spring of constant
k
in parallel with a shock-absorbing
unit generating a nearly constant force of 700 lb over 0:25 ft.
If the bumper is of type 2, find the value of
k
necessary to
stop the car when the bumper is compressed 0:25 ft.
Solution
Dynamics 2e 453
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
454 Solutions Manual
Problem 3.33
What would it mean for the static or kinetic friction coefficients to be negative? Is this possible? Can either
the static or kinetic friction coefficients be greater than 1? If yes, explain and give an example.
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
permission of McGraw-Hill, is prohibited.
Dynamics 2e 455
Problem 3.34
Packages for transporting delicate items (e.g., a laptop or glass) are designed
to “absorb” some of the energy of the impact in order to protect the contents.
These energy absorbers can get pretty complicated to model (e.g., the mechan-
ics of styrofoam peanuts is not easy), but we can begin to understand how
they work by modeling them as a linear elastic spring of constant
k
that is
placed between the contents (an expensive vase) of mass
m
and the package
P
. Assuming that
mD3kg
and that the box is dropped from a height of
1:5
m, determine the magnitude of the maximum displacement of the vase
relative to the box, as well as the magnitude of the maximum force exerted
on the vase by the packaging if
kD3500 N=m
. Treat the vase as a particle,
and neglect all forces except for gravity and the spring force. Assume that the
spring relaxes after the box is dropped and that it does not oscillate.
Solution