Dynamics 2e 707
Problem 4.31
Car bumpers are designed to limit the extent of damage to the car in
the case of low-velocity collisions. Consider a
1420 kg
passenger car
impacting a concrete barrier while traveling at a speed of
5:0 km=h
.
Model the car as a particle and consider two bumper models: (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 FSD2000 N over 10 cm.
If the bumper is of type 1 and if
kD9⇥104N=m
, find the spring
compression (distance) necessary to stop the car.
Solution
708 Solutions Manual
Problem 4.32
Car bumpers are designed to limit the extent of damage to the car in
the case of low-velocity collisions. Consider a
1420 kg
passenger car
impacting a concrete barrier while traveling at a speed of
5:0 km=h
.
Model the car as a particle and consider two bumper models: (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 FSD2000 N over 10 cm.
If the bumper is of type 1, find the value of
k
necessary to stop
the car when the bumper is compressed 10 cm.
Solution
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 709
Problem 4.33
Car bumpers are designed to limit the extent of damage to the car in
the case of low-velocity collisions. Consider a
1420 kg
passenger car
impacting a concrete barrier while traveling at a speed of
5:0 km=h
.
Model the car as a particle and consider two bumper models: (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 FSD2000 N over 10 cm.
If the bumper is of type 2, find the value of
k
necessary to stop
the car when the bumper is compressed 10 cm.
Solution
Referring to the FBD on the right, we model the car as a particle subject to its own
weight
mg
, the normal reaction with the ground
N
, and the force
Fspring CFS
due to
710 Solutions Manual
Problem 4.34
The pendulum shown is put in motion with a speed
v0
when
✓D0ı
. Letting
LD2ft
,
determine v0if the pendulum first comes to a stop at ✓D47ı.
Solution
Referring to the FBD at the right, we model the pendulum bob as a particle subject
only to the cord tension
Fc
and the weight
mg
. We use a polar coordinate system
Dynamics 2e 711
Problem 4.35
Point
A
is the highest point along the roller coaster ride section shown.
The inscribed circle at
A
has radius
⇢D25
m and center at
C
. If point
B
is on a horizontal line going through
C
and if the roller coaster has a speed
v0D45 km=h
at
A
, neglecting friction and air drag and treating the roller
coaster as a particle, determine the speed of the roller coaster at B.
Solution
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.
712 Solutions Manual
Problem 4.36
Assuming that the plunger of a pinball machine has negligible mass and
that friction is negligible, determine the spring constant
k
such that a
2:85 oz
ball is released with a speed
vD15 ft=s
, after pulling back the
plunger
2in:
from its rest position, i.e., from the position in which the
spring is uncompressed.
Solution
We model the ball as a particle subject only to the force of the plunger
Fs
(due to the spring), the weight
mg
, and the normal reaction
N
with
714 Solutions Manual
Problem 4.38
Consider a
3300 lb
car whose speed is increased by
35 mph
over a
distance of
200 ft
while traveling up a rectilinear incline with a
15
%
grade. Model the car as a particle, assume that the tires do not slip,
and neglect all sources of frictional losses and drag.
Determine the work done on the car by the engine if the car has
an initial speed of 30 mph.
Solution
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 715
Problem 4.39
A classic car is driving down an incline at
60 km=h
when its brakes
are applied. Treating the car as a particle, neglecting all forces except
gravity and friction, and assuming that the tires slip, determine the
coefficient of kinetic friction if the car comes to a stop in
55
m and
✓D20ı.
Solution
We model the car as a particle subject to its own weight
mg
, the
normal reaction with the ground
N
, and the friction force
F
.We