Dynamics 2e 717
Problem 4.41
Each of the two rubber tubes of the wrist rocket has an unstretched length
L0D1ft
. They are symmetrically pulled back so that
`D3ft
and then are
released from rest. The pellet
P
that is launched by the wrist rocket weighs
0:145 oz
. Neglect the mass of the rubber tubes and any change in height of the
pellet while it is in contact with the rubber tubes. Finally, let dD1:5 in:
If the desired launch speed of the pellet
P
is
100 mph
, determine the
required stiffness of each rubber tube.
Solution
NOTE: The quantity dD1:5 in:
Let
¿
be the position at which the rubber tubes are released and
¡
be the
718 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 719
Problem 4.42
Each of the two rubber tubes of the wrist rocket has an unstretched length
L0D1ft
. They are symmetrically pulled back so that
`D3ft
and then are
released from rest. The pellet
P
that is launched by the wrist rocket weighs
0:145 oz
. Neglect the mass of the rubber tubes and any change in height of the
pellet while it is in contact with the rubber tubes. Finally, let dD1:5 in:
If the stiffness of each rubber tube is
kD5lb=ft
, determine the range of
the pellet if it is launched at
45ı
with respect to the horizontal and if it lands at
the same height from which it was launched. Neglect air resistance.
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.
720 Solutions Manual
Substituting this result, Eqs. (2) and Eq. (4) into Eq. (1), we have
Dynamics 2e 721
Problem 4.43
The collar
C
of mass
mD2kg
slides freely on the rod
EF
. At the instant
shown, the collar
C
is moving downward with speed
v1D2:5 m=s
and
it is
1=3
of the way between
E
and
F
. The dimensions are
LD2:1
m,
wD1:9 m, hD2:3 m, and dD1:2 m.
If the unstretched length of the spring is
L0D1
m, and the spring
stiffness is
kD50 N=m
, determine the speed of the collar when it reaches
F. Assume that the attachment point at Adoes not impede the spring.
Solution
We denote by
¿
and
¡
the positions of
C
at the instant shown
and at
F
, respectively. Between
¿
and
¡
, we model
C
as
722 Solutions Manual
Problem 4.44
The collar
C
of mass
mD2kg
slides freely on the rod
EF
. At the instant
shown, the collar
C
is moving downward with speed
v1D2:5 m=s
and
it is
1=3
of the way between
E
and
F
. The dimensions are
LD2:1
m,
wD1:9 m, hD2:3 m, and dD1:2 m.
If the unstretched length of the spring is
L0D4
m and the spring
stiffness is
kD50 N=m
, determine the speed of the collar when it reaches
F. Assume that the attachment point at Adoes not impede the spring.
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 723
Problem 4.45
The collar
C
of mass
mD2kg
slides freely on the rod
EF
. At the instant
shown, the collar
C
is moving downward with speed
v1D2:5 m=s
and
it is
1=3
of the way between
E
and
F
. The dimensions are
LD2:1
m,
wD1:9 m, hD2:3 m, and dD1:2 m.
If the unstretched length of the spring is
L0D1
m and the spring
stiffness is
kD170 N=m
, show that the collar does not reach
F
. Assume
that the attachment point at Adoes not impede the spring.
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.
724 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 725
Problem 4.46
The crate of mass
mD35 kg
is attached to the springs with constants
k1D1kN=m
and
k2D2kN=m
.
Both springs are unstretched when ıD0and the box is centered between the two vertical walls.
If the crate is released from rest after being displaced a distance
ıD2
m and friction between the crate
and the surface on which it slides is negligible, determine the speed of the crate when it returns to ıD0.
Solution
We denote by
¿
and
¡
the release position of the crate and the position
corresponding to
ıD0
, respectively. Between
¿
and
¡
, we model the crate
726 Solutions Manual
Problem 4.47
The crate of mass
mD35 kg
is attached to the springs with constants
k1D1kN=m
and
k2D2kN=m
.
Both springs are unstretched when ıD0and the box is centered between the two vertical walls.
If the crate is released from rest after being displaced a distance
ıD2
m and the coefficient of kinetic
friction between the crate and the surface on which it slides is
kD0:2
, determine the speed of the crate
when ıD0.
Solution
We denote by
¿
and
¡
the release position of the crate and the position
corresponding to
ıD0
, respectively. Between
¿
and
¡
, we model the crate