416 Solutions Manual
Problem 3.10
A hammer hits a mass
m
on the end of a metal bar. In Chapter 5, we will see that this imparts an
instantaneous initial velocity
v0
at
xD0
to the mass. Treating the bar as a massless spring, determine
the equation of motion of the mass
m
. The equivalent spring constant of a bar in compression is given by
keq DEA=L
, where
E
is Young’s modulus of the bar,
A
is the cross-sectional area of the bar, and
L
is the
length of the bar.
Solution
Dynamics 2e 417
Problem 3.11
For the mass described in Prob. 3.10:
(a) Integrate the equation of motion to determine the speed of the mass v.x/ as a function of x:
(b)
Use the result found in Part (a) to obtain the position of the mass as a function of time
x.t /
from the
initial time up until the mass stops for the first time. Hint:
Ra2bx21=2 dx Dsin1pbx=a=pb
.
Solution
We model the mass
m
as a particle and neglect its vertical motion. We assume that the
particle does not maintain contact with the hammer after being put in motion. Since we are
418 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 419
Problem 3.12
The crate
A
of mass
m
and the wedge
B
on which it rests are moving
together down the incline with the acceleration
aB
as shown. The angle
of the incline is
✓D30ı
with respect to the horizontal. Given that the
coefficient of static friction between the crate and the wedge is
sD0:6
,
determine the maximum value of
aB
before the crate starts to slip on the
wedge.
Solution
420 Solutions Manual
Problem 3.13
The crate
A
of mass
m
and the wedge
B
on which it rests are moving
together up the incline with the acceleration
aB
as shown. The angle
of the incline is
✓D30ı
with respect to the horizontal. Given that the
coefficient of static friction between the crate and the wedge is
sD0:6
,
determine the maximum value of
aB
before the crate starts to slip on the
wedge.
Solution
Dynamics 2e 421
Problem 3.14
A suitcase is released from rest at
A
on the
✓D30ı
ramp. It slides
a distance
`D25 ft
and then goes over the edge at
B
and drops a
height
hD5ft
. Determine the horizontal distance
d
to the landing
spot at C.
Assume that friction on the incline between
A
and
B
is negligi-
ble.
Solution
We model the motion of the suitcase
A
from
B
to
C
as projectile
motion. This motion is completely determined by the velocity of
422 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 423
Problem 3.15
A suitcase is released from rest at
A
on the
✓D30ı
ramp. It slides
a distance
`D25 ft
and then goes over the edge at
B
and drops a
height
hD5ft
. Determine the horizontal distance
d
to the landing
spot at C.
Assume that the coefficient of static friction is insufficient to
prevent slipping and that the coefficient of kinetic friction on the
incline between Aand Bis kD0:3.
Solution
424 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 425
Problem 3.16
A vehicle is stuck on the railroad tracks as a
430;000 lb
locomotive is approaching with a speed of
75 mph
.
As soon as the problem is detected, the locomotive’s emergency brakes are activated, locking the wheels
and causing the locomotive to slide.
If the coefficient of kinetic friction between the locomotive and the track is
0:45
, what is the minimum
distance
d
at which the brakes must be applied to avoid a collision? What would that distance be if instead
of a locomotive, there was a
30⇥106lb
train? Treat the locomotive and the train as particles, assume that
the railroad tracks are rectilinear and horizontal, and note that only the locomotive’s brakes are applied.
Solution