838 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 839
Problem 4.126
Two blocks Aand Bweighing 123 and 234 lb, respectively, are released
from rest as shown. At the moment of release the spring is unstretched.
Model
A
and
B
as particles, neglect air resistance, and assume that the
cord is inextensible. Determine the maximum speed attained by block
B
and the distance from the floor where the maximum speed is achieved if
˛D35ı
, the static and kinetic friction coefficients are
sD0:25
and
kD0:2, respectively, and the spring constant is kD25 lb=ft.
Solution
840 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 841
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.
842 Solutions Manual
Problem 4.127
Spring scales work by measuring the displacement of a spring that supports both the
platform of mass
mp
and the object, of mass
m
, whose weight is being measured.
In your solution, note that most scales read zero when no mass
m
has been placed
on them; that is, they are calibrated so that the weight reading neglects the mass
of the platform
mp
. Assume that the spring is linear elastic with spring constant
k
. If the mass
m
is gently placed on the spring scale (i.e., it is released from zero
height above the scale), determine the maximum velocity attained by the mass
m
as
the spring compresses.
Solution
Once placed on the scale, the object of mass
m
will travel together with the
support platform. Therefore we can model the object and the platform as a single
Dynamics 2e 843
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permission of McGraw-Hill, is prohibited.
844 Solutions Manual
Problem 4.128
A cyclist is riding with a constant speed
vD25 km=h
over an inclined
road with
✓D15ı
. The combined mass of the cyclist and bicycle is
85 kg
. Neglecting aerodynamic drag, determine the number of calories
(
1
C
D4:184 kJ
) burned by the cyclist in the course of
15 min
if his muscle
efficiency is 25%.
Solution
We model the cyclist and the bicycle as a particle subject to its own weight
mg, the propelling force F, and the reaction Nnormal to the incline.
Dynamics 2e 845
Problem 4.129
The mass
A
is pressed against the linear elastic spring with stiff-
ness
kD500 N=m
such that the spring compresses a distance
ıD15 cm
. The mass is then released in the position shown and
slides a distance
dD1:2
m up the incline. The mass leaves the
incline at
B
and becomes a projectile. The angle of the incline is
✓D30ı
, and the height
hD0:9
m. Neglecting friction between
A
and the incline while
A
is on the incline, determine the range
R
where the mass first lands on the horizontal surface
C
.
A
has
mass mD0:25 kg.
Solution
NOTE: Ahas mass mD0:25 kg.
We define
¿
to be the position of
A
at release, and
¡
to be at
B
.
846 Solutions Manual
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 847
Problem 4.130
For the two pulley systems shown, the same block
B
, weighing
150 lb
, is being lifted by applying the same constant force
FD80 lb
.
If the two systems are released from rest, determine the power
developed by the force Fin the two cases 1s after release.
Solution
The two cases differ from one another by the type of pulley system
used. We observe that, neglecting the inertia of the pulley system
848 Solutions Manual
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permission of McGraw-Hill, is prohibited.