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436 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 437
Problem 3.23
A metal ball with mass
mD0:15 kg
is dropped from rest in a fluid. The magnitude
of the resistance due to the fluid is given by
Cdv
, where
Cd
is a drag coefficient
and
v
is the ball’s speed. If
CdD2:1 kg=s
, determine the ball’s speed
4
s after
release.
Solution
To determine the ball’s speed we need to determine the ball’s acceleration. In turn, we can
determine the ball’s acceleration by applying Newton’s second law. We model the ball as a particle
438 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 439
Problem 3.24
A metal ball weighing
0:35 lb
is dropped from rest in a fluid. The magnitude of the
resistance due to the fluid is given by
Cdv
, where
Cd
is a drag coefficient and
v
is
the ball’s speed. It is observed that
2
s after release, the speed of the ball is
25 ft=s
.
Determine the value of Cd.
Solution
440 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 441
Problem 3.25
A horse is lifting a
500 lb
crate by moving to the right at a
constant speed
v0D3ft=s
. Observing that
B
is fixed and
letting
hD6ft
and
`D14 ft
, determine the tension in the
rope when the horizontal distance
d
between
B
and point
A
on the horse is
10 ft
. Treat all rope segments between
B
and
C
as vertical, and ignore the change in the amount of rope that
wraps around the pulley at B.
Solution
We neglect the inertia of the pulleys and the cord as well as the horizontal motion of
the crate. We model the cord as inextensible and the crate as a particle. Performing an
442 Solutions Manual
Problem 3.26
The centers of two spheres
A
and
B
with masses
mAD1kg
and
mBD2kg
are a distance
r0D1
m apart.
B
is fixed in space, and
A
is initially at
rest. Using Eq. (1.5) on p. 3, which is Newton’s universal law of gravitation,
determine the speed with which
A
impacts
B
if the radii of the two spheres are
rAD0:05
m and
rBD0:15
m. Assume that the two masses are infinitely far
from any other mass so that they are only influenced by their mutual attraction.
Solution
Dynamics 2e 443
Problem 3.27
Spring scales work by measuring the displacement of a spring that supports
both the platform and the object, of mass
m
, whose weight is being measured.
Neglect the mass of the platform on which the mass sits and assume that the
spring is uncompressed before the mass is placed on the platform. In addition,
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 reading on the scale after
the mass is released.
Solution
The scale’s reading is the value of the spring force supporting the platform. The latter is
determined by the position of the weight placed on the platform. This implies that we need
444 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 445
Problem 3.28
Spring scales work by measuring the displacement of a spring that supports
both the platform and the object, of mass
m
, whose weight is being measured.
Neglect the mass of the platform on which the mass sits and assume that the
spring is uncompressed before the mass is placed on the platform. In addition,
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 speed attained by the
mass mas the spring compresses.
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.
