100 Solutions Manual
Problem 2.60
Referring to Example 2.8 on p. 56, and defining terminal velocity as the velocity at which a falling object
stops accelerating, determine the skydiver’s terminal velocity without performing any integrations.
Solution
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Dynamics 2e 101
Problem 2.61
Referring to Example 2.8 on p. 56, determine the distance
d
traveled by the skydiver from the instant the
parachute is deployed until the difference between the velocity and the terminal velocity is 10% of the
terminal velocity.
of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the
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102 Solutions Manual
Problem 2.62
In a physics experiment, a sphere with a given electric charge is constrained to move along a rectilinear
guide with the following acceleration:
aDa0sin.2⇡s=/
, where
a0D8m=s2
,
⇡
is measured in radians,
sis the position of the sphere measured in meters, s, and D0:25 m.
If the sphere is placed at rest at
sD0
and then gently nudged away from this position, what is the
maximum speed that the sphere could achieve, and where would this maximum occur?
Solution
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 103
Problem 2.63
In a physics experiment, a sphere with a given electric charge is constrained to move along a rectilinear
guide with the following acceleration:
aDa0sin.2⇡s=/
, where
a0D8m=s2
,
⇡
is measured in radians,
sis the position of the sphere measured in meters, s, and D0:25 m.
Suppose that the velocity of the sphere is equal to zero for
sD=4
. Determine the range of motion of
the sphere, that is, the interval along the
s
axis within which the sphere moves. Hint: Determine the speed
of the sphere and the interval along the saxis within which the speed has admissible values.
Solution
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permission of McGraw-Hill, is prohibited.
104 Solutions Manual
Problem 2.64
The acceleration of an object in rectilinear free fall while immersed in a linear viscous
fluid is
aDgCdv=m
, where
g
is the acceleration of gravity,
Cd
is a constant
drag coefficient, vis the object’s velocity, and mis the object’s mass.
Letting
t0D0
and
v0D0
, find the velocity as a function of time and find the
terminal velocity.
Solution
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 105
Problem 2.65
The acceleration of an object in rectilinear free fall while immersed in a linear viscous
fluid is
aDgCdv=m
, where
g
is the acceleration of gravity,
Cd
is a constant
drag coefficient, vis the object’s velocity, and mis the object’s mass.
Letting s0D0and v0D0, find the position as a function of velocity.
Solution
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106 Solutions Manual
Problem 2.66
A
1:5 kg
rock is released from rest at the surface of a calm lake. If the resistance
offered by the water as the rock falls is directly proportional to the rock’s velocity,
the rock’s acceleration is
aDgCdv=m
, where
g
is the acceleration of gravity,
Cd
is a constant drag coefficient,
v
is the rock’s velocity, and
m
is the rock’s mass.
Letting CdD4:1 kg=s, determine the rock’s velocity after 1:8 s.
Solution
We recall that aDdv=dt. Using the given expression for awe can write
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 107
Problem 2.67
A
3:1 lb
rock is released from rest at the surface of a calm lake, and its acceleration
is
aDgCdv=m
, where
g
is the acceleration of gravity,
CdD0:27 lbs=ft
is a
constant drag coefficient, vis the rock’s velocity, and mis the rock’s mass.
Determine the depth to which the rock will have sunk when the rock achieves
99% of its terminal velocity.
Solution
We begin by determining the expression of the terminal velocity, which we denote by
vterm
. This is the
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permission of McGraw-Hill, is prohibited.
108 Solutions Manual
Problem 2.68
A
3:1 lb
rock is released from rest at the surface of a calm lake, and its acceleration
is
aDgCdv=m
, where
g
is the acceleration of gravity,
CdD0:27 lbs=ft
is a
constant drag coefficient, vis the rock’s velocity, and mis the rock’s mass.
Determine the rock’s velocity after it drops 5ft.
Solution
We recall that
aDdv=dt
. To relate the acceleration to position, we can use the chain rule and write
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 109
Problem 2.69
Suppose that the acceleration of an object of mass
m
along a straight line is
aDgCdv=m
, where the
constants
g
and
Cd
are given and
v
is the object’s velocity. If
v.t/
is unknown and
v.0/
is given, can you
determine the object’s velocity with the following integral?
v.t/ Dv.0/ CZt
0✓gCd
mv◆dt:
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permission of McGraw-Hill, is prohibited.