130 Solutions Manual
Problem 2.85
The spool of paper used in a printing process is unrolled with velocity
vp
and acceleration
ap
. The
thickness of the paper is h, and the outer radius of the spool at any instant is r.
If the velocity at which the paper is unrolled is constant, determine the angular acceleration
˛s
of the
spool as a function of
r
,
h
, and
vp
. Evaluate your answer for
hD0:0048 in:
, for
vpD1000 ft=min
, and
two values of r, that is, r1D25 in:and r2D10 in:
Solution
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Dynamics 2e 131
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132 Solutions Manual
Problem 2.86
The spool of paper used in a printing process is unrolled with velocity
vp
and acceleration
ap
. The
thickness of the paper is h, and the outer radius of the spool at any instant is r.
If the velocity at which the paper is unrolled is not constant, determine the angular acceleration
˛s
of
the spool as a function of
r
,
h
,
vp
, and
ap
. Evaluate your answer for
hD0:0048 in:
,
vpD1000 ft=min
,
apD3ft=s2, and two values of r, that is, r1D25 in:and r2D10 in:
2⇡˛s:(6)
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 133
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.
134 Solutions Manual
Problem 2.87
The spool of paper used in a printing process is unrolled with velocity
vp
and acceleration
ap
. The
thickness of the paper is h, and the outer radius of the spool at any instant is r.
If the velocity at which the paper is unrolled is constant, determine the angular acceleration
˛s
of
the spool as a function of
r
,
h
, and
vp
. Plot your answer for
hD0:0048 in:
and
vpD1000 ft=min
as a
function of rfor 1in:r25 in. Over what range does ˛svary?
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 135
The above function can now be plotted. The plot below was generated usingMathematica with the following
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.
136 Solutions Manual
Problem 2.88
Derive the constant acceleration relation in Eq. (2.32), starting from Eq. (2.24). State what assumption you
need to make about the acceleration
a
to complete the derivation. Finally, use Eq. (2.27), along with the
result of your derivation, to derive Eq. (2.33). Be careful to do the integral in Eq. (2.27) before substituting
your result for
v.t/
(try it without doing so, to see what happens). After completing this problem, notice
that Eqs. (2.32) and (2.33) are not subject to the same assumption you needed to make to solve both parts
of this problem.
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permission of McGraw-Hill, is prohibited.
Dynamics 2e 137
Problem 2.89
The discussion in Example 2.12 revealed that the angle
✓
had to be greater than
✓min D0:716ı
. Find an
analytical expression for ✓min in terms of h,w, and d.
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permission of McGraw-Hill, is prohibited.
138 Solutions Manual
Problem 2.90
A stomp rocket is a toy consisting of a hose connected to a “blast pad” (i.e., an air bladder)
at one end and to a short pipe mounted on a tripod at the other end. A rocket with a
hollow body is mounted onto the pipe and is propelled into the air by “stomping” on
the blast pad. Some manufacturers claim that one can shoot a rocket over
200 ft
in the
air. Neglecting air resistance, determine the rocket’s minimum initial speed such that it
reaches a maximum flight height of 200 ft.
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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Dynamics 2e 139
Problem 2.91
An airplane flying horizontally at elevation
hD150 ft
and at a constant speed
v0D80 mph
drops a
package
P
when passing over point
O
. Determine the horizontal distance
d
between the drop point and
point Bat which the package hits the ground.
Solution
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permission of McGraw-Hill, is prohibited.