Unlock document.
This document is partially blurred.
Unlock all pages and 1 million more documents.
Get Access
2nd Edition
Gary L. Gray
The Pennsylvania State University
Francesco Costanzo
The Pennsylvania State University
often to obtain the most up-to-date version. In particular, as of December 16, 2009, please note the following:
_The solutions for Chapters 1, 2, and 4–9 have been accuracy checked and are in their final form.
_
The solutions for Chapter 3 have been accuracy checked and should be error free. We will be adding
some additional detail to these solutions in the coming weeks.
_
The solutions for Chapter 10 are a work in progress. The solutions for the first 29 problems in the
We welcome your input.
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.
Accuracy of Numbers in Calculations
Throughout this book, we will generally assume that the data given for problems is accurate to three significant
digits. When calculations are performed, intermediate results are stored in the memory of a calculator or
computer using the full precision these machines offer. However, when these intermediate results are reported
in this solutions manual, they are rounded to four significant digits. Final results are also rounded to four
significant digits.
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.
Chapter 7 Solutions
Problem 7.1
The roadster weighs
2750 lb
, its mass is evenly distributed between
its front and rear wheels, and it accelerates from 0 to
60 mph
in
7:0
s. If the acceleration is uniform and if the rear wheels do not
slip, determine the forces on each of the front and rear wheels
due to the pavement. Also determine the minimum coefficient of
static friction compatible with this motion. Assume that the mass
is evenly distributed between the right and left sides of the car,
neglect the rotational inertia of the front wheels, and assume that
the front wheels roll freely.
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 1421
Computation.
Substituting Eqs. (4) and (5) into Eqs. (1)–(3) results in the following system of three
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.
Problem 7.2
The conveyor is moving the cans at a constant speed
v0D18 ft=s
when,
to proceed to the next step in packaging, the cans are transferred onto
a stationary surface at
A
. If each can weighs
0:95 lb
,
wD2:71 in:
,
hD5in:
, and
kD0:3
between the cans and the stationary surface,
determine the time and distance it takes for each can to stop. In addition,
show that the cans don’t tip. Treat each can as a uniform circular cylinder.
2N ` DIG˛can:(3)
Force Laws.
Since the cans must slip relative to the stationary surface, the
friction law is
FDkN: (4)
Comparing
`
with
w=2
, we have
`D0:06250 ft
which is smaller than
w=2 D0:1129 ft
. Therefore, this
solution is ok and we have shown that the cans do not tip.
Since the horizontal acceleration is constant, we can compute the stopping time and distance using
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 1423
Problem 7.3
Determine the maximum acceleration
a0
of the conveyor so that the
cans do not tip over the cleats. The cleats completely prevent slipping,
but are not tall enough to dynamically influence tipping. Treat each
can as a uniform circular cylinder of mass m.
Solution
Since we are looking for the largest acceleration for the conveyer so that the cans
do not tip, we place the normal force at the bottom corner of the can as shown
in the FBD on the right.
Balance Principles.
Using the Cartesian system defined next to the FBD, the
Newton-Euler equations for a can are
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.
Problem 7.4
The file cabinet, which weighs
230 lb
, is being pushed to the right with a
horizontal force of
70 lb
, which is applied a distance
h
from the floor. If
the mass center
G
of the file cabinet is
dD24 in:
from the floor and the
width of the file cabinet is
wD15 in:
, determine the maximum height
h
at
which the file cabinet can be pushed so that it does not tip, and determine
the corresponding acceleration of the file cabinet. Assume that friction
between the file cabinet and the floor is negligible.
Solution
Since we want tipping of the cabinet to be imminent, the normal force is located
at the corner of the cabinet as shown in the FBD on the right. No friction force is
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 1425
Problem 7.5
The uniform slender bar
AB
has a weight
WAB D150 lb
while the
crate’s weight is
WCD500 lb
. The bar
AB
is rigidly attached to the
cage containing the crate. Neglect the mass of the cage, and assume
that the mass of the crate is uniformly distributed. Furthermore, let
LD8:5 ft, dD2:5 ft, hD4ft, and wD6ft.
If the trolley is accelerating with
a0D11 ft=s2
, determine
so
that the bar-crate system translates with the trolley.
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.
