978-0073380308 Chapter 7 Solution Manual Part 1

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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.

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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.

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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

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.

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Dynamics 2e 1421

Computation.

Substituting Eqs. (4) and (5) into Eqs. (1)–(3) results in the following system of three

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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

. 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.

2N ` DIG˛can:(3)

Force Laws.

Since the cans must slip relative to the stationary surface, the

friction law is

FDkN: (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

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Dynamics 2e 1423

Problem 7.3

Determine the maximum acceleration

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

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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

from the floor. If

the mass center

of the file cabinet is

dD24 in:

from the floor and the

width of the file cabinet is

wD15 in:

, determine the maximum height

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

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Dynamics 2e 1425

Problem 7.5

The uniform slender bar

has a weight

WAB D150 lb

while the

crate’s weight is

WCD500 lb

. The bar

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



that the bar-crate system translates with the trolley.

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