978-0073380308 Chapter 7 Solution Manual Part 2

Kinematic Equations.

Since the system is translating with the trolley, there is no rotation and the

y

components of acceleration are zero, which implies

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Dynamics 2e 1427

Problem 7.6

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 bar-crate system is translating with the trolley so that

D26ı, determine the acceleration a0of the trolley.

2CWAB

2sin DID˛CCIG˛AB

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Kinematic Equations.

Since the system is translating with the trolley, there is no rotation and the

y

components of acceleration are zero, which implies

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Dynamics 2e 1429

Problem 7.7

A person is pushing a lawnmower of mass

mD38 kg

and with

hD0:75

m,

dD0:25

m,

`AD0:28

m, and

`BD0:36

m. Assuming

that the force exerted on the lawnmower by the person is completely

horizontal and that the mass center of the lawnmower is at

G

, and

neglecting the rotational inertia of the wheels, determine the minimum

value of this force that causes the rear wheels (labeled

A

) to lift off

the ground. In addition, determine the corresponding acceleration of

the mower.

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Problem 7.8

The mower is self-propelled through its rear wheels. If a person were

to apply a purely horizontal force, would this force help or hinder

the rear wheels’ contribution to the forward motion of the mower?

That is, would the rear wheels slip less easily or more easily?

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Dynamics 2e 1431

Problem 7.9

The stationary wheel loader is lifting the load at

B

vertically

with acceleration

a0D10 ft=s2

. If the weight of the load

B

is

10;000 lb

, the weight of the wheel loader is

33;000 lb

,

`D118 in:

,

hD90 in:

, and

dD27 in:

, determine the reactions on each of its

four wheels if the wheel loader is laterally symmetric. In addition,

compute the static load on each of the four wheels (i.e., with

a0D0

) and compare it with the corresponding dynamic load.

The center of mass of the wheel loader is at A.

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1432 Solutions Manual

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Dynamics 2e 1433

Problem 7.10

The stationary wheel loader is lifting the load at

B

vertically with

acceleration

a0

. If the weight of the load

B

is

10;000 lb

, the

weight of the wheel loader is

33;000 lb

,

`D118 in:

,

hD90 in:

,

and

dD27 in:

, determine the largest value of

a0

for which the

reaction on each of the rear wheels does not drop below

1000 lb

.

The center of mass of the wheel loader is at A.

FrD1000 lb:

Kinematic Equations.

Since neither the wheel loader nor the crate rotate, all angular accelerations are

0D0; (1)

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1434 Solutions Manual

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Dynamics 2e 1435

Problem 7.11

The door is at rest when the man

M

starts pushing it to the right

with a constant horizontal force of

40 lb

. If the weight of the door

is

300 lb

, its width and height are both

`D10 ft

, its center of

mass

G

is at its geometric center, and the man pushes at a height

hD4ft

, determine the speed of the door after it has moved

10 ft

and determine the reactions at the rollers Aand B.

2hCNB

2NA

2DIG˛d;

where

Wd

is the weight of the door and

˛d

is its angular accelera-

tion.

Force Laws. All forces are accounted for on the FBD.

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