978-0073380308 Chapter 7 Solution Manual Part 3

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permission of McGraw-Hill, is prohibited.

Dynamics 2e 1437

Problem 7.12

The

300 lb

door is at rest when the man

M

starts pushing it to the

right. If the width and height of the door are both

`D10 ft

, its

center of mass

G

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

height

hD4ft

, determine the horizontal force with which he must

push if he is to move the door

10 ft

to the right in

3

s, and determine

the reactions at the rollers Aand B.

Solution

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Solving, we obtain

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Dynamics 2e 1439

Problem 7.13

The portable hydraulic crane with mass

mGD60 kg

is stationary as

it lifts the crate with mass

mCD110 kg

vertically with acceleration

aCD2:5 m=s2

. The mass center of the crate is at

C

and the mass

center of the crane is at

G

. If

dD0:145

m,

`D1:3

m, and

hD

0:27

m, determine the reaction on each of the two front

F

and the two

rear Rwheels.

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Computation.

Substituting the kinematic equations into the Newton-Euler equations, the first of the

Newton-Euler equations gives 0D0and the second and third become

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Dynamics 2e 1441

Problem 7.14

The portable hydraulic crane with mass

mGD60 kg

is stationary as it

lifts the crate with mass

mCD110 kg

vertically with acceleration

aC

.

The mass center of the crate is at

C

and the mass center of the crane

is at

G

. If

dD0:145

m,

`D1:3

m, and

hD0:27

m, determine the

maximum value of the acceleration

aC

, such that no wheel reaction

exceeds

400

N. Assume that the crane is laterally symmetric so that

the loads on the front wheels are equal and the loads on the rear

wheels are equal.

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Kinematic Equations.

Since neither the crate or crane are rotating or moving in the

x

direction, the

kinematic equations are:

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Dynamics 2e 1443

Problem 7.15

During takeoff, the thrust from each of the two engines of a Boeing

737 is

TD95 kN

. The mass center of the airplane is located at

G

, the horizontal distance between the main landing gear and

G

is

dD5:15

m, the horizontal distance between the front landing

gear and the main landing gear is

`D11:1

m, and the height of the

mass center above the ground is

hD2:36

m. The mass of the plane

is

mD74;200 kg

, and the thrust from each engine is a distance

ıD1:15 m above the ground.

As the airplane begins its takeoff, the lift

L

from its wings can

be neglected. Determine the normal reaction on the front landing

gear and each of the two wheels of the main landing gear at the start

of takeoff.

Solution

An FBD of the plane at the start of takeoff is shown on the right, where

F

f

is the force on the front landing gear and

Fm

is the force on each

of the two wheels of the main landing gear. We have neglected the lift

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1444 Solutions Manual

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Dynamics 2e 1445

Problem 7.16

During takeoff, the thrust from each of the two engines of a Boeing

737 is

TD95 kN

. The mass center of the airplane is located at

G

, the horizontal distance between the main landing gear and

G

is

dD5:15

m, the horizontal distance between the front landing

gear and the main landing gear is

`D11:1

m, and the height of the

mass center above the ground is

hD2:36

m. The mass of the plane

is

mD74;200 kg

, and the thrust from each engine is a distance

ıD1:15 m above the ground.

Assuming that the wings are the only surfaces generating lift

during takeoff, determine the lift

L

generated by each wing when

the normal force on the main landing gear is 25% of its initial takeoff

value. The line of action of Lgoes through G.

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