978-0073380308 Chapter 8 Solution Manual Part 14

Problem 8.77

The rear-wheel-drive car can go from rest to

60 mph

in

tD8

s.

Assume that the wheels are all identical and that their geometric

centers coincide with their mass centers. Let

Mrear

be the average

moment applied to one of the rear wheels during

t

and computed

relative to the wheel’s center. Finally, let

Mfront

be the average mo-

ment applied to one of the front wheels during

t

and computed

relative to the wheel’s center. Modeling the wheels as rigid bod-

ies, determine which of the following statements is true and why:

(a)

ˇˇMrearˇˇ<ˇˇMfrontˇˇ

, (b)

ˇˇMrearˇˇDˇˇMfrontˇˇ

, (c)

ˇˇMrearˇˇ>

ˇˇMfrontˇˇ.

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Dynamics 2e 1789

Problem 8.78

The rear-wheel-drive car can go from rest to

60 mph

in

tD8

s.

Assume that its wheels are identical, with their geometric centers

coinciding with their mass centers. Let

Favg

be the average friction

force acting on the system during

t

due to contact with the

ground. Modeling the car and the wheels as rigid bodies, does the

value of

Favg

change whether or not we account for the rotational

inertia of the wheels? Why?

Solution

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Problem 8.79

A uniform disk of mass

m

and radius

R

rolls to the right without slip, such

that the speed of the center of mass is

vG

. Provide an expression for the linear

momentum of the disk in terms of the given quantities. In addition, provide

an expression for the angular momentum of the disk relative to

O

, the point of

contact with the ground. Express your answers using the component system

shown.

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Dynamics 2e 1791

Problem 8.80

At the instant shown, the eccentric wheel with center at

O

and center of mass

at

G

is rotating counterclockwise without slip with an angular speed

!wD

10 rad=s

. The weight of the wheel is

WD90 lb

. In addition, let

RD2ft

,

hD1ft

, and the radius of gyration

kGD1:45 ft

. At the instant shown,

determine the linear momentum of the disk and the angular momentum about

C

, the point of contact with the ground. Express your answers in the component

system shown.

Solution

Let

EvG

and

Epw

denote the velocity of

G

and the linear momentum of the wheel, respectively. The linear

Problem 8.81

The top of the Space Needle in Seattle, Washington, hosts a revolving

restaurant that goes through one full revolution every

47 min

under

the action of a motor with a power output of

1:5 hp

. The portion

of the restaurant that rotates is a ring-shaped turntable with internal

and external radii

riD33:3 ft

and

roD47:3 ft

, respectively, and

approximate weight

WD125 tons

(

1ton D2000 lb

). Use the given

values of power output and angular speed to estimate the torque

M

that the engine provides. Then, assuming that the motor can provide

a constant torque equal to

M;

neglecting all friction, and modeling

the turntable as a uniform body, determine the time

ts

that it takes

to spin up the revolving restaurant from rest to its working angular

speed.

Solution

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Dynamics 2e 1793

Computation. Substituting Eq. (2), the first of Eqs. (3), and Eqs. (4) into Eq. (1), we have

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Problem 8.82

A rotor, spinning freely about the fixed point

O

, consists of a thin uniform bar

AB

that functions as a hub

and two identical blades pinned at

A

and

B

, respectively. The dimensions of the system are:

dD0:5

m,

`D5

m, and

wD0:3

m. The bar

AB

has a mass

mAB D30 kg

, and each of the blades has a mass

mbD20 kg

. Each blade can be modeled as a uniform thin plate. The angular speed is

!rD100 rpm

when

the angle

✓

is equal to

90ı

. At some point, an internal mechanism causes the blades to change orientation

relative to

AB

in such a way that

✓

becomes constant and equal to

180ı

. Neglecting aerodynamic forces

and friction at the bearings at O, determine the angular speed of the rotor after ✓D180ı.

Solution

Referring to the figure below, since the rotor is spinning freely in the horizontal plane, the system is not acted

upon by any force or moment that would promote or hinder its rotation. Hence, the system can be considered

isolated. This implies that the angular momentum of the system about any point is conserved. We denote

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

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Dynamics 2e 1795

Kinematic Equations. The initial angular velocity is known:

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1796 Solutions Manual

A uniform disk of mass

mD20 kg

and radius

RD0:75

m is being pulled

to the left with a constant horizontal force

P

by the cord wrapped around it.

Assume that the disk starts from rest and that it rolls without slip.

If

PD30

N, apply the impulse-momentum principles to determine the

angular speed of the disk after 4s.

Solution

We model the disk as a rigid body subject only to its own weight

mg

, the force

P

,

and the components

F

and

N

of the contact force between the disk and the ground.

We denote by

t1D0

the initial time and by

t2D4

s, the time at which the answer

to the problem needs to be provided. We select

G

as the moment center for the

Dynamics 2e 1797

Eliminating the time integral of Ffrom the above two equations, we have

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