978-0073380308 Chapter 7 Solution Manual Part 8

Problem 7.37

The composite body lies in the vertical plane and is rotating with angular

speed

!bD11 rad=s

at the instant shown. The mass of the disk

D

is

mbD4kg

, the mass of the bar

AB

is

mAB D1:5 kg

, the length of the

bar

AB

is

LD50 cm

, and the radius of the disk is

RD10 cm

. At the

instant shown, determine the angular acceleration of the composite body

and the horizontal and vertical reactions on the body at A.

2mbg.L CR/ DIC˛AB CIE˛DCmAB aCy L

2CmbaEy .L CR/; (3)

where the mass moments of inertia are given by

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Dynamics 2e 1487

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Problem 7.38

The bar

AB

is pinned to a fixed support at

A

at one end and to

the center of the bike wheel

B

at its other end. The bike wheel

is spinning with angular speed

!0D50 rad=s

when it is gently

placed on the horizontal surface. The mass of the bike wheel is

mwD2:5 kg

, its radius is

RD33 cm

, and its mass moment of

inertia is IBD0:2486 kgm2.

If the mass of bar

AB

is negligible and the coefficient of kinetic

friction between the wheel and the surface is

kD0:6

, determine

the time it takes for the wheel to come to a complete stop, and find

the reactions at Aand Bon bar AB.

fFAB

p2DmwaBx;

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Dynamics 2e 1489

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Problem 7.39

The bar

AB

is pinned to a fixed support at

A

at one end and to

the center of the bike wheel

B

at its other end. The bike wheel

is spinning with angular speed

!0D50 rad=s

when it is gently

placed on the horizontal surface. The mass of the bike wheel is

mwD2:5 kg

, its radius is

RD33 cm

, and its mass moment of

inertia is IBD0:2486 kgm2.

If the mass of bar

AB

is

mAB D1:5 kg

and the coefficient of

kinetic friction between the wheel and the surface is

kD0:6

,

determine the time it takes for the wheel to come to a complete stop,

and find the reactions at Aand Bon bar AB.

Solution

Since bar

AB

has mass, the FBD of the bar and of the wheel are as shown on

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Dynamics 2e 1491

Computation. Substituting the kinematics equations and the force law in to Eqs. (1)–(6), we obtain

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Problem 7.40

The bar

AB

is pinned to a fixed support at

A

at one end and to

the center of the bike wheel

B

at its other end. The bike wheel

is spinning with angular speed

!0D50 rad=s

when it is gently

placed on the horizontal surface. The mass of the bike wheel is

mwD2:5 kg

, its radius is

RD33 cm

, and its mass moment of

inertia is IBD0:2486 kgm2.

If the mass of bar

AB

is

mAB D1:5 kg

, determine the coefficient

of kinetic friction between the wheel and the surface so that it takes

2

s to come to a complete stop. In addition, find the reactions at

A

and Bon bar AB for these conditions.

Solution

Since bar

AB

has mass, the FBD of the bar and of the wheel are as shown on

the right, where

F

f

is the friction force between the wheel and the ground and

Cis the mass center of bar AB.

Balance Principles.

Using the FBDs on the right, the Newton-Euler equa-

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Dynamics 2e 1493

Computation. Substituting the kinematics equations and the force law in to Eqs. (1)–(6), we obtain

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Problem 7.41

Assume that the plane is on the ground, and model each of its two

propeller blades as a rectangular plate of mass

mD29 kg

, length

LD137 cm

, and width

wD20 cm

. If the engine torque

MO

applied to the propeller shaft is

410 Nm

, determine the time it

takes for the blades to achieve an angular speed of

2000 rpm

if the

blades start from rest. What would be the required time if, instead,

the blades were modeled as thin rods of length Land mass m?

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Dynamics 2e 1495

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