978-0073380308 Chapter 7 Solution Manual Part 20

Problem 7.97

An SUV is pushing a large drum to the right with force

P

, using

its front bumper. The drum has mass

m

and radius of gyration

kG

. The static and kinetic friction coefficients between the drum

and the ground and between the drum and the SUV are

s

and

k

,

respectively.

(a)

Assuming that there is no slipping between the drum and

the ground, determine the acceleration of the drum and the

minimum value of sthat is consistent with this motion.

(b)

Determine the acceleration of point

G

and the angular accel-

eration of the drum if

P

is increased so that the drum slips

relative to the ground.

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Dynamics 2e 1607

Computation.

Substituting Eqs. (4), (5), and (7) into the Newton-Euler equations yields the following

Part (b)

When there is slipping between the ground and the drum, then we must enforce the following kinetic friction

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Problem 7.98

The disk

A

rolls without slipping on a horizontal surface. End

B

of

bar

BC

is pinned to the edge of the disk

A

, and end

C

of the bar

BC

can slide freely along the horizontal surface. In addition, bar

BC

is pushed by the force

PDmg

at its left end. The mass of

bar

BC

is

mBC

, and the mass of the disk

A

is

mA

. The system is

initially at rest.

Determine the acceleration of the center of the disk

A

and the

angular acceleration of bar

BC

immediately after the force

P

is

applied if mADmBC Dm.

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permission of McGraw-Hill, is prohibited.

Dynamics 2e 1609

Kinematic Equations. Since the disk rolls without slip on a horizontal surface, we have

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Problem 7.99

The disk

A

rolls without slipping on a horizontal surface. End

B

of

bar

BC

is pinned to the edge of the disk

A

, and end

C

of the bar

BC

can slide freely along the horizontal surface. In addition, bar

BC

is pushed by the force

PDmg

at its left end. The mass of

bar

BC

is

mBC

, and the mass of the disk

A

is

mA

. The system is

initially at rest.

Determine the acceleration of the center of disk

A

and the angu-

lar acceleration of bar

BC

immediately after force

P

is applied if

mBC Dmand the mass of the disk mAis negligible.

2ByCNC2

3RDIG˛b;(6)

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permission of McGraw-Hill, is prohibited.

Dynamics 2e 1611

where we have used the fact that, at the instant of release, all velocities are zero. Relating the acceleration of

point Cto that of B, we obtain

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Problem 7.100

The crank

AB

in the slider-crank mechanism is rotating counterclockwise with constant angular velocity

!AB

. The crankshaft radius is

R

, the length of the connecting rod

BC

is

L

, and the distance from the

mass center of the connecting rod

D

to the end of the crank at

B

is

d

. The mass of the connecting rod is

mD, the mass moment of inertia of the connecting rod is ID, and the mass of the piston is mC.

(a)

Using the component system shown, determine the

x

and

y

components of the forces on the

connecting rod at Band Cas functions of the crank angle .

(b)

Using

!AB D5700 rpm

,

RD48:5 mm

,

LD141 mm

,

dD36:4 mm

,

mDD0:439 kg

,

IDD

0:00144 kgm2

, and

mCD0:434 kg

, plot each of the four force components, the magnitude of the

forces at

B

and

C

, and the moment acting on the connecting rod about point

D

, all as a function of

, for one full rotation of the crank.

Hint: The kinematics of this problem have been considered in Example 6.10 on p. 480.

Solution

Part (a)

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Dynamics 2e 1613

R2cos23

R2cos2

Computation.

Now that we have the accelerations of

C

,

D

and the angular acceleration of

BC

in terms of

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permission of McGraw-Hill, is prohibited.

Substituting Eqs. (6), (7), (9), and (11) into Eqs. (12)–(15), after simplification, we have

AB cos 

<

AB “RL2R2cos2

.L2R2cos /3=2 sin Rsin2

Part (b)

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permission of McGraw-Hill, is prohibited.

1#%L

R&2

%% L

R&2#Cos!Θ“2&

3

2

Sin!Θ“2

%L

R&2#Cos!Θ“2

%L

R&2#Cos!Θ“2

1#%L

Sin!Θ“2

The Mathematica code defining the angular acceleration, the problem’s parameters, and the plotting com-

mands is as follows:

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July 6, 2012