978-0073380308 Chapter 8 Solution Manual Part 10

Force Laws. Due to the choice of datum,

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Dynamics 2e 1749

Problem 8.57

The figure shows the cross section of a garage door with length

LD9ft

and weight

WD175 lb

. At

A

and

B

, there are rollers of negligible

mass constrained to move in the guide whose horizontal portion is at

a distance

HD11 ft

from the ﬂoor. The door’s motion is assisted by

two springs, each with constant

k

(only one spring is shown). The door

is released from rest when

dD26 in:

and the spring is stretched

4in:

Neglecting friction, knowing that, when

A

touches the ﬂoor,

B

is in

the vertical portion of the guide, and modeling the door as a uniform

thin plate, determine the minimum value of

k

so that

A

will strike the

ground with a speed no greater than 1ft=s.

Solution

We model the door as a thin rigid body subject to its own weight

W

, the

Problem 8.58

The figure shows the cross section of a garage door with length

LD2:5

m and mass

mD90 kg

. At the ends

A

and

B

, there are

rollers of negligible mass constrained to move in the guide whose

horizontal portion is at a distance

HD3

m from the ﬂoor. The door’s

motion is assisted by two counterweights

C

, each of mass

mC

(only

one counterweight is shown). If the door is released from rest when

dD53 cm

, neglecting friction and modeling the door as a uniform

thin plate, determine the minimum value of

mC

so that

A

will strike

the ground with a speed no greater than 0:25 m=s.

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permission of McGraw-Hill, is prohibited.

Dynamics 2e 1751

Computation. Substituting Eqs. (2)–(4) into Eq. (1), we have

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Problem 8.59

The uniform thin rod

AB

is pin-connected to the slider

S

, which moves along

the frictionless guide, and to the disk

D

, which rolls without slip over the

horizontal surface. The pins at

A

and

B

are frictionless, and the system is

released from rest. Neglect the vertical dimension of S.

Letting

LD1:75

m and

RD0:6

m, assuming that

S

and

D

are of neg-

ligible mass, that the mass of rod

AB

is

mAB D7kg

, and that the system is

released from the angle

✓0D65ı

, determine the speed of the slider

S

when it

strikes the ground.

of McGraw-Hill, and must be surrendered upon request of McGraw-Hill. Any duplication or distribution, either in print or electronic form, without the

permission of McGraw-Hill, is prohibited.

Dynamics 2e 1753

where we have used the expression for !AB in Eq. (5). Next, we now observe that, in ¡we have

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permission of McGraw-Hill, is prohibited.

Problem 8.60

The uniform thin rod

AB

is pin-connected to the slider

S

, which moves along

the frictionless guide, and to the disk

D

, which rolls without slip over the

horizontal surface. The pins at

A

and

B

are frictionless, and the system is

released from rest. Neglect the vertical dimension of S.

Letting

LD4:5 ft

and

RD1:2 ft

, assuming that AB is of negligible mass,

the weight of

S

is

WSD3lb

,

D

is a uniform disk of weight

WDD9lb

, and

the system is released from the angle

✓0D67ı

, determine the speed of the

slider Swhen it strikes the ground.

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permission of McGraw-Hill, is prohibited.

Dynamics 2e 1755

Kinematic Equations. We observing that Smoves only in the vertical direction, so

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permission of McGraw-Hill, is prohibited.

Problem 8.61

The uniform thin rod

AB

is pin-connected to the slider

S

, which moves along

the frictionless guide, and to the disk

D

, which rolls without slip over the

horizontal surface. The pins at

A

and

B

are frictionless, and the system is

released from rest. Neglect the vertical dimension of S.

Letting

LD1:75

m and

RD0:6

m, assuming that the mass of

S

is

mSD4:2 kg

,

D

is a uniform disk of mass

mDD12 kg

, the mass of AB is

mAB D7kg

, and that the system is released from the angle

✓D69ı

, determine

the speed and the direction of motion of point

B

when the slider

S

strikes the

ground.

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permission of McGraw-Hill, is prohibited.

Dynamics 2e 1757

Force Laws.

Due to the choice of datum, and recalling that the size of the slider is being ignored, we have

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permission of McGraw-Hill, is prohibited.