978-0073380308 Chapter 6 Solution Manual Part 8

Problem 6.52

A ball of radius

RAD3in:

is rolling without slip in a stationary

spherical bowl of radius

RBD8in:

Assume that the ball’s mo-

tion is planar. Express your answers using the component system

shown.

If the speed of the center of the ball is

vAD1:75 ft=s

and if

the ball is moving down and to the right, determine the angular

velocity of the ball.

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Dynamics 2e 1221

Problem 6.53

A ball of radius

RAD3in:

is rolling without slip in a stationary

spherical bowl of radius

RBD8in:

Assume that the ball’s mo-

tion is planar. Express your answers using the component system

shown.

If the angular speed of the ball

j!Aj D 4rad=s

is counterclock-

wise, determine the velocity of the center of the ball.

Solution

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permission of McGraw-Hill, is prohibited.

Problem 6.54

In the mechanism shown, the block

B

is constrained to move vertically

and is attached to the bar

BD

. The point

A

on the bar

AD

is fixed.

Express all your answers in the component system shown.

At the instant shown, the block

B

is moving downward at

2:5 ft=s

,

D45ı

, and

D30ı

. If

`D12 in:

and

dD8in:

, determine the

angular velocity of bar AD at this instant.

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 1223

Problem 6.55

In the mechanism shown, the block

B

is constrained to move vertically

and is attached to the bar

BD

. The point

A

on the bar

AD

is fixed.

Express all your answers in the component system shown.

At the instant shown, bar

AD

is rotating counterclockwise at the

angular speed

!AD D13 rad=s

,

D45ı

, and

D30ı

. If

`D24 in:

and

dD16 in:, determine the velocity of the block Bat this instant.

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.

Problem 6.56

In the mechanism shown, the block

B

is constrained to move vertically

and is attached to the bar

BD

. The point

A

on the bar

AD

is fixed.

Express all your answers in the component system shown.

At the instant shown, the block

B

is moving downward at

1:5 m=s

,

D45ı

, and

D30ı

. If

`D1:2

m and

dD0:8

m, determine the

angular velocity of bar AD and the velocity of point Cat this instant.

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.

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.

Problem 6.57

One way to convert rotational motion into linear motion and vice versa is

with the use of a mechanism called a Scotch yoke, which consists of a

crank

C

that is connected to a slider

B

by a pin

A

. The pin rotates with

the crank while sliding within the yoke, which, in turn, rigidly translates

with the slider. This mechanism has been used, for example, to control

the opening and closing of valves in pipelines. Letting the radius of the

crank be

RD1:5 ft

, determine the angular velocity

!C

of the crank so

that the maximum speed of the slider is vBD90 ft=s.

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permission of McGraw-Hill, is prohibited.

Dynamics 2e 1227

Problem 6.58

The system shown consists of a wheel of radius

RD14 in:

rolling on a

horizontal surface. A bar

AB

of length

LD40 in:

is pin-connected to the

center of the wheel and to a slider

A

that is constrained to move along a

vertical guide. Point Cis the bar’s midpoint.

If, when

D72ı

, the wheel is moving to the right so that

vBD7ft=s

,

determine the angular velocity of the bar, as well as the velocity of the

slider A.

Solution

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.

Problem 6.59

The system shown consists of a wheel of radius

RD14 in:

rolling on a

horizontal surface. A bar

AB

of length

LD40 in:

is pin-connected to the

center of the wheel and to a slider

A

that is constrained to move along a

vertical guide. Point Cis the bar’s midpoint.

If, when

D53ı

, the slider is moving downward with a speed

vAD8ft=s, determine the velocity of points Band C.

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 1229

Problem 6.60

The system shown consists of a wheel of radius

RD14 in:

rolling on a

horizontal surface. A bar

AB

of length

LD40 in:

is pin-connected to the

center of the wheel and to a slider

A

that is constrained to move along a

vertical guide. Point Cis the bar’s midpoint.

If the wheel rolls without slip with a constant counterclockwise an-

gular velocity of

10 rad=s

, determine the velocity of the slider

A

when

D45ı.

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.