978-0073380308 Chapter 7 Solution Manual Part 6

Problem 7.26

The system shown lies in the vertical plane. The trolley

A

is

moving to the right with a constant acceleration

aA

. Attached

to the trolley by a pin is a thin uniform bar

AB

of mass

m

and

length

L

. Attached to the end of the bar

AB

by a pin is a thin

uniform bar

BC

of mass

m

and length

L

. When the trolley

A

is accelerating at constant

aA

, the angles



and



are both

constant. Determine these two constant angles in this steady

state as functions of one or more of the given quantities (i.e.,

L

,

m, and aA). Note that cos.

2x/ Dsin x.

Solution

Separating the two bars, their FBDs are shown at the right, where

D

is the

mass center of bar AB and Eis the mass center of bar BC .

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Dynamics 2e 1467

In addition, since neither bar is rotating, the

x

component of acceleration of the mass center of each of the

bars must equal the acceleration of point A, that is

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Problem 7.27

Following up on Example 7.5 on p. 542, now assume that the pivot point

O

is close to the center of mass

of the batter so that it is a distance

ıD3in:

from the knob of the bat at

A

. Determine the location of the

center of percussion

P

relative to the knob at

A

, and show that the position of

P

is independent of the

location of point

C

at which the batter grips the bat. Recall that

P

is the point at which the ball should

be hit so that, no matter how large the force applied at

P

to the bat by the ball, the lateral force (i.e.,

perpendicular to the bat) felt by the batter at the grip

C

is zero. Assume the bat has mass

m

, its mass

center is at

G

, and

IG

is its mass moment of inertia. Evaluate your answer for a typical bat used in Major

League Baseball whose weight is

32 oz

and whose length is

34 in:

,

`D22:5 in:

,

mD0:0630 slug

, and

IGD0:0413 slugft2. Ignore the weight force on the bat.

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12 ft

12 in:D1ft to obtain the numerical results.

We see that the location of the center of percussion, which is determined by

d

, is independent of

h

, and

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Problem 7.28

For the centrifuge rotor and test tube given in Example 7.6 on

p. 544, assume that all the test tubes are locked into their horizontal

position and that the rotor is uniformly accelerated from rest to

60;000 rpm

in

9:5 min

. Determine, as a function of time, the

forces and moments on one of the test tubes during this spin-up

phase of motion. Assume that each test tube and its contents can

be modeled as a uniform circular cylinder with a mass of

10

g,

and ignore gravity.

Solution

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permission of McGraw-Hill, is prohibited.

Dynamics 2e 1471

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Problem 7.29

The spool is pinned at its center at

O

, about which it can spin freely. The radius of the

spool is

RD0:15

m, its radius of gyration is

kOD0:11

m, and the mass of the spool

is

msD5kg

. The mass

B

is suspended from the periphery of the spool by a chain of

negligible mass that moves over the spool without slip. The mass of Bis mBD7kg.

If the system is released from rest, determine the angular acceleration of the spool

and the tension in the chain.

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Dynamics 2e 1473

Solving these four equations for the four unknowns, we obtain

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Problem 7.30

The spool is pinned at its center at

O

, about which it can spin freely. The radius of the

spool is

RD0:15

m, its radius of gyration is

kOD0:11

m, and the mass of the spool

is

msD5kg

. The mass

B

is suspended from the periphery of the spool by a chain of

negligible mass that moves over the spool without slip. The mass of Bis mBD7kg.

If the system is released from rest, determine the number of revolutions of the spool

and the time it takes for mass Bto achieve a speed of 10 m=s.

Solution

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Dynamics 2e 1475

Solving these four equations for the four unknowns, we obtain

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