Problem 6.21
The rectangular block is attached to a rod that runs through the
block along a diagonal. The rod is mounted in bearings at
A
and
B
that allow it to rotate about its own axis. The given dimensions are
hD8:5 cm
,
`D20 cm
, and
dD22 cm
. Express all your answers
using the component system shown.
If, at the instant shown, the rod is rotating with an angular speed
of
50 rad=s
, it is increasing at a rate of
10 rad=s2
, and the rotation is
counterclockwise as viewed from
A
looking toward
B
, determine
the velocity and acceleration of point C.
2O{C`
2O
As for the angular velocity and angular acceleration of the bar, since its axis of rotation is the line
AB
and its
angular velocity is counterclockwise as viewed from Ato B, we can write E!band E˛bas
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Dynamics 2e 1181
For the acceleration of C, we substitute Eq. (3), the second of Eqs. (4), and Eq. (5) into Eq. (2) to obtain
dO{hO|C`O
k
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Problem 6.22
At the instant shown, the paper is being unrolled with a speed
vpD7:5 m=s
and an acceleration
apD1m=s2
. If, at this instant,
the outer radius of the roll is
rD0:75
m, determine the angular
velocity !sand acceleration ˛sof the roll.
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rD1:333 rad=s2;(9)
where we have used
apD1m=s2
and
rD0:75
m. Using the second of Eqs. (6) and the last of Eqs. (9) to
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Problem 6.23
At the instant shown, the propeller is rotating with an angular
velocity
!pD400 rpm
in the positive
´
direction and it is slowing
down at
2rad=s2
, where the
´
axis is also the spin axis of the
propeller. Compute the velocity and acceleration of
Q
, which
is
14 ft
away from the spin axis. Express your answer in the
cylindrical component system shown, which has its origin at
O
on the
´
axis and its unit vector
OuR
pointing radially toward point
Q.
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Dynamics 2e 1185
Problem 6.24
The hammer of a Charpy impact toughness test machine has the geometry
shown, where
G
is the mass center of the hammer head. Use Eqs. (6.8)
and (6.13) and write your answers in terms of the component system shown.
Determine the velocity and acceleration of
G
, assuming
`D500 mm
,
hD65 mm, dD25 mm, P
D 5:98 rad=s, and R
D 8:06 rad=s2.
0:06500 m, we can evaluate EvGto obtain
EvGD.0:1495 Our3:379 Ou/m=s:
For the acceleration of Gwe have
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Problem 6.25
The hammer of a Charpy impact toughness test machine has the geometry
shown, where
G
is the mass center of the hammer head. Use Eqs. (6.8)
and (6.13) and write your answers in terms of the component system shown.
Determine the velocity and acceleration of
G
as a function of the
geometric parameters shown, P
and R
.
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v0O{D `!AB O{)!AB D v0=`: (3)
Relating the velocity of Cto that of A, we obtain
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where we have used Eq. (7). Substituting Eqs. (3) and (5) into Eq. (8), we obtain
0
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Dynamics 2e 1189
Problem 6.27
In a contraption built by a fraternity, a person is sitting at the center of
a swinging platform with length
LD12 ft
that is suspended by two
identical arms each of length
HD10 ft
. Determine the angle
and
the angular speed of the arms if the person is moving upward and to
the left with a speed vpD25 ft=s at the angle D33ı.
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