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PROBLEM 11.166
The pin at B is free to slide along the circular slot DE
and along the rotating rod OC. Assuming that the rod
OC rotates at a constant rate
, (a) show that the
acceleration of pin B is of constant magnitude,
(b) determine the direction of the acceleration of pin B.
PROBLEM 11.167
To study the performance of a racecar, a high-speed camera is
positioned at Point A. The camera is mounted on a mechanism
which permits it to record the motion of the car as the car
travels on straightway BC. Determine (a) the speed of the car in
terms of b, ,
and ,
(b) the magnitude of the acceleration in
terms of b,
,
,
and .
cos
PROBLEM 11.167 (Continued)
2
2(2tan)
cos
a
PROBLEM 11.168
After taking off, a helicopter climbs
in a straight line at a constant angle
.
Its flight is tracked by radar from
Point A. Determine the speed of the
helicopter in terms of d,,
,
and .
r
PROBLEM 11.168 (Continued)
Using the expressions for r and r
from above
2
tan sin cos
1/ 2
2
tan (tan sin cos ) 1
d
(tan cos sin )
PROBLEM 11.169
At the bottom of a loop in the vertical plane,
an airplane has a horizontal velocity of 315
mi/h and is speeding up at a rate of 10 ft/s2.
The radius of curvature of the loop is 1 mi.
The plane is being tracked by radar at O.
What are the recorded values of , , rr
and
for this instant?
SOLUTION
PROBLEM 11.169 (Continued)
2
2
22
2
cos sin 10 cos 36.87 40.425 sin 36.87 32.255 ft/s
sin cos 10 sin 36.87 40.425 cos 36.87 26.34 ft/s
rt n
tn
rr
aa a
aa a
arr rar
3000 3000
2
0.0315 rad/s
PROBLEM 11.170
Pin C is attached to rod BC and slides freely in the slot of rod OA
which rotates at the constant rate .
At the instant when 60 ,
determine (a) and ,r
(b) and .r
Express your answers in terms
of d and .
222
3
rd
PROBLEM 11.171
For the racecar of Problem 11.167, it was found that it took 0.5
s for the car to travel from the position
60
to the position
35
.
Knowing that
25 m,b
determine the average speed
of the car during the
0.5-s
interval.
PROBLEM 11.167
To study the performance of a racecar, a
high-speed camera is positioned at Point A. The camera is
mounted on a mechanism which permits it to record the motion
of the car as the car travels on straightway BC. Determine
(a) the speed of the car in terms of b,
,
and
,
(b) the
magnitude of the acceleration in terms of b,
,
,
and
.
SOLUTION
PROBLEM 11.172
For the helicopter of Problem 11.168, it was found that when the helicopter was at B, the distance and the
angle of elevation of the helicopter were r
3000 ft
and
20 ,
respectively. Four seconds later, the radar
station sighted the helicopter at r
3320 ft
and
23.1 .
Determine the average speed and the angle of
climb
of the helicopter during the 4-s interval.
PROBLEM 11.168
After taking off, a helicopter climbs in a straight line at a constant angle
.
Its flight is
tracked by radar from Point A. Determine the speed of the helicopter in terms of d,
,
,
and
.
SOLUTION
PROBLEM 11.173
A particle moves along the spiral shown. Determine the magnitude
of the velocity of the particle in terms of b, , and .
SOLUTION
2
1
22
21
PROBLEM 11.174
A particle moves along the spiral shown. Determine the magnitude of the
velocity of the particle in terms of b, , and .
34
PROBLEM 11.175
A particle moves along the spiral shown. Knowing that
is
constant and denoting this constant by ,
determine the
magnitude of the acceleration of the particle in terms of b,
, and
.
PROBLEM 11.176
A particle moves along the spiral shown. Knowing that
is constant and
denoting this constant by ,
determine the magnitude of the acceleration of
the particle in terms of b, , and
.
436 4
PROBLEM 11.177
The motion of a particle on the surface of a right circular cylinder is
defined by the relations R A, 2,t
and sin 2 ,zB nt
where A and
B are constants and n is an integer. Determine the magnitudes of the
velocity and acceleration of the particle at any time t.
PROBLEM 11.178
Show that
sin
rh
knowing that at the instant shown, step
AB of the step exerciser is rotating counterclockwise at a
constant rate
.
P
PROBLEM 11.178 (Continued)
PROBLEM 11.179
The three-dimensional motion of a particle is defined by the relations (1 ), 2 ,
t
R
Ae t
and
(1 ).
t
zB e
Determine the magnitudes of the velocity and acceleration when (a) t 0, (b) t .
PROBLEM 11.180*
For the conic helix of Problem 11.95, determine the angle that the osculating plane forms with the y axis.
PROBLEM 11.95
The three-dimensional motion of a particle is defined by the position vector
r
(Rt cos
n
t)
i
ct
j
(Rt sin
n
t)
k
. Determine the magnitudes of the velocity and acceleration of the particle.
(The space curve described by the particle is a conic helix.)
22
(2cos sin ) 2 (2sin cos )
nn n nn n nn n
nnnn n nnn
Rc t t t R t c t t t
ij k
PROBLEM 11.180* (Continued)
1/ 2
2
222222
22
1/ 2
2
222222
42
2
42
nn n
n
nn
Rc t R t
Rt
ctRt
The angle
that the osculating plane forms with y axis (see the above diagram) is equal to
22
4
n
ct
