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PROBLEM 11.131 (Continued)
Therefore 520
or 25.964
PROBLEM 11.132
As part of a department store
display, a model train D runs on a
slight incline between the store’s
up and down escalators. When the
train and shoppers pass Point A,
the train appears to a shopper on
the up escalator B to move
downward at an angle of 22° with
the horizontal, and to a shopper
on the down escalator C to move
upward at an angle of 23° with the
horizontal and to travel to the left.
Knowing that the speed of the
escalators is 3 ft/s, determine the
speed and the direction of the
train.
sin (22 2.0728 )
D
1.024 ft/s
D
v
2.07°
PROBLEM 11.132 (Continued)
Alternate solution using components.
(3 ft/s)
B
v
30 (2.5981 ft/s) (1.5 ft/s)
ij
//DBDBCDC
11 2 2
2.5981 1.5 ( cos 22 ) ( sin 22 ) 2.5981 1.5 ( cos 23 ) ( sin 23 )uu u u
ij i j ij i j
Separate into components, transpose, and change signs.
1
2
1
2
D
PROBLEM 11.133
Determine the smallest radius that should be used for a
highway if the normal component of the acceleration of a car
traveling at 72 km/h is not to exceed 2
0.8 m/s .
0.8 m/s
500 m
PROBLEM 11.134
Determine the maximum speed that the cars of the roller-coaster
can reach along the circular portion AB of the track if
is 25 m
and the normal component of their acceleration cannot exceed 3 g.
AB
Problem 11.135
Human centrifuges are often used to simulate different
acceleration levels for pilots and astronauts. Space shuttle
pilots typically face inwards towards the center of the gondola
in order to experience a simulated 3g forward acceleration.
Knowing that the astronaut sits 5 m from the axis of rotation
and experiences 3 g’s inward, determine her velocity.
A
PROBLEM 11.136
The diameter of the eye of a stationary hurricane is 20 mi and the
maximum wind speed is 100 mi/h at the eye wall, r 10 mi.
Assuming that the wind speed is constant for constant r and
decreases uniformly with increasing r to 40 mi/h at r 110 mi,
determine the magnitude of the acceleration of the air at (a) r 10
mi, (b) r 60 mi, (c) r 110 mi.
580800
PROBLEM 11.137
The peripheral speed of the tooth of a 10-in.-diameter circular saw blade is 150 ft/s when the power to the saw
is turned off. The speed of the tooth decreases at a constant rate, and the blade comes to rest in 9 s. Determine
the time at which the total acceleration of the tooth is 2
130 ft/s .
t
PROBLEM 11.138
A robot arm moves so that P travels in a circle about Point B,
which is not moving. Knowing that P starts from rest, and its speed
increases at a constant rate of 10 mm/s2, determine (a) the
magnitude of the acceleration when t 4 s, (b) the time for the
magnitude of the acceleration to be 80 mm/s2.
n
where 0.8 m 800 mm
2
(40) 2 mm/s
n
a
tn
2
10.20 mm/sa
(b) Time when 2
80 mm/sa
222
2
nt
aaa
PROBLEM 11.139
A monorail train starts from rest on a curve of radius 400 m and accelerates at the constant rate .
t
a If the
maximum total acceleration of the train must not exceed 2
1.5 m/s , determine (a) the shortest distance in
which the train can reach a speed of 72 km/h, (b) the corresponding constant rate of acceleration .
t
a
2
(20) 1.000 m/s
400
n
v
a
1
(20)
v
t
PROBLEM 11.140
A motorist starts from rest at Point A on a circular entrance ramp
when t 0, increases the speed of her automobile at a constant
rate and enters the highway at Point B. Knowing that her speed
continues to increase at the same rate until it reaches 100 km/h
at Point C, determine (a) the speed at Point B, (b) the
magnitude of the total acceleration when t 20 s.
B
23.27 m/s
B
v 83.8 km/h
B
v
(22.99) 3.524 m/s
v
tn
PROBLEM 11.141
Racecar A is traveling on a straight portion of the track while
racecar B is traveling on a circular portion of the track. At the
instant shown, the speed of A is increasing at the rate of 10
m/s
2
, and the speed of B is decreasing at the rate of 6 m/s
2
. For
the position shown, determine (a) the velocity of B relative to
A, (b) the acceleration of B relative to A.
55.56 m/s
B
v
50°
/
BA
30.96 42.56
/
189.5 km/h
BA
v
54.0°
Tangential accelerations: 2
() 10 m/s
At
a
2
(55.56)
( ) 10.288
300
Bn
a
2
( ) 10.288 m/s
Bn
a
40°
PROBLEM 11.142
At a given instant in an airplane race, airplane A is flying
horizontally in a straight line, and its speed is being increased
at the rate of
2
8 m/s . Airplane B is flying at the same altitude
as airplane A and, as it rounds a pylon, is following a circular
path of 300-m radius. Knowing that at the given instant the
speed of B is being decreased at the rate of 2
3 m/s ,
determine,
for the positions shown, (a) the velocity of B relative to A,
(b) the acceleration of B relative to A.
/
BA
PROBLEM 11.143
A race car enters the circular portion of a track that has a radius
of 70 m. When the car enters the curve at point P, it is
travelling with a speed of 120 km/h that is increasing at 5 m/s
2
.
Three seconds later, determine (a) the total acceleration of the
car in xy components, (b) the linear velocity of the car in xy
components.
2
48.33 33.37 m/s
70
n
a
y
PROBLEM 11.144
An airplane flying at a constant speed of 240 m/s makes a banked horizontal turn.
What is the minimum allowable radius of the turn if the structural specifications
require that the acceleration of the airplane shall never exceed 4g?
PROBLEM 11.145
A golfer hits a golf ball from Point A with an initial velocity of 50 m/s at an angle
of 25° with the horizontal. Determine the radius of curvature of the trajectory
described by the ball (a) at Point A, (b) at the highest point of the trajectory.
2
(9.81 m/s ) cos 25
or 281 m
A
2
B
v
Then
2
9.81 m/s
B
or 209 m
B
PROBLEM 11.146
Three children are throwing
snowballs at each other. Child A
throws a snowball with a horizontal
velocity v0. If the snowball just
passes over the head of child B and
hits child C, determine the radius of
curvature of the trajectory
described by the snowball (a) at
Point B, (b) at Point C.
22 22
(15.504) (2)(9.81)(1) 259.97 m /s
B
v
PROBLEM 11.146 (Continued)
(9.81 m/s )(15.504 m/s)
At Point C 1 m 2 m 3 m
C
h
(9.81 m/s )(15.504 m/s)
PROBLEM 11.147
Coal is discharged from the tailgate A of a dump truck with an
initial velocity 2 m/s
Av50. Determine the radius of
curvature of the trajectory described by the coal (a) at Point A,
(b) at the point of the trajectory 1 m below Point A.
() 4.687m/s
By
v
() 4.687
By
Bx
v
cos 74.6
B
ag
22
2() ()
B
xBy
B
vv
v
9.81cos 74.6
B
PROBLEM 11.148
From measurements of a photograph, it has been found that as the
stream of water shown left the nozzle at A, it had a radius of
curvature of 25 m. Determine (a) the initial velocity
v
A
of the
stream, (b) the radius of curvature of the stream as it reaches its
maximum height at B.
A
A
14.01 m/s
A
v
36.9°
2
B
v
B
