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PROBLEM 15.17
The earth makes one complete revolution on its axis in 23 h 56 min. Knowing that the mean radius of the
earth is 3960 mi, determine the linear velocity and acceleration of a point on the surface of the earth
(a) at the equator, (b) at Philadelphia, latitude 40° north, (c) at the North Pole.
PROBLEM 15.18
A series of small machine components being moved by a
conveyor belt pass over a 120 mm radius idler pulley. At the
instant shown, the velocity of Point A is 300 mm/s to the left
and its acceleration is 180 mm/s2 to the right. Determine (a) the
angular velocity and angular acceleration of the idler pulley,
(b) the total acceleration of the machine component at B.
PROBLEM 15.19
A series of small machine components being moved by a
conveyor belt pass over a 120-mm-radius idler pulley. At the
instant shown, the angular velocity of the idler pulley is 4 rad/s
clockwise. Determine the angular acceleration of the pulley for
which the magnitude of the total acceleration of the machine
component at B is
2
2400 mm/s .
PROBLEM 15.20
The belt sander shown is initially at rest. If the driving drum B
has a constant angular acceleration of 120 rad/s2 counter-
clockwise, determine the magnitude of the acceleration of the
belt at Point C when (a) t = 0.5 s, (b) t = 2 s.
PROBLEM 15.21
The rated speed of drum B of the belt sander shown is 2400 rpm.
When the power is turned off, it is observed that the sander
coasts from its rated speed to rest in 10 s. Assuming uniformly
decelerated motion, determine the velocity and acceleration of
Point C of the belt, (a) immediately before the power is turned
off, (b) 9 s later.
PROBLEM 15.22
The two pulleys shown may be operated with the V belt in any of three
positions. If the angular acceleration of shaft A is 6 rad/s2 and if the
system is initially at rest, determine the time required for shaft B to
reach a speed of 400 rpm with the belt in each of the three positions.
PROBLEM 15.23
Three belts move over two pulleys without slipping in the speed
reduction system shown. At the instant shown the velocity of
Point A on the input belt is 2 ft/s to the right, decreasing at the
rate of 6 ft/s2. Determine, at this instant, (a) the velocity and
acceleration of Point C on the output belt, (b) the acceleration
of Point B on the output pulley.
PROBLEM 15.23 (Continued)
(a) Velocity and acceleration of Point C.
32
2(3) 0.5 ft/s
12
C
vr
ω
= = =
0.5 ft/s
C=v
2
32
2
( ) (9) 1.5 ft/s
12
Ct
ar
α
= = =
2
1.5 ft/s
C
=
a
(b) Acceleration of Point B.
2 22
42
4
( ) (3) 3 ft/s
12
Bn
ar
ω
= = =
2
( ) 3 ft/s
Bn
=a
2
42
4
( ) (9) 3 ft/s
12
Bt
ar
α
= = =
2
( ) 3 ft/s
Bt=
a
2
4.24 ft/s
B
=a
45°
PROBLEM 15.24
A gear reduction system consists of three gears A, B, and C. Knowing
that gear A rotates clockwise with a constant angular velocity
A
ω
= 600 rpm, determine (a) the angular velocities of gears B and C,
(b) the accelerations of the points on gears B and C which are in contact.
PROBLEM 15.25
A belt is pulled to the right between cylinders A and B. Knowing that the
speed of the belt is a constant 5 ft/s and no slippage occurs, determine (a) the
angular velocities of A and B, (b) the accelerations of the points which are in
contact with the belt.
