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PROBLEM 12.50 (Continued)
2
v
pilot
B
PROBLEM 12.51
A carnival ride is designed to allow the general public to experience high acceleration motion. The ride rotates
about Point O in a horizontal circle such that the rider has a speed v0. The rider reclines on a platform A which
rides on rollers such that friction is negligible. A mechanical stop prevents the platform from rolling down the
incline. Determine (a) the speed v0 at which the platform A begins to roll upwards, (b) the normal force
experienced by an 80-kg rider at this speed.
SOLUTION
PROBLEM 12.52
A curve in a speed track has a radius of 1000 ft and a rated speed of 120 mi/h.
(See Sample Problem 12.7 for the definition of rated speed). Knowing that a
racing car starts skidding on the curve when traveling at a speed of 180 mi/h,
determine (a) the banking angle
θ
, (b) the coefficient of static friction between the
tires and the track under the prevailing conditions, (c) the minimum speed at
which the same car could negotiate that curve.
SOLUTION
PROBLEM 12.52 (Continued)
PROBLEM 12.53
Tilting trains, such as the American Flyer which will run from
Washington to New York and Boston, are designed to travel
safely at high speeds on curved sections of track which were
built for slower, conventional trains. As it enters a curve, each
car is tilted by hydraulic actuators mounted on its trucks. The
tilting feature of the cars also increases passenger comfort by
eliminating or greatly reducing the side force
s
F
(parallel to the
floor of the car) to which passengers feel subjected. For a train
traveling at 100 mi/h on a curved section of track banked
through an angle
6
θ
= °
and with a rated speed of 60 mi/h,
determine (a) the magnitude of the side force felt by a passenger
of weight W in a standard car with no tilt
( 0),
φ
=
(b) the
required angle of tilt
φ
if the passenger is to feel no side force.
(See Sample Problem 12.7 for the definition of rated speed.)
SOLUTION
s
PROBLEM 12.53 (Continued)
PROBLEM 12.54
Tests carried out with the tilting trains described in Problem 12.53
revealed that passengers feel queasy when they see through the car
windows that the train is rounding a curve at high speed, yet do
not feel any side force. Designers, therefore, prefer to reduce, but
not eliminate, that force. For the train of Problem 12.53, determine
the required angle of tilt
φ
if passengers are to feel side forces
equal to 10% of their weights.
SOLUTION
PROBLEM 12.54 (Continued)
22
PROBLEM 12.55
A 3-kg block is at rest relative to a parabolic dish which rotates at a
constant rate about a vertical axis. Knowing that the coefficient of
static friction is 0.5 and that r = 2 m, determine the maximum
allowable velocity v of the block.
PROBLEM 12.56
A polisher is started so that the fleece along the circumference
undergoes a constant tangential acceleration of
2
m/s 4
. Three
seconds after a polisher is started from rest, small tufts of
fleece from along the circumference of the 225-mm-diameter
polishing pad are observed to fly free of the pad. At this
instant, determine (a) the speed v of a tuft as it leaves the pad,
(b) the magnitude of the force required to free a tuft if the
average mass of a tuft is 1.6 mg.
SOLUTION
tuft
PROBLEM 12.57
A turntable A is built into a stage for use in a theatrical production.
It is observed during a rehearsal that a trunk B starts to slide on the
turntable 10 s after the turntable begins to rotate. Knowing that the
trunk undergoes a constant tangential acceleration of 0.24
2
m/s ,
determine the coefficient of static friction between the trunk and
the turntable.
SOLUTION
First we note that
( ) constant
Bt
a=
implies uniformly accelerated motion.
s
PROBLEM 12.58
The carnival ride from Prob 12.51 is modified so that
the 80 kg riders can move up and down the inclined
wall as the speed of the ride increases. Assuming
that the friction between the wall and the carriage is
negligible, determine the position h of the rider if the
speed v0 = 13 m/s.
SOLUTION
PROBLEM 12.59
The carnival ride from Prob 12.51 is modified so that
the 80 kg riders can move up and down the inclined
wall as the speed of the ride increases. Knowing that
the coefficient of static friction between the wall and
the platform is 0.2, determine the range of values of
the constant speed v0 for which the platform will
remain in the position shown.
SOLUTION
min
PROBLEM 12.59 (Continued)
Finding the maximum speed so that rider does not slide up the wall:
Free Body Diagram of Rider: Equations of Motion:
min 18.81 m/sv=
PROBLEM 12.60
A semicircular slot of 10-in. radius is cut in a flat plate which rotates about
the vertical AD at a constant rate of 14 rad/s. A small, 0.8-lb block E is
designed to slide in the slot as the plate rotates. Knowing that the
coefficients of friction are
0.35
s
µ
=
and
0.25,
k
µ
=
determine whether
the block will slide in the slot if it is released in the position corresponding to
(a)
80 ,
θ
= °
(b)
40 .
θ
= °
Also determine the magnitude and the direction
of the friction force exerted on the block immediately after it is released.
SOLUTION
1(26 10 sin ) ft
ρ
PROBLEM 12.60 (Continued)
(a) We have
80
θ
= °
4.4924 lb
ρ
=
PROBLEM 12.60 (Continued)
PROBLEM 12.60 (Continued)
PROBLEM 12.61
A small block B fits inside a lot cut in arm OA which rotates in a vertical plane at a
constant rate. The block remains in contact with the end of the slot closest to A and
its speed is 1.4 m/s for
0 150 .
θ
≤≤ °
Knowing that the block begins to slide when
150 ,
θ
= °
determine the coefficient of static friction between the block and the slot.
SOLUTION
s
PROBLEM 12.62
The parallel-link mechanism ABCD is used to transport a component I between manufacturing processes at
stations E, F, and G by picking it up at a station when
0
θ
=
and depositing it at the next station when
180 .
θ
= °
Knowing that member BC remains horizontal throughout its motion and that links AB and CD rotate
at a constant rate in a vertical plane in such a way that
2.2 ft/s,
B
v=
determine (a) the minimum value of the
coefficient of static friction between the component and BC if the component is not to slide on BC while being
transferred, (b) the values of
θ
for which sliding is impending.
