PROBLEM 12.50 (Continued)
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 v
0
. 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 v
0
at which the platform A begins to roll upwards, (b) the normal force
experienced by an 80-kg rider at this speed.
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
, (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.
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
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),
(b) the
required angle of tilt
if the passenger is to feel no side force.
(See Sample Problem 12.7 for the definition of rated speed.)
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
if passengers are to feel side forces
equal to 10% of their weights.
PROBLEM 12.54 (Continued)
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.