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**Unformatted text preview: **(magnitude and direction) does the seat
exert on a rider when the rider is halfway between top
and bottom? 8.00 m 2.50 m θ Figure P6.61 Figure P6.59 (Color Box/FPG) 60. A space station, in the form of a large wheel 120 m in
diameter, rotates to provide an “artiﬁcial gravity” of
3.00 m/s2 for persons situated at the outer rim. Find
the rotational frequency of the wheel (in revolutions
per minute) that will produce this effect.
61. An amusement park ride consists of a rotating circular
platform 8.00 m in diameter from which 10.0-kg seats
are suspended at the end of 2.50-m massless chains
(Fig. P6.61). When the system rotates, the chains make
an angle
28.0° with the vertical. (a) What is the
speed of each seat? (b) Draw a free-body diagram of a
40.0-kg child riding in a seat and ﬁnd the tension in the
chain.
62. A piece of putty is initially located at point A on the rim
of a grinding wheel rotating about a horizontal axis.
The putty is dislodged from point A when the diameter
through A is horizontal. The putty then rises vertically
and returns to A the instant the wheel completes one
revolution. (a) Find the speed of a point on the rim of
the wheel in terms of the acceleration due to gravity
and the radius R of the wheel. (b) If the mass of the
putty is m, what is the magnitude of the force that held
it to the wheel? 63. An amusement park ride consists of a large vertical
cylinder that spins about its axis fast enough that any
person inside is held up against the wall when the ﬂoor
drops away (Fig. P6.63). The coefﬁcient of static friction between person and wall is s , and the radius of
the cylinder is R. (a) Show that the maximum period of
revolution necessary to keep the person from falling is
T (4 2R s /g )1/2. (b) Obtain a numerical value for T Figure P6.63 180 CHAPTER 6 Circular Motion and Other Applications of Newton’s Laws if R 4.00 m and s 0.400. How many revolutions
per minute does the cylinder make?
64. An example of the Coriolis effect. Suppose air resistance is
negligible for a golf ball. A golfer tees off from a location precisely at i 35.0° north latitude. He hits the
ball due south, with range 285 m. The ball’s initial velocity is at 48.0° above the horizontal. (a) For what
length of time is the ball in ﬂight? The cup is due south
of the golfer ’s location, and he would have a hole-inone if the Earth were not rotating. As shown in Figure
P6.64, the Earth’s rotation makes the tee move in a circle of radius RE cos i (6.37 106 m) cos 35.0°, completing one revolution each day. (b) Find the eastward
speed of the tee, relative to the stars. The hole is also
moving eastward, but it is 285 m farther south and thus
at a slightly lower latitude f . Because the hole moves
eastward in a slightly larger circle, its speed must be
greater than that of the tee. (c) By how much does the
hole’s speed exceed that of the tee? During the time the
ball is in ﬂight, it moves both upward and downward, as
well as southward wit...

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