**Unformatted text preview: **e puck? (c) the speed of the
puck? that, when the mass sits a distance L up along the sloping side, the speed of the mass must be
v (g L sin )1/2 m
L θ Figure P6.55 Figure P6.51 WEB Problems 51 and 52. 53. Because the Earth rotates about its axis, a point on the
equator experiences a centripetal acceleration of
0.033 7 m/s2, while a point at one of the poles experiences no centripetal acceleration. (a) Show that at the
equator the gravitational force acting on an object (the
true weight) must exceed the object’s apparent weight.
(b) What is the apparent weight at the equator and at
the poles of a person having a mass of 75.0 kg? (Assume
the Earth is a uniform sphere and take g 9.800 m/s2.)
54. A string under a tension of 50.0 N is used to whirl a
rock in a horizontal circle of radius 2.50 m at a speed of
20.4 m/s. The string is pulled in and the speed of the
rock increases. When the string is 1.00 m long and the
speed of the rock is 51.0 m/s, the string breaks. What is
the breaking strength (in newtons) of the string?
55. A child’s toy consists of a small wedge that has an acute
angle ( Fig. P6.55). The sloping side of the wedge is
frictionless, and a mass m on it remains at constant
height if the wedge is spun at a certain constant speed.
The wedge is spun by rotating a vertical rod that is
ﬁrmly attached to the wedge at the bottom end. Show 56. The pilot of an airplane executes a constant-speed loopthe-loop maneuver. His path is a vertical circle. The
speed of the airplane is 300 mi/h, and the radius of the
circle is 1 200 ft. (a) What is the pilot’s apparent weight
at the lowest point if his true weight is 160 lb? (b) What
is his apparent weight at the highest point? (c) Describe
how the pilot could experience apparent weightlessness
if both the radius and the speed can be varied. (Note:
His apparent weight is equal to the force that the seat
exerts on his body.)
57. For a satellite to move in a stable circular orbit at a constant speed, its centripetal acceleration must be inversely proportional to the square of the radius r of the
orbit. (a) Show that the tangential speed of a satellite is
proportional to r 1/2. (b) Show that the time required
to complete one orbit is proportional to r 3/2.
58. A penny of mass 3.10 g rests on a small 20.0-g block supported by a spinning disk (Fig. P6.58). If the coefﬁ- Disk Penny 12.0 cm
Block Figure P6.58 179 Problems
cients of friction between block and disk are 0.750 (static) and 0.640 (kinetic) while those for the penny and
block are 0.450 (kinetic) and 0.520 (static), what is the
maximum rate of rotation (in revolutions per minute)
that the disk can have before either the block or the
penny starts to slip?
59. Figure P6.59 shows a Ferris wheel that rotates four times
each minute and has a diameter of 18.0 m. (a) What is
the centripetal acceleration of a rider? What force does
the seat exert on a 40.0-kg rider (b) at the lowest point
of the ride and (c) at the highest point of the ride?
(d) What force...

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