CP7e: Ch. 1 Problems

17. (a) What is the tangential
acceleration of a bug on the rim of a 10‐in.‐
diameter disk if the disk moves from rest to
an angular speed of 78 rev/min in 3.0 s? (b)
When the disk is at its final speed, what is
the tangential velocity of the bug? (c) One
second after the bug starts from rest, what
are its tangential acceleration, centripetal
acceleration, and total acceleration?
18. A race car starts from rest on a
circular track of radius 400 m. The car’s
speed increases at the constant rate of 0.500
m/s 2 . At the point where the magnitudes of
the centripetal and tangential accelerations
are equal, determine (a) the speed of the
race car, (b) the distance traveled, and (c)
the elapsed time.
19. A 55.0‐kg ice‐skater is moving at 4.00
m/s when she grabs the loose end of a rope,
the opposite end of which is tied to a pole.
She then moves in a circle of radius 0.800 m
around the pole. (a) Determine the force
exerted by the horizontal rope on her arms.
(b) Compare this force with her weight.
21. A certain light truck can go around a
flat curve having a radius of 150 m with a
maximum speed of 32.0 m/s. With what
maximum speed can it go around a curve
having a radius of 75.0 m?
22. The cornering performance of an
automobile is evaluated on a skid pad,
where the maximum speed that a car can
maintain around a circular path on a dry,
flat surface is measured. Then the
centripetal acceleration, also called the
lateral acceleration, is calculated as a
multiple of the free‐fall acceleration g. The
main factors affecting the performance of
the car are its tire characteristics and
suspension system. A Dodge Viper GTS can
negotiate a skid pad of radius 61.0 m at 86.5
km/h. Calculate its maximum lateral
acceleration.
23. A 50.0‐kg child stands at the rim of a
merry‐go‐round of radius 2.00 m, rotating
with an angular speed of 3.00 rad/s. (a)
What is the child’s centripetal acceleration?
(b) What is the minimum force between her
feet and the floor of the carousel that is
required to keep her in the circular path? (c)
What minimum coefficient of static friction
is required? Is the answer you found
reasonable? In other words, is she likely to
stay on the merry‐go‐round?