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**Unformatted text preview: **the ball? Discuss the
differences in trajectories between the two shots. ADDITIONAL PROBLEMS
46. An 1 800-kg car passes over a bump in a road that follows the arc of a circle of radius 42.0 m as in Figure
P6.46. (a) What force does the road exert on the car as
the car passes the highest point of the bump if the car
travels at 16.0 m/s? (b) What is the maximum speed the
car can have as it passes this highest point before losing
contact with the road?
47. A car of mass m passes over a bump in a road that follows the arc of a circle of radius R as in Figure P6.46.
(a) What force does the road exert on the car as the car
passes the highest point of the bump if the car travels at
a speed v ? (b) What is the maximum speed the car can
have as it passes this highest point before losing contact
with the road? v Figure P6.46 Problems 46 and 47. 48. In one model of a hydrogen atom, the electron in orbit
around the proton experiences an attractive force of
about 8.20 10 8 N. If the radius of the orbit is 5.30
10 11 m, how many revolutions does the electron make
each second? (This number of revolutions per unit time
is called the frequency of the motion.) See the inside
front cover for additional data.
49. A student builds and calibrates an accelerometer, which
she uses to determine the speed of her car around a
certain unbanked highway curve. The accelerometer is
a plumb bob with a protractor that she attaches to the
roof of her car. A friend riding in the car with her observes that the plumb bob hangs at an angle of 15.0°
from the vertical when the car has a speed of 23.0 m/s.
(a) What is the centripetal acceleration of the car
rounding the curve? (b) What is the radius of the
curve? (c) What is the speed of the car if the plumb bob
deﬂection is 9.00° while the car is rounding the same
curve?
50. Suppose the boxcar shown in Figure 6.13 is moving with
constant acceleration a up a hill that makes an angle
with the horizontal. If the hanging pendulum makes a
constant angle with the perpendicular to the ceiling,
what is a ?
51. An air puck of mass 0.250 kg is tied to a string and allowed to revolve in a circle of radius 1.00 m on a fric- 178 CHAPTER 6 Circular Motion and Other Applications of Newton’s Laws tionless horizontal table. The other end of the string
passes through a hole in the center of the table, and a
mass of 1.00 kg is tied to it (Fig. P6.51). The suspended
mass remains in equilibrium while the puck on the
tabletop revolves. What are (a) the tension in the string,
(b) the force exerted by the string on the puck, and
(c) the speed of the puck?
52. An air puck of mass m1 is tied to a string and allowed
to revolve in a circle of radius R on a frictionless horizontal table. The other end of the string passes
through a hole in the center of the table, and a mass
m 2 is tied to it (Fig. P6.51). The suspended mass remains in equilibrium while the puck on the tabletop revolves. What are (a) the tension in the string? (b) the
central force exerted on th...

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