1) A particularly scary roller coaster contains a loop-the-loop in which the car and rider are completely upside
down. If the radius of the loop is
with what minimum speed must the car traverse the loop so that the
rider does not fall out while upside down at the top? Assume the rider is not strapped to the car.
A) 11.4 m/s
B) 12.5 m/s
C) 10.1 m/s
D) 14.9 m/s
2) A 1000-kg car is moving at 30 m/s around a horizontal unbanked curve whose diameter is 0.20 km. What is
the magnitude of the friction force required to keep the car from sliding?
A) 9000 N
C) 300 N
E) 3000 N
B) 9800 N
D) 900 N
3) The curved section of a horizontal highway is a circular unbanked arc of radius 740 m. If the coefficient of
static friction between this roadway and typical tires is 0.40, what would be the maximum safe driving speed for
this horizontal curved section of highway?
A) 54 m/s
B) 52 m/s
C) 50 m/s
D) 48 m/s
E) 46 m/s
6) A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of a circular dive. What is
the radius of curvature of the circular part of the path in which the plane is flying?
A) 640 m
B) 1200 m
C) 7100 m
D) 9200 m
8) A Ferris wheel has radius 5.0 m and makes one revolution every 8.0 s with uniform rotation. A person who
normally weighs 670 N is sitting on one of the benches attached at the rim of the wheel. What is the apparent
weight (the normal force exerted on her by the bench) of the person as she passes through the highest point of
her motion?
17) A 20-g bead is attached to a light 120-cm-long string as shown in the figure. This bead moves in a
horizontal circle with a constant speed of 1.5 m/s. What is the tension in the string if the angle α is measured to
be 25°?
A) 0.089 N
B) 0.041 N
C) 0.20 N
D) 0.22 N
E) 0.46 N
18) A 20-g bead is attached to a light 120 cm-long string as shown in the figure. If the angle α is measured to be
18°, what is the speed of the mass?
A) 0.55 m/s
B) 2.0 m/s
C) 3.8 m/s
D) 1.3 m/s
E) 1.1 m/s
32) As a 70-kg person stands at the seashore gazing at the tides (which are caused by the Moon), how large is
the gravitational force on that person due to the Moon? The mass of the Moon is 7.35 × 1022 kg, the distance
to the Moon is 3.82 × 108 m, and G = 6.67 × 10-11 N ∙ m2/kg2.
A) 0.24 N
B) 0.024 N
C) 0.0024 N
D) 0.00024 N
1) Answer: A
2) Answer: A
3) Answer: A
6) Answer: D
8) Answer: 460 N
17) Answer: D
18) Answer: E
32) Answer: C
33) A very dense 1500-kg point mass (A) and a dense 1200-kg point mass (B) are held in place 1.00 m apart on
a frictionless table. A third point mass is placed between the other two at a point that is 20.0 cm from B along
the line connecting A and B. When the third mass is suddenly released, find the magnitude and direction (toward
A or toward B) of its initial acceleration. (G = 6.67 × 10-11 N ∙ m2/kg2)
44) Planet Z-34 has a mass equal to one-third that of Earth and a radius equal to one-third that of Earth. With g
representing, as usual, the acceleration due to gravity at the surface of Earth, the acceleration due to gravity at
the surface of Z-34 is
A) g/3.
B) 3g.
C) 6g.
D) g/9.
E) 9g.
53) An object weighs 432 N on the surface of the earth. The earth has radius R. If the object is raised to a
height of 3R above the earth's surface, what is its weight?
A) 108 N
B) 48.0 N
C) 27.0 N
D) 305 N
E) 144 N
69) A satellite having orbital speed V orbits a planet of mass M. If the planet had half as much mass, the orbital
speed of the satellite at the same distance from the center would be
B) 2V.
C) V.
E) V/2.
A) V .
D) V/ .
4) A satellite is in orbit around a planet. The orbital radius is 34.0 km and the gravitational acceleration at that
height is 2.3 m/s2. What is the satellite's orbital speed?
A) 280 m/s
B) 8.8 m/s
C) 28 m/s
D) 88 m/s
5) A 23 kg mass is connected to a nail on a frictionless table by a (massless) string of length
1.3 m. If the tension in the string is 51 N while the mass moves in a uniform circle on the table, how long does it
take for the mass to make one complete revolution?
A) 4.8 s
B) 3.8 s
C) 4.5 s
D) 5.2 s
6) A new roller coaster contains a loop-the-loop in which the car and rider are completely upside down. If the
radius of the loop is 13.2 m, with what minimum speed must the car traverse the loop so that the rider does not
fall out while upside down at the top? Assume the rider is not strapped to the car.
A) 11.4 m/s
B) 12.5 m/s
C) 10.1 m/s
D) 14.9 m/s
7) A tetherball is on a 2.1 m string that makes an angle of 44° with the vertical as it moves around the pole in a
horizontal plane. If the mass of the ball is 1.3 kg, what is the ball's speed?
A) 3.7 m/s
B) 2.9 m/s
C) 3.4 m/s
D) 4.2 m/s
33) Answer: 1.8 × 10-6 m/s2, toward B
44) Answer: B
53)Answer: C
69) Answer: D
4) Answer: A
5) Answer: A
6) Answer: A
7) Answer: A
8) In an amusement park ride, passengers stand inside an 8 m radius cylinder. Initially, the cylinder rotates with
its axis oriented along the vertical. After the cylinder has acquired sufficient speed, it tilts into a vertical plane,
that is, the axis tilts into the horizontal, as shown in the figure. Suppose that, once the axis has tilted into the
horizontal, the ring rotates once every 4.5 s. If a rider's mass is 40 kg, with how much force does the ring push
on her at the top of the ride?
A) 230 N
B) 620 N
C) 1000 N
D) 390 N
14) A 90 g bead on a 60 cm long string is swung in a vertical circle about a point 200 cm above the floor. The
tension in the string when the bead is at the very bottom of the circle is 2.2 N. A very sharp knife is suddenly
inserted, as shown in the figure, to cut the string directly below the point of support. How far to the right of the
center of the circle does the ball hit the floor?
A) 160 cm
B) 200 cm
C) 240 cm
D) 190 cm
8) Answer: A
14) Answer: A
15) The figure shows a 3.0 kg ball tied to the end of a 50 cm long string being swung in a circle in a vertical
plane at constant speed. The center of the circle is h = 510 cm above the floor. The ball is swung at the
minimum speed necessary to make it over the top without the string going slack. If the string is released at the
instant the ball is at the top of the loop, how far to the right of the center of the circle does the ball hit the
ground?
A) 240 cm
B) 230 cm
C) 210 cm
D) 0.0 cm
16) What is the magnitude of the force exerted by Earth on the Moon?
A) 2.01 × 1020 N
B) 7.67 × 1028 N
C) 2.01 × 1026 N
D) 7.67 × 1031 N
15) Answer: A
16) Answer: A