Download AP Practice Test Circular motion and gravitation MPC

AP Practice Test Circular motion and gravitation MPC 1) An object moves in a circular path at a constant speed. Compare the direction of the
object's velocity and acceleration vectors.
A) Both vectors point in the same direction.
B) The vectors point in opposite directions.
C) The vectors are perpendicular to each other.
D) The acceleration is zero but the velocity is constant.
Answer: C
2) The Moon is accelerated toward the earth, so it is gradually getting closer to the earth.
A) True
B) False
C) The moon is not accelerated toward the earth.
Answer: B
3) When a car goes around a circular curve on a horizontal road at constant speed, what
force causes it to follow the circular path?
A) the normal force from the road
B) the friction force from the road
C) gravity
D) No force causes the car to do this because the car is traveling at constant speed and
therefore has no acceleration.
Answer: B
4) A car goes around a circular curve on a horizontal road at constant speed. What is the
direction of the friction force on the car due to the road?
A) tangent to the curve in the forward direction
B) tangent to the curve opposite to the direction of the car's motion
C) perpendicular to the curve outward
D) perpendicular to the curve inward
E) There is no friction on the car because its speed is constant.
Answer: D
5) If you swing a bucket of water fast enough in a vertical circle, at the highest point the
water does not spill out. This happens because an outward force balances the pull of
gravity on the water.
A) True
B) False
Answer: B
6) Two cars go around a banked curve at the proper speed for the banking angle. One car
has tires with excellent traction, while the other car has bald slippery tires. Which of
these cars is more likely to slide on the pavement as it goes around the curve?
A) the car with the new tires
B) the car with the bald tires
C) Neither car will slide.
D) It depends on if the pavement is wet or dry.
Answer: C
7) Two small balls, A and B, attract each other gravitationally with a force of magnitude
F. If we now double both masses and the separation of the balls, what will now be the
magnitude of the attractive force on each one?
A) 16F
B) 8F
C) 4F
D) F
E) F/4
Answer: D
8) A spaceship is traveling to the Moon. At what point is it beyond the pull of Earth's
gravity?
A) when it gets above the atmosphere
B) when it is half-way there
C) when it is closer to the Moon than it is to Earth
D) It is never beyond the pull of Earth's gravity.
Answer: D
9) An piece of space debris is released from rest at an altitude that is two earth radii from
the center of the earth. Compared to its weight on Earth, the weight of this debris is
A) zero.
B) the same as on the surface of the earth.
C) one-half of its weight on the surface of the earth.
D) one-third of its weight on the surface of the earth.
E) one-quarter of its weight on the surface of the earth.
Answer: E
10) A hypothetical planet has a mass of one-half that of the earth and a radius of twice
that of the earth. What is the acceleration due to gravity on the planet in terms of g, the
acceleration due to gravity at the surface of the earth?
A) g
B) g/2
C) g/4
D) g/8
E) g/16
Answer: D
11) Planet A has twice the mass of Planet B. From this information, what can we
conclude about the acceleration due to gravity at the surface of Planet A compared to that
at the surface of Planet B?
A) The acceleration due to gravity on Planet A must be twice as great as the acceleration
due to gravity on Planet B.
B) The acceleration due to gravity on Planet A must be four times as great as the
acceleration due to gravity on Planet B.
C) The acceleration due to gravity on Planet A is the same as the acceleration due to
gravity on Planet B.
D) The acceleration due to gravity on Planet A is greater than the acceleration due to
gravity on Planet B, but we cannot say how much greater.
E) We cannot conclude anything about the acceleration due to gravity on Planet A
without knowing the radii of the two planets.
Answer: E
12) If Earth had twice its present mass but it orbited at the same distance from the sun as
it does now, its orbital period would be
A) 4 years.
B) 3 years.
C) 2 years.
D) 1 year.
E) 6 months.
Answer: D
13) Let the orbital radius of a planet be R and let the orbital period of the planet be T.
What quantity is constant for all planets orbiting the sun, assuming circular orbits?
A) T/R
B) T/R2
C) T2/R3
D) T3/R2
E) T2/R
Answer: C
14) An object moves with a constant speed of 30 m/s on a circular track of radius 150 m.
What is the acceleration of the object?
A) 0 m/s2
B) 0.17 m/s2
C) 5.0 m/s2
D) 6.0 m/s2
Answer: D
15) You are driving at
of your acceleration?
A) 36.0 m/s2
B) 1.20 m/s2
C) 20.8 m/s2
D) 0.833 m/s2
Answer: A
on a freeway curve of radius
What is the magnitude
16) A jet plane flying 600 m/s experiences an acceleration of 4.0 g when pulling out of
the circular section of a dive. What is the radius of curvature of this section of the dive?
A) 1.2 km
B) 5.8 km
C) 0.64 km
D) 9.2 km
E) 7.0 km
Answer: D
17) 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
B) 9800 N
C) 300 N
D) 900 N
E) 3000 N
Answer: A
18) A 0.50-kg toy is attached to the end of a 1.0-m very light string. The toy is whirled in
a horizontal circular path on a frictionless tabletop. If the maximum tension that the
string can withstand without breaking is 350 N. What is the maximum speed the mass
can have without breaking the string?
A) 700 m/s
B) 26 m/s
C) 19 m/s
D) 13 m/s
Answer: B
19) One way that future space stations may create artificial gravity is by rotating the
station. Consider a cylindrical space station 380 m in diameter that is rotating about its
longitudinal axis. Astronauts walk on the inside surface of the space station. How long
will it take for each rotation of the cylinder if it is to provide "normal" gravity for the
astronauts?
A) 28 s
B) 39 s
C) 6.2 s
D) 4.4 s
Answer: A
20) A 1000-kg car is slowly picking up speed as it goes around a horizontal unbanked
curve whose radius is 100 m. The coefficient of static friction between the tires and the
road is 0.35. At what speed will the car begin to skid sideways?
A) 9.3 m/s
B) 24 m/s
C) 34 m/s
D) 35 m/s
E) 19 m/s
Answer: E
21) Pulling out of a dive, the pilot of an airplane guides his plane into a vertical circle
with a radius of 600 m. At the bottom of the dive, the speed of the airplane is 150 m/s.
What is the apparent weight of the 70-kg pilot at that point?
A) 3300 N
B) 690 N
C) 2600 N
D) 490 N
E) 1400 N
Answer: A
22) In order to simulate weightlessness for astronauts in training, they are flown in a
vertical circle. If the passengers are to experience weightlessness, how fast should an
airplane be moving at the top of a vertical circle with a radius of 2.5 km?
A) 79 m/s
B) 310 m/s
C) 260 m/s
D) 160 m/s
E) 510 m/s
Answer: D
23) In a carnival ride, passengers stand with their backs against the wall of a cylinder.
The cylinder is set into rotation and the floor is lowered away from the passengers, but
they remain stuck against the wall of the cylinder. For a cylinder with a 2.0-m radius,
what is the minimum speed that the passengers can have so they do not fall if the
coefficient of static friction between the passengers and the wall is 0.25?
A) 8.9 m/s
B) 2.3 m/s
C) 3.0 m/s
D) 4.9 m/s
E) It depends on the mass of the passengers.
Answer: A
24) 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
Answer: E
25) A car traveling at a steady 20 m/s rounds an 80-m radius horizontal unbanked curve
with the tires on the verge of slipping. What is the maximum speed with which this car
can round a second unbanked curve of radius 320 m if the coefficient of static friction
between the car's tires and the road surface is the same in both cases?
A) 160 m/s
B) 80 m/s
C) 70 m/s
D) 40 m/s
E) 30 m/s
Answer: D
26) A future use of space stations may be to provide hospitals for severely burned
persons. It is very painful for a badly burned person on Earth to lie in bed. In a space
station, the effect of gravity can be reduced or even eliminated. How long should each
rotation take for a doughnut-shaped hospital of 200-m radius so that persons on the outer
perimeter would experience 1/10 the normal gravity of Earth?
A) 91 min
B) 8.7 min
C) 4.6 min
D) 1.5 min
E) 0.011 min
Answer: D
27) A 600-kg car is going around a banked curve with a radius of 110 m at a steady speed
of 24.5 m/s. What is the appropriate banking angle so that the car stays on its path
without the assistance of friction?
A) 29.1°
B) 13.5°
C) 33.8°
D) 56.2°
E) 60.9°
Answer: A
28) A highway curve of radius 100 m, banked at an angle of 45°, may be negotiated
without friction at a speed of
A) 22 m/s.
B) 31 m/s.
C) 44 m/s.
D) 67 m/s.
Answer: B
29) What is the gravitational force acting on a 59-kg person due to another 59-kg person
standing 2.0 m away? We can model each person as a small sphere. (G = 6.67 × 10-11 N
· m2/kg2)
A) 5.8 × 10-8 N
B) 8.5 × 103 N
C) 1.2 × 10-7 N
D) 9.8 × 10-10 N
E) 2.0 × 10-9 N
Answer: A
30)
Mass
Radius
Orbital radius Orbital period
Moon A 4.0 × 1020 kg unknown
2.0 × 108 m 4.0 × 106 s
Moon B 1.5 × 1020 kg 2.0 × 105 m 3.0 × 108 m
unknown
Mithra is an unknown planet that has two moons, A and B, in circular orbits around it.
The table summarizes the hypothetical data about these moons. What is the magnitude of
the maximum gravitational force that Moon A exerts on Moon B? (G = 6.67 × 10-11 N ·
m2/kg2)
A) 1.6 × 1013 N
B) 4.4 × 1013 N
C) 1.0 × 1014 N
D) 2.0 × 1014 N
E) 4.0 × 1014 N
Answer: E
31) The earth has radius R. A satellite of mass 100 kg is in orbit at an altitude of 3R
above the earth's surface. What is the satellite's weight at the altitude of its orbit?
A) 61 N
B) 110 N
C) 9000 N
D) 16,000 N
Answer: A
32) The captain of a spaceship orbiting planet X discovers that to remain in orbit at
from the planet's center, she needs to maintain a speed of
What is the mass
-11
2
2
of planet X? (G = 6.67 × 10
N · m /kg )
19
A) 2.8 × 10 kg
B) 4.2 × 1017 kg
C) 2.8 × 1016 kg
D) 4.2 × 1014 kg
Answer: A
33) You are the science officer on a visit to a distant solar system. Prior to landing on a
planet you measure its diameter to be 1.8 × 107 m. You have previously determined that
the planet orbits 2.9 × 1011 m from its star with a period of 402 earth days. Once on the
surface you find that the acceleration due to gravity is 19.5 m/s2. What are the masses of
(a) the planet and (b) the star? (G = 6.67 × 10-11 N · m2/kg2)
A) (a) 2.4 kg ×
kg, (b) 1.2 kg ×
kg
B) (a) 4.3 kg ×
kg, (b) 1.2 kg ×
kg
C) (a) 2.4 kg ×
kg, (b) 7.1 kg ×
kg
D) (a) 4.3 kg ×
kg, (b) 7.1 kg ×
kg
Answer: A
Long Free Response
You have been given the assignment of developing an experimental procedure and data
tables that will allow you to measure centripetal force and acceleration acting on an
object.
a. What materials commonly found in a science lab or classroom would you need to
conduct this experiment? Explain what you would use each piece of equipment
for. (Note that you do not have access to computers or computer-based measuring
devices such as motion detectors, smart pulleys, or other probe ware.)
b. What experimental procedure would you use to measure centripetal force and
acceleration acting on an object?
c. Describe your procedures as a series of ordered steps, use the diagram to identify what
measurements you would make, and identify which equipment from part (a) you
would use in your data collection.
d. Create appropriate data table(s) with clearly-labeled headers that you would use to
record the data from your experiment.
e. Create appropriate graphs from data tables that shows the relationships important to
visualize and measure forces acting on an object?
f. Clearly describe how you will analyze the data you have collected for each part of the
experiment and justify your explanations.
Short Free Response
1) Sarah drives at a constant speed of 15 m/s around a circular horizontal curve of
diameter 60 m. What are the magnitude and direction of her acceleration?
Answer: 7.5 m/s2 toward the center of the circle
2) The maximum acceleration a pilot can stand without blacking out is about 7.0 g. In an
endurance test for a jet plane's pilot, what is the maximum speed he can tolerate if he is
spun in a horizontal circle of diameter 85 m?
Answer: 54 m/s
3) The Moon is 3.84 × 108 m from Earth and takes 27.3 days to complete each orbit.
What are the magnitude and direction of the acceleration of the Moon, assuming a
circular orbit?
Answer: 2.72 × 10-3 m/s2, toward Earth
4) A small 175-g ball on the end of a light string is revolving uniformly on a frictionless
surface in a horizontal circle of diameter 1.0 m. The ball makes 2.0 revolutions every 1.0
s.
(a) What are the magnitude and direction of the acceleration of the ball?
(b) Find the tension in the string.
Answer: (a) 79.0 m/s2 toward the center of the circle (b) 13.8 N
5) A curved portion of highway has a radius of curvature of 65 m. As a highway
engineer, you want to bank this curve at the proper angle for a steady speed of 22 m/s.
(a) What banking angle should you specify for this curve?
(b) At the proper banking angle, what normal force and what friction force does the
highway exert on a 750-kg car going around the curve at the proper speed?
Answer: (a) 37° (b) 9200 N (normal force), 0 N (friction)
6) What is the magnitude of the gravitational force that two small 7.00-kg balls exert on
each other when they are 35.0 cm apart? (G = 6.67 × 10-11 N · m2/kg2)
Answer: 2.67 × 10-8 N
7) A large telescope of mass 8410 kg is in a circular orbit around the earth, making one
revolution every 927 minutes. What is the magnitude of the gravitational force exerted on
the satellite by the earth? (G = 6.67 × 10-11 N · m2/kg2, Mearth = 6.0 × 1024 kg)
Answer: 3.4 × 103 N