Download AP Projectile,circular, gravitation test (final)

AP Physics Gravitation, Circular, projectile
1. Each of five satellites makes a circular orbit about an object that is much more massive than any of the satellites.
The mass and orbital radius of each satellite are given below. Which satellite has the greatest speed?
Mass
(A) ½m
(B) m
(C) m
(D) m
(E) 2m
Radius
R
½R
R
2R
R
2. Two planets have the same size, but different masses, and no atmospheres. Which of the following would be the
same for objects with equal mass on the surfaces of the two planets?
I. The rate at which each would fall freely
II. The amount of mass each would balance on an equal-arm balance
III. The amount of momentum each would acquire when given a certain impulse
(A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III
3. A person weighing 800 newton’s on Earth travels to another planet with twice the mass and twice the radius of
Earth. The person's weight on this other planet is most nearly
(A) 400 N (B) 800√2 N (C) 800 N (D) 800√2 (E) 1,600 N
4. Mars has a mass 1/10 that of Earth and a diameter 1/2 that of Earth. The acceleration of a falling body near the
surface of Mars is most nearly
(A) 0.25 m/s2 (B) 0.5 m/s2 (C) 2 m/s2 (D) 4 m/s2 (E) 25 m/s2
5. If Spacecraft X has twice the mass of Spacecraft Y, then true statements about X and Y include which of the
following?
I. On Earth. X experiences twice the gravitational force that Y experiences.
II. On the Moon, X has twice the weight of Y.
III. When both are in the same circular orbit, X has twice the centripetal acceleration of Y.
(A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III
6. The planet Mars has mass 6.4 × 1023 kilograms and radius 3.4 × 106 meters. The acceleration of an object in
free-fall near the surface of Mars is most nearly
(A) zero (B) 1.0 m/s2 (C) 1.9 m/s2 (D) 3.7 m/s2 (E) 9.8 m/s2
7. A new planet is discovered that has twice the Earth's mass and twice the Earth's radius. On the surface of this
new planet, a person who weighs 500 N on Earth would experience a gravitational force of
(A) 125 N (B) 250 N (C) 500 N (D) 1000 N (E) 2000 N
8. One object at the surface of the Moon experiences the same gravitational force as a second object at the surface
of the Earth. Which of the following would be a reasonable conclusion?
(A) both objects would fall at the same acceleration
(B) the object on the Moon has the greater mass
(C) the object on the Earth has the greater mass
(D) both objects have identical masses
(E) the object on Earth has a greater mass but the Earth has a greater rate of rotation.
9. A ball which is thrown upward near the surface of the Earth with a velocity of 50 m/s will come to rest about 5
seconds later. If the ball were thrown up with the same velocity on Planet X, after 5 seconds it would be still
moving upwards at nearly 31 m/s. The magnitude of the gravitational field near the surface of Planet X is what
fraction of the gravitational field near the surface of the Earth?
(A) 0.16 (B) 0.39 (C) 0.53 (D) 0.63 (E) 1.59
10. When a person stands on a rotating merry-go-round, the frictional force exerted on the person by the
merry-go-round is
(A) greater in magnitude than the frictional force exerted on the person by the merry-go-round
(B) opposite in direction to the frictional force exerted on the merry-go-round by the person
(C) directed away from the center of the merry-go-round
(D) zero if the rate of rotation is constant
(E) independent of the person's mass
11. A ball attached to a string is whirled around in a horizontal circle having a radius r. If the radius of the circle is
changed to 4r and the same centripetal force is applied by the string, the new speed of the ball is which of the
following?
(A) One-quarter the original speed (B) One-half the original speed
(C) The same as the original speed (D) Twice the original speed
(E) Four times the original speed
12. A racing car is moving around the circular track of radius 300 meters shown above. At the instant when the car's
velocity is directed due east, its acceleration is directed due south and has a magnitude of 3 meters per second
squared. When viewed from above, the car is moving
(A) clockwise at 30 m/s ( B) clockwise at 10 m/s (C) counterclockwise at 30 m/s
(D) counterclockwise at 10 m/s (E) with constant velocity
13. The horizontal turntable shown above rotates at a constant rate. As viewed from above, a coin on the turntable
moves counterclockwise in a circle as shown. Which of the following vectors best represents the direction of the
frictional force exerted on the coin by the turntable when the coin is in the position shown?
A)
(B)
(C)
(D)
(E)
14. In which of the following situations would an object be accelerated?
I. It moves in a straight line at constant speed.
II. It moves with uniform circular motion.
III. It travels as a projectile in a gravitational field with negligible air resistance.
(A) I only (B) III only (C) I and II only (D) II and III only (E) I, II, and III.
15.An automobile moves at constant speed down one hill and up another hill along the smoothly curved surface
shown above. Which of the following diagrams best represents the directions of the velocity and the
acceleration of the automobile at the instant that it is at the lowest position. as shown?
(A)
(B)
(C)
(D)
(E)
16. A car initially travels north and then turns to the left along a circular curve. This causes a package on the seat of
the car to slide toward the right side of the car. Which of the following is true of the net force on the package
while it is sliding?
(A) The force is directed away from the center of the circle.
(B) The force is directed north.
(C) There is not enough force directed north to keep the package from sliding.
(D) There is not enough force tangential to the car's path to keep the package from sliding.
(E) There is not enough force directed toward the center of the circle to keep the package from sliding.
17. A child has a toy tied to the end of a string and whirls the toy at constant speed in a horizontal circular path of
radius R. The toy completes each revolution of its motion in a time period T. What is the magnitude of the
acceleration of the toy?
(A) Zero (B) 24 2Tπ R (C) T 2πR (D) g (E) 2πg
18. A compressed spring mounted on a disk can project a small ball. When the disk is not rotating, as shown in the
top view above, the ball moves radially outward. The disk then rotates in a counterclockwise direction as seen
from above, and the ball is projected outward at the instant the disk is in the position shown above. Which of
the following best shows the subsequent path of the ball relative to the ground?
19. Inside a washing machine, the radius of the cylinder where the clothes sit is 0.50 m. In one of its settings the
machine spins the cylinder at 2.0 revolutions per second. What is the acceleration of an item of clothing?
(A) 0.080 m/s2 (B) 1.6 m/s2 (C) 8.0 m/s2 (D) 79 m/s2 (E) 25 m/s2
20. A mass m moves on a curved path from point X to point Y. Which of the following diagrams indicates a
possible combination of the net force F on the mass, and the velocity v and acceleration a of the mass at the
location shown?
21. A figure of a dancer on a music box moves counterclockwise at constant speed around the path shown above.
The path is such that the lengths of its segments, PQ, QR, RS, and SP, are equal. Arcs QR and SP are
semicircles. Which of the following best represents the magnitude of the dancer's acceleration as a function of
time t during one trip around the path, beginning at point P ?
22. A child whirls a ball at the end of a rope, in a uniform circular motion. Which of the following statements is
NOT true?
(A) The speed of the ball is constant (B) The velocity is of the ball is constant (C) The radius is constant
(D) The magnitude of the ball's acceleration is constant
(E) The acceleration of the ball is directed radially inwards towards the center
23. What is the centripetal acceleration of an object (mass = 50 g) on the end of an 80-cm string rotating at a
constant rate of 4 times a second?
(A) 25 m/s2 (B) 32 m/s2 (C) 100 m/s2 (D) 500 m/s2 (E) 2500 m/s2
24. What net force is necessary to keep a 1.0 kg puck moving in a circle of radius 0.5 m on a horizontal frictionless
surface with a speed of 2.0 m/s?
(A) 0 N (B) 2.0 N (C) 4.0 N (D) 8.0 N (E) 16 N
25. A projectile is fired with initial velocity vo at an angle θ0 with the horizontal and follows the trajectory shown
above. Which of the following pairs of graphs best represents the vertical components of the velocity and
acceleration, v and a, respectively, of the projectile as functions of time t?
Questions 26 – 27
A ball is thrown and follows the parabolic path shown above. Air friction is negligible. Point Q is the highest
point on the path. Points P and R are the same height above the ground.
26. How do the speeds of the ball at the three points compare?
(A) vP < vQ < vR (B) vR < vQ < vP (C) vQ < vR < vP (D) vQ< vP = vR (E) vP = vR < vQ
27. Which of the following diagrams best shows the direction of the acceleration of the ball at point P?
(A)
(B)
(C)
(D)
(E)
28. A rock of mass m is thrown horizontally off a building from a height h, as shown above. The speed of the rock
as it leaves the thrower’s hand at the edge of the building is v0.
How much time does it take the rock to travel from the edge of the building to the ground?
(A)
(B)
(C)
(D)
(E)
29. A projectile is fired from the surface of the Earth with a speed of 200 meters per second at an angle of 30°
above the horizontal. If the ground is level, what is the maximum height reached by the projectile?
(A) 5 m (B) 10 m (C) 500 m (D) 1,000 m (E) 2,000 m
30. A rock is dropped from the top of a 45-meter tower, and at the same time a ball is thrown from the top of the
tower in a horizontal direction. Air resistance is negligible. The ball and the rock hit the level ground a
distance of 30 meters apart. The horizontal velocity of the ball thrown was most nearly
(A) 5 m/s (B) 10 m/s (C) 14.1 m/s (D) 20 m/s (E) 28.3 m/s
31. In the absence of air friction, an object dropped near the surface of the Earth experiences a constant acceleration
of about 9.8 m/s2 This means that the
(A) speed of the object increases 9.8 m/s during each second
(B) speed of the object as it falls is 9.8 m/s .
(C) object falls 9.8 meters during each second
(D) object falls 9.8 meters during the first second only
(E) rate of change of the displacement with respect to time for the object equals 9.8 m/s 2
32. An object is dropped from rest from the top of a 400 m cliff on Earth. If air resistance is negligible, what is the
distance the object travels during the first 6 s of its fall?
(A) 30 m (B) 60 m (C) 120 m (D) 180 m (E) 360 m
33. Robin Hood aims his longbow horizontally at a target's bull's eye 30 m away. If the arrow strikes the target
exactly 1.0 m below the bull's eye, how fast did the arrow move as it was shot from the bow? Assume air
resistance is negligible.
(A) 6.0 m/s (B) 13 m/s (C) 33 m/s (D) 67 m/s (E) 150 m/s
34. The diagram below shows four cannons firing shells with different masses at different angles of elevation. The
horizontal component of the shell's velocity is the same in all four cases. In which case will the shell have the
greatest range if air resistance is neglected?
(A) cannon A (B) cannon B only (C) cannon C only (D) cannon D
(E) Both cannons B and C have the greatest range
35. A punter in a football game kicks the ball with an initial speed of 28.3 m/s at an angle of 60° with respect to the
ground. The ball is in the air for a total of 5.00 s before hitting the ground. If we assume that air resistance is
negligible, what would be the ball's horizontal displacement?
(A) 0 m (B) 14.2 m (C) 24.5 m (D) 70.8 m (E) 122.5 m
36. In the absence of air resistance, if an object were to fall freely near the surface of the Moon,
(A) its velocity could never exceed 10 m/s.
(B) its acceleration would gradually decrease until the object moves with a terminal velocity.
(C) the acceleration is constant.
(D) it will fall with a constant speed.
(E) the acceleration is zero
37. A ball is thrown into the air at an angle θ as measured from the horizontal with a velocity v. The horizontal
velocity of the ball will be directly proportional to which of the following
(A) the angle θ (B) the sine of the angle θ (C) the cosine of the angle θ (D) the tangent of the angle θ
(E) the value of the gravitational acceleration