[ Questions #1#14  Questions #15#28  Questions #29#40 ] [ #1  #2  #3  #4  #5  #6  #7  #8  #9  #10  #11  #12  #13  #14 ] 
1. Which of the following statements are true of an object moving in a circle at a constant speed? Include all that apply.
Answer: CF A is false; if the motion is in a circle at constant speed, the net force is perpendicular to the direction of motion and there is neither a component parallel nor antiparallel to the direction of motion.) B is false; it is centripetal force which causes the circular motion. Inertia (which is NOT a force) is merely the tendency of any moving object to continue in its straightline constant speed path. C is true; an object which moves in a circle must have a net inward force. There are many instances of individual outwards forces which are exceeded by an individual inward force (e.g., see #5 below). D is false; acceleration occurs when there is a change in velocity. Since the direction of the velocity vector is changing, there is an acceleration  an inward acceleration. E is false; the acceleration and net force are always directed in the same direction. In this case, F and a are directed inward; this happens to be perpendicular to the tangential velocity vector. F is true; if the net force is 0 N, then the moving object will maintain its state of motion. At the instant that F_{net} becomes 0 N, the object is moving tangent to the circle. G is false; the acceleration is directed inwards; only the velocity is directed tangent to the circle. 
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For questions #2#5, identify the type of force which causes the following boldfaced objects to travel along a circular path.
2. An eraser is tied to a string swung in a horizontal circle.
a. gravity 
b. normal 
c. tension 
d. applied 
e. friction 
f. spring 
g. electrical 
h. magnetic 
a. gravity 
b. normal 
c. tension 
d. applied 
e. friction 
f. spring 
g. electrical 
h. magnetic 
4. A car makes a sharp righthand turn along a level roadway.
a. gravity 
b. normal 
c. tension 
d. applied 
e. friction 
f. spring 
g. electrical 
h. magnetic 
5. A roller coaster car passes through a loop. Consider the car at the bottom of the loop.
a. gravity 
b. normal 
c. tension 
d. applied 
e. friction 
f. spring 
g. electrical 
h. magnetic 
Answers: 2. C  Tension (A string is attached to the eraser and pulls it towards the center point of the circle.) 3. A  Gravity (All masses attract with a force of gravity. In the case of the moon and the earth, gravity pulls on the moon in a direction which is roughly perpendicular to its path.) 4. E  Friction (Once the wheels are turned, friction can push perpendicular to the wheels' direction, pushing the car towards the center of the circle.) 5. B  Normal (There are two forces at the bottom of the loop; gravity pulls outwards from the center; but the normal force exceeds the magnitude of gravity, pushing inwards with sufficient force to supply the needed centripetal force.) 
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For Questions #2#5: 
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6. A physics teacher ties an eraser to the end of a string and then whirls it in a counterclockwise circle. If the teacher lets go of the string, then the eraser hits a student (or several students) in the classroom. If the string is let go when the eraser is at point X on the diagram at the right, then which student(s) in the class will the eraser hit? Write the initials in this space: ________________
Answer: JG and AF Once the centripetal force is no longer present, the eraser will follow its straightline, inertial path. This path would be directed tangent to the circle and would pass through the locations where JG and AF are sitting. View a reasonably cool animation. 
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7. Which of the following statements are true about gravitational force? Identify all that apply.
Answer: BCDF A is false; gravitational forces are universal (Newton's big idea); they act between any two objects which have mass. B is true; if the distance is increased, then the force is decreased. C is true; this is always the case. It is not true however to say that the gravitational force is equal to mass•9.8 m/s/s. The value of g varies with location and so at distances significantly further from the earth's surface, g is reduced and the gravitational force must be computed using a different value of g. D is true; weight and gravitational force are synonymous. E is false; gravitational force is dependent upon the product of the two masses. Both masses are important in the computation. F is true; for every action there is an equal and opposite reaction. This is Newton's third law, an inescapable reality about forces. G is false; doubling the separation distance will make the force onefourth the size. H is false; placing the object at two earthradii above earth's surface will put 3earth radii from earth's center. This is equivalent to increasing the separation distance by a factor of 3; this decreases the force by a factor of 9. I is false; orbiting astronauts must be experiencing the force of gravity. Without this force, there would be no centripetal force and no orbit. 
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8. Which of the following statements are true about the acceleration of gravity? Identify all that apply.
Answer: BCEFG A is false; check out the equation  g = GM_{central}/R^{2}. The value of g does not depend upon the object's mass. B is true; check out the equation again. The acceleration of gravity created by the earth depends upon the earth's mass. C is true; check out the equation one more time. The separation distance is located in the denominator of the equation, indicating an inverse relationship. D is false; like statement A, this statement makes a claim that the acceleration of gravity depends upon the mass of the object. It does not. In the derivation of g from the Universal Gravitation equation, the mass cancels. :) E is true; g is inversely proportional to the square of the distance; a doubling of the distance means that you must divide the force of gravity value by 4 (2^{2}) to obtain the new force of gravity value. F is true; the acceleration of gravity is the acceleration which is caused by gravity when it is the only force. For an orbiting satellite, gravity is the only force. G is true; according to the equation, the g value is directly proportional to the mass of the earth. An increase in M results in a proportional increase in g. H is false; g is approximately 10 m/s/s on earth's surface. Doubling the mass of the earth would increase g to approximately 20 m/s/s. Then doubling the distance from the surface of the earth to its center would decrease g by a factor of 4. The new acceleration of gravity value would be approximately 5 m/s/s. Clearly, these two alterations do not offset each other. 
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9. Which of the following statements are true about satellites? Identify all that apply.
Answer: AGH A is true; a projectile is an object upon which gravity is the only force. Gravity is the only force on a satellite. Therefore a satellite is a projectile. Click to view a waycool animation. B is false; most satellites follow elliptical paths. Some are very elliptical (e.g., Haley's comet); others are only slightly elliptical. C is false; the mass of a satellite does not effect its orbital velocity. Just look at the equation for orbital velocity of satellites: v = SQRT(G•M_{central}/R); the mass in the equation is the mass of the central body. D is false; as seen in the equation above, the orbital velocity varies directly with the square root of the mass of the planet. E is false; high altitude satellites are further from the central body's center. As such, the gravitational forces are smaller; a slower speed is required of such satellites in order to safely orbit. This inverse relationship is consistent with the equation for orbital velocity. F is false; by definition, a geosynchronous satellite maintains the same position radially above the surface of the earth. It is likely that it orbits a circle or near circle; yet this is not the definition. G is true; this is Kepler's second law applied to satellites. In order to sweep out equal areas in equal times, a satellite must be moving faster when closest to the earth. See a clever animation. H is true; this statement reflects the inverse relationship between distance and acceleration of gravity as found in the g equation and discussed in the above question. 
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10. Which of the following statements are true about the motion of planets about the sun? Identify all that apply.
Answer: ACDE A is true; gravity is the only force acting upon a planet. Think about it  what other physical push or pull can you identify as acting upon the earth. (People pushing on it and pulling it don't count.) B is false; their trajectories are indeed elliptical. Yet in most cases, the ellipses are very close to a circle since the eccentricities are very close to 0. C is true; this is in accord with Kepler's third law: T^{2}/R^{3} = constant. Expressing this equation another way depicts the direct relationship between T and R: T^{2 }= constant • R^{3}. D is true; this is Kepler's second law of planetary motion. In order to sweep out equal areas in equal times, a satellite must be moving faster when closest to the earth. See a clever animation. E is true; at all times during the orbital path, the velocity of the planet is tangent to the path. Since the path has a slightly elliptical nature to it, the force and acceleration vector are not necessarily perpendicular to this velocity vector. The perpendicular orientation of the F and a vectors relative to the v vector is unique to circular motion. An excellent and informative graphic about this can be found online. F is false; see above explanation and the link to the informative graphic. G is false; the net force is a gravitational force. Gravitational forces vary inversely with distance. Thus, a planet will experience less force when furthest from the sun. You might really need to view the informative graphic. 
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11. Explain how something can be moving at a constant speed yet be accelerating at the same time.
Answer: The object would have to be traveling in a curved path since it is accelerating. Acceleration is defined as a change in velocity over a change in time. If the speed is staying the same, then the velocity must be changing by altering the direction in which the object is heading. A force is required to do this. See an informative animation and further explanation. 
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12. How did Newton come up with the idea that the moon is actually "falling" toward the Earth.
Answer: Newton made the connection between objects falling (accelerating) towards the earth and objects in space which are accelerating towards the earth while they are in circular motion around the earth. Both are being pulled by the earth due to the gravitational force. The moon stays in orbit due to it having the appropriate tangential velocity that keeps it from coming closer to the earth's surface. The moon, however, is still accelerating at the rate any object would have at that distance from the earth. In a sense, the moon is falling around the earth rather than into the earth. 
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13. Distinguish between true and apparentweightlessness.
Answer: True weightlessness occurs when there is an absence of gravitational force on an object. This is not a likely occurrence since every mass in the universe is attracted to every other mass in the universe with some force of gravity. All objects would experience some degree of gravitational attraction (though it may be considerably small). Apparent weightlessness is the sensation of not experiencing any external contact forces. This occurs when an object is in freefall. Even though the object may have a large force on it, it wouldn't register on a scale that was in freefall with it. Astronauts appear this way on the space shuttle. 
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14. Describe the apparent weight of a person in an elevator while upward, accelerating downward, and not accelerating.
Answer: When one stands upright on a scale, the scale measures the force of the scale pushing upwards on the body. As such, the scale does not measure one's true weight, but one's apparent weight. An elevator accelerating someone up must not only apply a force to provide the acceleration but also oppose the gravitational force on the person. Therefore, a scale would register a number larger than the gravitational force if the person is accelerating upward. In this case, a person would experience an apparent weight which is greater than usual. Likewise, if the person is accelerating downward the scale reading must be less than the gravitational force since the gravitational force is accelerating them downward. As such, the person's apparent weight is less than what they are accustomed to experiencing. If the elevator is moving at constant velocity or at rest, the scale reading must match the gravitational force in order to have a net force of 0. The apparent weight would be equal to the actual weight of the person. 
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Last update: 5/2/02