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Quiz 5

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1. Suppose that a planet was found to orbit the Sun, and that its path was an ellipse with eccentricity of 0.5. If the planet always moved at the same speed, would it satisfy Kepler's second law? Choose the best answer of the four below. 1. Yes, because when an object sweeps out equal areas in equal time, it must travel slower when it is closer to the planet. 2. No, because when an object sweeps out equal areas in equal time, it must travel slower when it is closer to the planet. 3. Yes, because when an object sweeps out equal areas in equal time, it must travel faster when it is closer to the planet. 4. No, because when an object sweeps out equal areas in equal time, it must travel faster when it is closer to the planet.

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1. Suppose that a planet was found to orbit the Sun, and that its path was an ellipse with eccentricity of 0.5. If the planet always moved at the same speed, would it satisfy Kepler's second law? Choose the best answer of the four below. 1. Yes, because when an object sweeps out equal areas in equal time, it must travel slower when it is closer to the planet. 2. No, because when an object sweeps out equal areas in equal time, it must travel slower when it is closer to the planet. 3. Yes, because when an object sweeps out equal areas in equal time, it must travel faster when it is closer to the planet. 4. No, because when an object sweeps out equal areas in equal time, it must travel faster when it is closer to the planet.

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2. If you measured your weight with very high precision scale, would you see a difference between your weight at the top of a mountain versus at the bottom of the mountain? Select the best answer. 1. Yes, because the force that Earth exerts on me would be slightly less because my mass increases as I move away from Earth. 2. Yes, because the force that Earth exerts on me would be slightly less because I am slightly farther from it. 3. No, my weight will be the same everywhere. 4. Yes, because the force that Earth exerts on me would be slightly less because my mass decreases as I move away from Earth.

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2. If you measured your weight with very high precision scale, would you see a difference between your weight at the top of a mountain versus at the bottom of the mountain? Select the best answer. 1. Yes, because the force that Earth exerts on me would be slightly less because my mass increases as I move away from Earth. 2. Yes, because the force that Earth exerts on me would be slightly less because I am slightly farther from it. 3. No, my weight will be the same everywhere. 4. Yes, because the force that Earth exerts on me would be slightly less because my mass decreases as I move away from Earth.

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Bob Beamon

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3. Newton's Law of Gravity is F = G*m1*m2/(r*r). This equation states that if the distance between two objects increases by a factor of three, the force they exert on each other 1. decreases by a factor of nine. 2. increases by a factor of nine. 3. does not change. 4. increases by a factor of three. 5. decreases by a factor of three.

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3. Newton's Law of Gravity is F = G*m1*m2/(r*r). This equation states that if the distance between two objects increases by a factor of three, the force they exert on each other 1. decreases by a factor of nine. 2. increases by a factor of nine. 3. does not change. 4. increases by a factor of three. 5. decreases by a factor of three.

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4. Newton's Law of Gravity is F = G*m1*m2/(r*r). This equation states that if the distance between two objects increases by a factor of three, the force they exert on each other 1. decreases by a factor of nine. 2. increases by a factor of nine. 3. does not change. 4. increases by a factor of three. 5. decreases by a factor of three.

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4. Newton's Law of Gravity is F = G*m1*m2/(r*r). This equation states that if the distance between two objects increases by a factor of three, the force they exert on each other 1. decreases by a factor of nine. 2. increases by a factor of nine. 3. does not change. 4. increases by a factor of three. 5. decreases by a factor of three.

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5. Newton's Law of Gravity is F = G*m1*m2/(r*r) This equation states that if the mass of each object increased by a factor of two, the force that object 1 exerts on object 2 1. decreases by a factor of 4. 2. increases by a factor of 4. 3. does not change. 4. increases by a factor of 2. 5. decreases by a factor of 2.

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5. Newton's Law of Gravity is F = G*m1*m2/(r*r) This equation states that if the mass of each object increased by a factor of two, the force that object 1 exerts on object 2 1. decreases by a factor of 4. 2. increases by a factor of 4. 3. does not change. 4. increases by a factor of 2. 5. decreases by a factor of 2.

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6. In class, we came up with an equation that related a planet's orbital speed, v, with its distance from the sun, r given the sun had mass M, v*v = G*M/r Why is this equation consistent with Kepler's second law? 1. According to Kepler's second law, the further the planet is from the sun, the slower it moves. According to this equation, the larger r is, the smaller v is. 2. According to Kepler's second law, the further the planet is from the sun, the slower it moves. According to this equation, the larger r is, the larger the gravitational force of the sun is on the planet. 3. According to Kepler's second law, the further the planet is from the sun, the slower it moves. According to this equation, the larger r is, the larger the weight of the planet. 4. According to Kepler's second law, the further the planet is from the sun, the faster it moves. According to this equation, the larger r is, the larger v is.

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6. In class, we came up with an equation that related a planet's orbital speed, v, with its distance from the sun, r given the sun had mass M, v*v = G*M/r Why is this equation consistent with Kepler's second law? 1. According to Kepler's second law, the further the planet is from the sun, the slower it moves. According to this equation, the larger r is, the smaller v is. 2. According to Kepler's second law, the further the planet is from the sun, the slower it moves. According to this equation, the larger r is, the larger the gravitational force of the sun is on the planet. 3. According to Kepler's second law, the further the planet is from the sun, the slower it moves. According to this equation, the larger r is, the larger the weight of the planet. 4. According to Kepler's second law, the further the planet is from the sun, the faster it moves. According to this equation, the larger r is, the larger v is.

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7. In the following figure, at which position would the force of gravity due to Earth be about the same, but in opposite direction, as the force of gravity due to Mars? Note that Mars has a smaller mass than Earth. 1. 1 2. 2 3. 3

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7. In the following figure, at which position would the force of gravity due to Earth be about the same, but in opposite direction, as the force of gravity due to Mars? Note that Mars has a smaller mass than Earth. 1. 1 2. 2 3. 3

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8. Given that Earth is much larger and more massive than the Moon, how does the strength of the gravitational force that the Moon exerts on Earth compare to the gravitational force that Earth exerts on the Moon? Student 1: I thought that whenever one object exerts a force on the second object, the second object also exerts a force that is equal in strength, but in the other direction. So even if Earth is bigger and more massive than the Moon, they still pull on each other with a gravitational force of the same strength, just in different directions. Student 2: I disagree. I said that Earth exerts the stronger force because it is way bigger than the Moon. Because its mass is bigger, the gravitational force Earth exerts has to be bigger too. I think that you are confusing Newton’s third law with the law of gravity. Which student is correct? 1. Student 1 2. Student 2

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8. Given that Earth is much larger and more massive than the Moon, how does the strength of the gravitational force that the Moon exerts on Earth compare to the gravitational force that Earth exerts on the Moon? Student 1: I thought that whenever one object exerts a force on the second object, the second object also exerts a force that is equal in strength, but in the other direction. So even if Earth is bigger and more massive than the Moon, they still pull on each other with a gravitational force of the same strength, just in different directions. Student 2: I disagree. I said that Earth exerts the stronger force because it is way bigger than the Moon. Because its mass is bigger, the gravitational force Earth exerts has to be bigger too. I think that you are confusing Newton’s third law with the law of gravity. Which student is correct? 1. Student 1 2. Student 2

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9. If the mass of the Earth was twice as large but its radius was the same, what would happen to your mass and weight? 1. Your mass and weight would both be unchanged. 2. Your mass would decrease and your weight would be the same. 3. Your mass would increase and your weight would be the same. 4. Your mass and weight would both increase. 5. Your mass would be the same and your weight would increase.

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9. If the mass of the Earth was twice as large but its radius was the same, what would happen to your mass and weight? 1. Your mass and weight would both be unchanged. 2. Your mass would decrease and your weight would be the same. 3. Your mass would increase and your weight would be the same. 4. Your mass and weight would both increase. 5. Your mass would be the same and your weight would increase.

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10. If the mass of the Earth was twice as large and its radius was the same, what would its density be? 1. Its density would be one quarter of its current value 2. Its density would be the same 3. Its density would be one eighth of its current value 4. Its density would be one half of its current value 5. Its density would be twice its current value

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10. If the mass of the Earth was twice as large and its radius was the same, what would its density be? 1. Its density would be one quarter of its current value 2. Its density would be the same 3. Its density would be one eighth of its current value 4. Its density would be one half of its current value 5. Its density would be twice its current value

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11. According to Newton's Law of Gravity, if the mass of each object increased by a factor of four, the force that object 1 exerts on object 2 1. does not change. 2. increases by a factor of 2. 3. decreases by a factor of 4. 4. increases by a factor of 16. 5. decreases by a factor of 2. 6. increases by a factor of four

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11. According to Newton's Law of Gravity, if the mass of each object increased by a factor of four, the force that object 1 exerts on object 2 1. does not change. 2. increases by a factor of 2. 3. decreases by a factor of 4. 4. increases by a factor of 16. 5. decreases by a factor of 2. 6. increases by a factor of four

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12. Newton's Law of Gravity is F = G*m1*m2/(r*r) This equation states that if the distance between two objects increases by a factor of nine, the force they exert on each other 1. decreases by a factor of eighty-one. 2. does not change. 3. increases by a factor of three. 4. decreases by a factor of nine. 5. increases by a factor of nine.

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12. Newton's Law of Gravity is F = G*m1*m2/(r*r) This equation states that if the distance between two objects increases by a factor of nine, the force they exert on each other 1. decreases by a factor of eighty-one. 2. does not change. 3. increases by a factor of three. 4. decreases by a factor of nine. 5. increases by a factor of nine.

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13. Suppose you are on the moon and you drop two balls from the same height, one with mass1=m and the other with mass2=2m. A student notes that Newton's second law says that their accelerations should be a1=F/m and a2=F/(2m), respectively. Is it correct to conclude mass 2 will take longer to hit the surface of the moon because its acceleration is smaller by a factor of two? 1. No. Both accelerations will be the same. Although mass 2 is heavier, the force that the moon exerts on it is a factor of two larger. 2. Yes, both accelerations will be the same and therefore they will both move at identical speeds as they fall.

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13. Suppose you are on the moon and you drop two balls from the same height, one with mass1=m and the other with mass2=2m. A student notes that Newton's second law says that their accelerations should be a1=F/m and a2=F/(2m), respectively. Is it correct to conclude mass 2 will take longer to hit the surface of the moon because its acceleration is smaller by a factor of two? 1. No. Both accelerations will be the same. Although mass 2 is heavier, the force that the moon exerts on it is a factor of two larger. 2. Yes, both accelerations will be the same and therefore they will both move at identical speeds as they fall.

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