Name Class Period. F = G m 1 m 2 d 2. G =6.67 x Nm 2 /kg 2

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1 Gravitational Forces 13.1 Newton s Law of Universal Gravity Newton discovered that gravity is universal. Everything pulls on everything else in the universe in a way that involves only mass and distance. G m 1 m 2 d 2 G =6.67 x Nm 2 /kg 2 The mass of the Earth is 5.98 x kg The mass of the Moon is 7.35 x kg The mass of the sun is 1.99 x kg The radius of the Earth is 3,959 miles (6,380,000 meters) The distance from the Earth to the Moon is 238,900 miles (3.84 x 10 8 m) The distance from the Earth to the Sun s is 92,960,000 miles (1.5 x m) 1. A monkey sits next to you on a park bench. Lets assume that your mass is 75-kg and the mass of the monkey is 50-kg. If the distance between your centers is 50 cm (0.50 m), what is the gravitational force of attraction between you and the monkey? Doc Fizzix Problem Set 1

2 2. Find the gravitational force of attraction between the Earth and the Moon. 3. Find the gravitational force of attraction between the Earth and the Sun. Doc Fizzix Problem Set 2

3 4. What is the force of gravity acting on a 2,000-kg spacecraft when it orbits two Earth radii from the Earth s center. 5. The gravitational force of attraction between two students sitting at their desks in a physics class is 3.20 x 10-8 N. If one student has a mass of 50.0 kg and the other has a mass of 60.0 kg, how far apart are the students sitting? Doc Fizzix Problem Set 3

4 6. Mars has a mass of about 6.4 x kg, and its moon Phobos has a mass of about 9.6 x kg. If the magnitude of the gravitational force between the two bodies is 4.6 x N, how far apart are Mars and Phobos? 7. How high above the surface of the Earth would you have to lift a 1-kg mass so it had a weight of 1-N? Find the answer in meters and then convert to miles. Doc Fizzix Problem Set 4

5 13.2 Gravitational Acceleration The acceleration of gravity of an object (planet), on its surface, is directly proportional to its mass and inversely proportional to it radius squared. g p = GM p r p 2 8. If the mass of the Earth remained constant, but the diameter of the Earth was cut in half, what would be the new acceleration of gravity on the surface of the Earth? b) Assume your mass is 75-kg then how much would you weigh? M p = r p = g p = b) 9. A hypothetical planet of apes has a radius 2.5 times that of Earth, but has the same mass. What is the acceleration of gravity at the surface of this planet? b) Assume your mass is 75-kg then how much would you weigh? M p = r p = g p = b) Doc Fizzix Problem Set 5

6 10. For this problem, assume you could hypothetically stand on the surface of a neutron star. Calculate the acceleration of gravity on the surface of a neutron star that has the same mass as our sun (ms= 1.99 x kg) but a radius of 10 km (10,000 m). b) Assume your mass is 75-kg then how much would you weigh? M p = r p = g p = b) Doc Fizzix Problem Set 6

7 13.3 Weightlessness and Apparent Weightlessness Weight is a measure of the acceleration of gravity acting on an object. Your apparent weight is the force a supporting surface pushes back with and we call that a normal force. When an elevator is accelerating up you will appear to weigh more and when an elevator is accelerating down you will appear to weigh less. For the following problems, up is assumed to be positive and down is negative. 11. What force must be applied to a 300-kg mass to accelerate it upward at 4 m/s 2? N ma Doc Fizzix Problem Set 7

8 12. A 2500-kg elevator accelerates upward at 1.6 m/s 2. Find the tension in the cable that lifts the elevator. 13. A 4-kg bag of potatoes is held by a string. If the tension in the string is 39.2 N, what is the state of motion of the bag (constant velocity or accelerated motion)? b) What should the tension be so that the bag accelerates upward at 1.8 m/s 2? b) Doc Fizzix Problem Set 8

9 14. An elevator is accelerating upward at a constant acceleration of 3 m/s 2. A man whose mass is 85 kg stands on a scale in the elevator. What is the reading of the scale? 15. A 60 kg monkey is standing in an elevator that moves up at a constant velocity of 5 m/s. If he were standing on a scale while in the elevator, what would be the reading of the scale? As the elevator approaches the proper floor, it decelerates at 2 m/s 2. b) What would the scale reading be while the elevator is decelerating? b) Doc Fizzix Problem Set 9

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