GRAVITATIONAL FIELDS PHYSICS 20 GRAVITATIONAL FORCES. Gravitational Fields (or Acceleration Due to Gravity) Symbol: Definition: Units:

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1 GRAVITATIONAL FIELDS Gravitational Fields (or Acceleration Due to Gravity) Symbol: Definition: Units: Formula Description This is the formula for force due to gravity or as we call it, weight. Relevant Mathematical Descriptions: This is the definition of gravitational fields. The field strength (intensity) at any point around the Earth can be found by using a test object (mass) and finding the weight to mass ratio of the test object at that point. In this formula we need to know the mass of the object producing the field, and the distance from the centre of that mass. Important numbers: mass of the Earth = kilograms radius of the Earth = x 10 6 m gravitational constant (G) = N m 2 / kg 2 1. Calculate the gravitational field strength on the surface of Mars. Mars has a radius of 3.43 x 10 6 m and a mass of 6.37 x kg. (3.61 N/kg) 2. At what distance from the Earth s surface is the gravitational field strength 7.33 N/kg? (1.01 x 10 6 m)

2 GRAVITATIONAL FIELDS 3. On the surface of planet X an object has a weight of 63.5 N and a mass of 22.5 kg. What is the gravitational field strength on the surface on planet X? (2.82 N/kg) 4. On the surface of planet Y, which was a mass of 4.83 x kg, an object has a weight of 50.0 N and a mass of 30.0 kg. What is the radius of the planet? (1.3 x 10 7 m) 5. What is the gravitational field strength 1.27 x 10 7 m (this is twice the Earth s radius) above the Earth s surface? (1.09 N/kg) 6. Planet B has a mass of 4.00 x kg and a radius of 6.0 x 10 5 m. What is the gravitational field strength on the surface of Planet B? (7.4 N/kg) 7. Two planets A and B have the same mass. However the gravitational field strength on the surface of planet A is 1.20 times the gravitational field strength on the surface of planet B. How does the radius of Planet A compare with the radius of Planet B? (0.913 times) 8. What is the weight of a 20.0 kg object on the surface of the moon? The mass of the moon is 7.34 x kg and the radius of the moon is 1.74 x 10 6 m. (32.3 N)

3 Newton s Law of Universal Gravitation Formula Description Relevant Mathematical Descriptions: Newton s Law of universal Gravitation States: That the gravitational force between two masses is directly proportional to the product of their mass. That the gravitational force between two masses varies inversely to the square of the distance between the centres of the masses. Important numbers: mass of the Earth = kilograms radius of the Earth = x 10 6 m gravitational constant (G) = N m 2 / kg 2 9. Two students are sitting 1.50 m apart. One student has a mass of 70.0 kg and the other has a mass of 52.0 kg. What is the gravitational force between them? (1.08 x 10-7 N) 10. What gravitational force does the moon produce on the Earth if the centres of the Earth and moon are 3.88 x 10 8 m apart and the moon has a mass of 7.34 x10 22 kg. (1.94 x N) 11. If the gravitational force between two objects of equal mass is 2.30 x 10-8 N when the objects are 10.0 m apart, what is the mass of each object? (1.86 x 10 2 kg) 12. Calculate the gravitational force on a 6.50 x10 2 kg spacecraft that is 4.15 x 10 6 m above the Earth s surface. (2.34 x 10 3 N)

4 13. The gravitational force between two objects that are 2.1 x 10-1 m apart is 3.2 x 10-6 N. If the mass of one object is 5.5 x 10 1 kg, what is the mass of the other object? (3.8 x 10 1 kg) 14. If two objects, each with a mass of 2.0 x 10 2 kg, produce a gravitational force between them of 3.7 x 10-6 N, what is the distance between them? (8.5 x10-1 m) 15. What is the gravitational force on a 70.0 kg object standing on the Earth s surface? (6.88 x 10 2 N) 16. What is the gravitational force on a 35.0 kg object standing on the Earth s surface? (3.44 x 10 2 N) 17. What is the gravitational force on a 70.0 kg object that is 6.37 x 10 6 m above the Earth s surface? (1.72 x10 2 N) 18. What is the gravitational force on a 70.0 kg object that is 3.18 x 10 6 m (half the radius of the Earth) above the Earth s surface? (3.06 x 10 2 N)

5 19. Three objects are all in a line, each with a mass of 10.0 kg. Each object is placed 5.00 x 10-1 m apart from each other. What is the net gravitational force on the centre object due to the other two objects? (0) 20. Three objects are all in a line, the first and second object has a mass of 10.0 kg while the third object has a mass of 15.0 kg. Each object is placed 5.00 x 10-1 m apart from each other. What is the net gravitational force on the centre object due to the other two objects? (1.33 x 10-6 N) 21. The gravitational force between two small masses A and B when placed a short distance apart is 3.24 x 10-7 N. What is the gravitational force between these objects if the masses of both A and B are doubled and the distance between them is tripled? (1.44 x 10-7 N)

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