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# Gravitational Force & Field 2012

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IBD Topic 6

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### Gravitational Force & Field 2012

1. 1. Topic 6: Fields and Forces 6.1 Gravitational Force and Field
2. 2. Gravitational Force & Fields What do you know about gravity? What does a gravitational field look like? Can we defy gravity? What does gravity affect?
3. 3. Gravitational Force and Field  Newton proposed that a force of attraction exists between any two masses.  This force law applies to point masses not extended masses  However the interaction between two spherical masses is the same as if the masses were concentrated at the centres of the spheres.
4. 4. Newton´s Law of Universal Gravitation Newton proposed that “every particle of matter in the universe attracts every other particle with a force which is directly proportional to the product of their masses, and inversely proportional to the square of their distance apart”
5. 5. This can be written as F = G m1m2 r2 Where G is Newton´s constant of Universal Gravitation It has a value of 6.67 x 10-11 Nm2 kg-2
6. 6. Calculate the gravitational pull of the Earth on the moon Mm =0.01230*Me Me =5.976 x 1024 kg R = 384400 km
7. 7. Calculate the mass of the Earth How do you determine the mass of the Earth?
8. 8. Gravitational Field Strength A mass M creates a gravitational field in space around it. If a mass m is placed at some point in space around the mass M it will experience the existance of the field in the form of a gravitational force
9. 9. We define the gravitational field strength as the ratio of the force the mass m would experience to the mass, M That is the gravitational field strength at a point, is the force exerted per unit mass on a particle of small mass placed at that point
10. 10.  The force experienced by a mass m placed a distance r from a mass M is  F = G Mm r2  And so the gravitational field strength of the mass M is given by dividing both sides by m  g = G M r2
11. 11. The units of gravitational field strength are N kg-1 The gravitational field strength is a vector quantity whose direction is given by the direction of the force a mass would experience if placed at the point of interest
12. 12. Field Strength at the Surface of a Planet If we replace the particle M with a sphere of mass M and radius R then relying on the fact that the sphere behaves as a point mass situated at its centre the field strength at the surface of the sphere will be given by g = G M R2
13. 13. If the sphere is the Earth then we have  g = G Me Re 2  But the field strength is equal to the acceleration that is produced on the mass, hence we have that the acceleration of free fall at the surface of the Earth, g  g = G Me Re 2
14. 14. Is g = 9.81 ? Use the data from before and verify whether the acceleration due to gravity is 9.81 ms-1