TOPIC 6.1: Gravitational Fields and Forces These notes were typed in association with Physics for use with the IB Diploma Programme by Michael Dickinson

What is gravity? Is there gravity in space? Why do astronauts float? What keeps the moon from flying off in space?

6.1 Gravitational Force and Field State Newton’s universal law of gravitation. Watch Veritesium Videos 1, 2, 3 1EFC4D01C EFC4D01C 6F1EFC4D01C

6.1 Gravitational Force and Field State Newton’s universal law of gravitation. Galileo ( ) – g = 9.81m/s 2, even with different masses. David Scott – feather and hammer dropped on the moon, Apollo 15 Isaac Newton( ) – Idea about a cannon ball that never hit the ground. Orbit period of the moon – 27.3days Radius of moons orbit – R M = x 10 8 m, R E = x 10 6 m mid-1600s Earth’s and Moon’s masses had been determined M M = 7.35 x kg M E = 5.98 x kg)

6.1 Gravitational Force and Field State Newton’s universal law of gravitation. From all that data Newton calculated the centripetal acceleration on the moon due to the earth’s gravitational attraction. ac= v 2 /r= (2πr/T) 2 x 1/ r = m/s 2 Compared this with the “g” 3600 times lower. Concluded gravitational force of attraction is inversely proportional to the square of the distance between the centers of the two object. F G ∝ 1/r 2

6.1 Gravitational Force and Field State Newton’s universal law of gravitation. Also concluded that the gravitational force was proportional to the product of the two masses. F G ∝ m 1 m 2 Combined = F G ∝ m 1 m 2 /r 2

6.1 Gravitational Force and Field State Newton’s universal law of gravitation. Equation and Formula Newton’s Law of Universal Gravitation – every object attracts every other object with a force that is proportional to the product of the two masses and inversely proportional to the square of the distance between them. F = G(m 1 m 2 / r 2 ) Universal law of gravitation G = 6.67 x Nm 2 kg -2

6.1 Gravitational Force and Field State Newton’s universal law of gravitation. Example 1 Calculate the gravitational force of attraction between you and the person sitting next to you! Assume your mass is 65kg, their mass is 55kg and the distance is 2m Answer 5.9x10 -8 N

6.1 Gravitational Force and Field State Newton’s universal law of gravitation. Class practice Find the distance between a kg billiard ball and a kg billiard ball if the magnitude of the gravitational force between them is 8.92 x N. Answer: 3.00 x m

6.1 Gravitational Force and Field State Newton’s universal law of gravitation. Practice: pg 242 Practice C #1, 2, 3a.

6.1 Gravitational Force and Field Define gravitational field strength. Gravitational field is like a “force field” that exist around every object. It is dependent on the mass of an object. So larger mass means a larger field. Smaller mass means smaller field. Definition and Formula Gravitational field strength – the force per unit mass acting on mass in a gravitational field g = F/m

6.1 Gravitational Force and Field Define gravitational field strength. Practice 2 A 2.45kg object feels a gravitational force of 4.0N at the surface of the Moon. Calculate the Moon’s gravitational field strength at its surface. Answer: 1.63 N/kg

6.1 Gravitational Force and Field Determine the gravitational field due to one or more point masses Solve problems involving gravitational forces and fields.

6.1 Gravitational Force and Field 6.1.3, Given that g = F/m and F = G(Mm)/r 2 g = gravitational field strength F = gravitational force M = mass of the planet m = mass of object in gravitational field Substitute for F and you get: g = G(Mm)/r 2 m = GM/r 2

6.1 Gravitational Force and Field 6.1.3, 6.1.4, Problem 3 Use the following data to calculate the gravitational field strength at the surface of the Earth. R E = x 10 6 m M E = 5.98 x kg Answer: 9.80 N/kg