The Law of Universal Gravitation

Today you need to know… The difference between the acceleration of gravity and the force of gravity. How to calculate the force of gravity between two objects. Fully understand that forces are not alone – they always act in pairs. All unbalanced forces are caused by acceleration.

LAW OF UNIVERSAL GRAVITATION Gravity is universal – everything is attracted to everything else – forces come in pairs. This attraction can be measured and is based on two things: 1. Mass 2. Distance

mass of object one (kg) mass of object two (kg) G = 6.67 x 10-11 Nm2/kg2 Gravitational Constant mass of object one (kg) The Force of Attraction (N) mass of object two (kg) distance between the centers of the two objects (m)

Understanding relationships between variables DIRECTLY INVERSELY The greater the mass the greater the force The force decreases as the square of the distance increases

Understanding relationships between variables How to solve problems regarding relationships between variables. 1. IGNORE G – it is always the same 2. Set up an original problem where everything is equal to 1 ex. 1= 1 x 1 12 3. Change only what the problem says. EXAMPLE PROBLEM: Two objects gravitationally attract each other with a force of 2 N. IF the distance between their centers is tripled, the new force of attraction is _______________ N. solution 1= 1 x 1 = 1 32 9 So the force is reduced by a factor of 9. 2/9 = The greater the mass the greater the force The force decreases as the square of the distance increases

Rules for Scientific Notation THE MATH Rules for Scientific Notation Final answer has only one digit to the left of the decimal Use the EE key

Constants G = 6.67 x 10-11 Nm2/kg2 This is the Gravitational Constant me = mass of the Earth (5.98 x 1024 kg) re = radius of the Earth (6.37 x 106 m)

EXAMPLE :Find the force between two objects 6371 km apart EXAMPLE :Find the force between two objects 6371 km apart. The first object has mass 70 kg, the second object has mass 6 x 1024 kg. F = (6.67 x 10-11 ) (70) (6 x 1024 ) = 63712 2.8 x1016 4.06 x 10 7 F= 6.90 X 10 8 N EXAMPLE: Two objects each have a mass of 1x10-3 kg. The force between the objects is 400 N. What is the distance between them? r = (6.67 x 10-11 ) (1x10-3) (1x10-3) = 400 6.67 x101-17 400

The Falling Apple Newton reasoned that the moon is falling toward Earth for the same reason an apple falls from a tree—they are both pulled by Earth’s gravity.

Newton’s Law of Universal Gravitation Newton discovered that gravity is universal. Everything pulls on everything else in a way that involves only mass and distance.

What is the force between the Earth and a mass of 1200 kg if the mass is 35000 meters above the Earth’s surface.

The Mass of the Earth https://www.youtube.com/watch?v=9yMQM5AN8mc Khan academy https://www.youtube.com/watch?v=Xcel427Ezl0