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Lecture_6

# Lecture_6 - 4.6 Fundamental Forces Currently there are 3...

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4.6 Fundamental Forces Currently there are 3 fundamental forces: 1. Gravitational Force 2. Strong Nuclear Force 3. Electroweak Force With the exception of the gravitational force, all the forces we will study this semester are related to the third fundamental force, the electroweak force. When I was in middle school, there were considered to be 4 fundamental forces: gravity, electrical, strong nuclear, and weak nuclear. Many theoretical scientists have spent much of their careers trying to reduce the # of fundamental forces down to one. Now let’s study the gravitational force. 4.7 The Gravitational Force It’s May 16, 1666, and Sir Isaac Newton is outside contemplating how the moon revolves around the Earth. While thinking, he notices an apple fall from a nearby tree and strike the ground. At that moment, he realized that the same pull that made the apple fall to the ground must also apply to the moon.

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The moon moves in a nearly perfect circle around the earth. Since it’s moving in a circle, its velocity is changing. v v v v Since its velocity is changing, there must be an acceleration. Since there is an acceleration, there must be a force. The same force that pulls the apple toward the earth must also pull the moon. This is the Gravitational Force . If gravity didn’t pull on the moon, it would continue to move in a straight line. The gravitational force from the earth pulls the moon away from its straight-line motion.
x Newton’s Universal Law of Gravitation: So How do you calculate the gravitational force between two objects? 2 2 1 r m m G F = Notice that the force is directly proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between them. Let’s consider two objects with masses m 1 and m 2 , and separate them by some distance r : m 1 m 2 r Then, The gravitational force equation is called an inverse square law. Nature loves inverse square laws, and we will encounter them again. G is the universal gravitational constant : kg m N 10 67259 . 6 2 11 × = - G Properties of Newton’s Law of Gravitation: 1. It grows weaker with distance. 2. It gets stronger for increasing masses. 4. It’s directed along the line containing the two masses. -F F Note: The forces on the two masses are equal but opposite as dictated by Newton’s 3 rd Law! 3. It is always attractive. D ( r is the distance between the centers of each mass.)

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What is the acceleration of a tennis ball falling near the surface of the earth? It’s – 9.8 m/s 2 , but why??? 2 E E B r m m G F = We can calculate the force on the ball: Mass of the ball Mass of the earth Radius of the earth But we can also write the force on the ball using Newton’s 2 nd Law: a m F B = These two forces have to be equal: 2 E E B B r m m G a m = 2 E E r m G a = This must be the acceleration of the ball. Let’s calculate it: 2 6 24 2 11 m) 10 (6.38 kg) 10 98 . 5 ( ) kg m N 10 67 . 6 ( × × × = - a g = = 2 m/s 8 . 9 COOL!
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