» In nature, there are two general types of forces: » » 1. Fundamental forces » 2. Non-fundamental forces.

2 Types of Forces

» In nature, there are two general types of forces:

» » 1. Fundamental forces» 2. Non-fundamental forces

2 Types of Forces

» 1. Fundamental forces: those that are truly unique in the sense that all other forces can be explained in terms of them. Only three have been discovered:

» Gravitational force» Strong Nuclear force: stabilizes the atomic nuclei » Electroweak force: has two manifestations:

˃ i) electromagnetic force which charged particles exert on one another

˃ ii) weak nuclear force which influences radioactive disintegration of some nuclei

2 Types of Forces

» 2. Non-Fundamental forces: are actually subsets of the fundamental forces. For instance, friction and tension forces are related to the electromagnetic force which arises from the interactions between electrically charged particles comprising atoms and molecules.

4.7 Gravity

» We've all been pretty darn accepting of the fact that we use 9.8 m/s2 for the gravitational acceleration on Earth.

» But why is that? What causes gravitational acceleration?

4.7 Gravity

» Newton’s Law of Universal Gravitation» Every particle in the universe exerts an attractive force on

every other particle. A particle is a piece of matter, small enough to be regarded as a mathematical point. For two particles that have masses m1 and m2 and are separated by a distance, r, the force that each exerts upon the other is directed along the line joining the particles and has a magnitude given by:

» » FW = G where G = 6.674 x 10-11 Nm2/kg2

»

» * G = the universal gravitational constant, found experimentally, and believed to be the same everywhere in the universe.

Example #1

» What is the magnitude of the gravitational force that acts on each of two students sitting next to each other.

» » FW = G where G = 6.674 x 10-11 Nm2/kg2

»

» * G = the universal gravitational constant, found experimentally, and believed to be the same everywhere in the universe.

Example #2

» What is the magnitude of the gravitational force that that the earth exerts on a 50kg person standing at the equator?

» » FW = G where G = 6.674 x 10-11 Nm2/kg2

» me=5.98x1024kg

» re=6.38x106m

Example #2

» What is the magnitude of the gravitational force that that the earth exerts on a 50kg person standing at the equator?

» » FW = 6.674 x 10-11 Nm2/kg2

» FW = (9.8m/s2)(mp) » the weight of an object is mass times the

acceleration due to gravity (g)» FW = mg

Weight

» Definition of Weight» The weight of an object on or above the earth is

the gravitational force that the Earth exerts on the object. The weight always acts downward, toward the center of the Earth.

» On or above any other astronomical body, the weight is the gravitational force exerted on the object by that body.

»

Weight

» *Notice that the farther one is from the center of the Earth, the less the Weight...

» on top of Everest? Less Weight. » Out in space? Less Weight.

Take home message

» F = ma is always true in an inertial reference frame.

» If we conveniently have something located on the surface of the Earth, we can define a = G . Plugging in values gives a ≈ 9.8 m/s2. And then:

» » Weight = FW = G = G * m = m a

Disclaimer

» **Note that the Law of Gravitation as written applies to particles as opposed to bigger objects, but it works very well as a close approximation for things like the Earth in which the mass of the object is symmetrically distributed about its center.

» When the mass is not evenly distributed about the center, we need calculus to come up with a more precise answer - the calculus students will learn how to do this type of thing around February or March of this year! :)

Example 3

» EX: The mass of the Earth is 5.98 x 1024 kg. » The radius of the Earth is 6.38 x 106 m. The mass

of Hubble is 11600 kg.» Find the weight of the Hubble Telescope when it

is:» a) resting on the surface of the Earth waiting to be

lifted into space, and » b) when it is in orbit 598 km above the Earth's

surface.

Example 3

» EX: The mass of the Earth is 5.98 x 1024 kg. » The radius of the Earth is 6.38 x 106 m. The mass of

Hubble is 11600 kg.» Find the weight of the Hubble Telescope when it is:» a) resting on the surface of the Earth waiting to be

lifted into space, and » b) when it is in orbit 598 km above the Earth's surface.» a) 1.14 x 105 N b) .950 x 105 N » *the 2nd answer is NOT in scientific notation…» Having the same power of 10 makes it easier to

compare them…

Example 4

» If the Lunar Module weighs 6 times MORE on earth than it does on the moon, but we want to have the same horizontal acceleration of the vehicle, is the required force on the moon:

» (a) the same, » (b) greater than, or » (c) less than, the force on the earth?

WHY?

Assignment

» P. 128 #20, 21, 24-25, 27-28, 30, 33