Energy Work Power PE KE Workenergy theorem momentum

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� � � Energy Work Power PE KE Work-energy theorem momentum Impulse momentum theorem

� � � Energy Work Power PE KE Work-energy theorem momentum Impulse momentum theorem Conservation of momentum Momentum Gravity Newton’s law of gravitation Weight Value of g

Momentum Chapter 6

Momentum Chapter 6

Key Concepts �Impulse �Momentum �The Impulse-Momentum Theorem �Conservation of Momentum

Key Concepts �Impulse �Momentum �The Impulse-Momentum Theorem �Conservation of Momentum

Impulse and Momentum � Impulse = Force x time Units are Newton-seconds: Ns �

Impulse and Momentum � Impulse = Force x time Units are Newton-seconds: Ns � Momentum = mass x velocity Units are kg m/s � An Impulse on an object causes a change in the object’s momentum � Newton’s 2 nd law gives us a relationship between impulse and momentum

The Impulse-Momentum Theorem �The impulse on an object is equal to its change in

The Impulse-Momentum Theorem �The impulse on an object is equal to its change in momentum

Conservation of Momentum � The total momentum of a group of interacting objects remains

Conservation of Momentum � The total momentum of a group of interacting objects remains the same in the absence of external forces � Examples: Cannon and cannonball Astronaut and wrench

Energy Chapter 7

Energy Chapter 7

Key Concepts �Work �Power �Kinetic Energy �Potential Energy �Conservation of Energy

Key Concepts �Work �Power �Kinetic Energy �Potential Energy �Conservation of Energy

Work � Work is done when a force is applied to an object and

Work � Work is done when a force is applied to an object and that object is displaced parallel to the direction of the force � Work = Force x distance (W=Fd) Units are Newton-meters (Nm) One Nm is also called a Joule (J)

� The object must move for work to be done Ex: you push a

� The object must move for work to be done Ex: you push a wall and the wall doesn’t move – no work is done � The displacement and the force must be parallel for work to be done Ex: A book slides across the table, but gravity does no work

Power �Power is the rate at which work is done �Power = Work /

Power �Power is the rate at which work is done �Power = Work / time (P = W / t) Units: J/s or Watts (W)

Kinetic Energy �Any is energy of motion moving object has kinetic energy �Mathematically: KE

Kinetic Energy �Any is energy of motion moving object has kinetic energy �Mathematically: KE = (1/2)mv 2

How Speed Affects KE �KE is proportional to speed squared (v 2) �Therefore, double

How Speed Affects KE �KE is proportional to speed squared (v 2) �Therefore, double the speed and the KE increases by 22 = 4 �Triple 3 2= 9 the speed and the KE increases by

Gravitational Potential Energy (GPE) �GPE is energy associated with an objects height above the

Gravitational Potential Energy (GPE) �GPE is energy associated with an objects height above the ground �Mathematically: m = mass g = 9. 8 m/s 2 h = height �The has GPE = mgh higher the object is, the more GPE it

Conservation of Energy � As the book falls, it loses GPE and gains KE

Conservation of Energy � As the book falls, it loses GPE and gains KE � In other words, GPE is being converted to KE � However, constant the total energy (GPE + KE) remains

Work and Kinetic Energy �Ex: You push an object on a frictionless surface �You

Work and Kinetic Energy �Ex: You push an object on a frictionless surface �You did work on the object and in the process changed its KE �It turns out the work done on an object exactly equals its change in KE �This is called the Work-Energy theorem �Mathematically: Work = ∆KE

Work and Potential Energy �Ex: You lift a book from the floor and put

Work and Potential Energy �Ex: You lift a book from the floor and put it on a bookcase �You did work on the object and in the process changed its GPE �The work done exactly equals the change in GPE �Mathematically: Work = ∆GPE

Chapter 9: Newton’s Law of Gravitation � Every object in the universe is attracted

Chapter 9: Newton’s Law of Gravitation � Every object in the universe is attracted to every other object � The force of gravity between two objects depends on their mass and the distance between them � Mathematically: F = (Gm 1 m 2)/d 2

How Distance Affects Gravity �The force of gravity is inversely proportional to distance squared

How Distance Affects Gravity �The force of gravity is inversely proportional to distance squared �Therefore, double the distance between two objects and the force becomes 22 = 4 times less �Triple the distance between 2 objects and the force becomes 32 = 9 times less

Ch. 36: Einstein’s Theory of Gravity �Relativity showed that space are time not separate

Ch. 36: Einstein’s Theory of Gravity �Relativity showed that space are time not separate and unrelated entities �They are united into one single entity called space-time �All events in the universe take place within the space-time continuum �Einstein visualized space-time as a fabric and showed that massive objects can warp this fabric

Curvature in Space-Time

Curvature in Space-Time

Objects will follow the curvature in space-time

Objects will follow the curvature in space-time

Light also follows curvature in spacetime

Light also follows curvature in spacetime

Black Holes �Massive stars will collapse violently at the end of their lives �The

Black Holes �Massive stars will collapse violently at the end of their lives �The remnants of this collapse can be so dense that even light cannot escape its gravity �These “black holes” create severe curvature in space-time

Space-Time Around a Black Hole

Space-Time Around a Black Hole

The Event Horizon �Each black hole is surrounded by a boundary called its Event

The Event Horizon �Each black hole is surrounded by a boundary called its Event Horizon �Anything that crosses the event horizon is lost forever �In other words, we cannot obtain information from anything within the event horizon �Physicists are still struggling to unlock the secrets of black holes

Worm Holes � Worm holes are portals through the curvature in space that connect

Worm Holes � Worm holes are portals through the curvature in space that connect two distant points in the universe

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