© 2004 Pearson Education Inc., publishing as Addison-Wesley 5. Universal Laws of Motion “ If I have seen farther than others, it is because I have stood on the shoulders of giants.” Sir Isaac Newton (1642 – 1727) Physicist

© 2004 Pearson Education Inc., publishing as Addison-Wesley 5.1 Describing Motion: Examples from Daily Life Distinguish between speed, velocity, and acceleration. What is the acceleration of gravity? How does the acceleration of gravity depend on the mass of a falling object? How do you know when a net force is acting on an object? Have you ever been weightless? Have you ever been massless? Our goals for learning:

© 2004 Pearson Education Inc., publishing as Addison-Wesley Objects in Motion speed – rate at which an object moves, i.e. the distance traveled per unit time [m/s; mi/hr] velocity – an object’s speed in a certain direction, e.g. “10 m/s moving east” acceleration – a change in an object’s velocity, i.e. a change in either speed or direction is an acceleration [m/s 2 ]

Galileo's Famous Experiment

© 2004 Pearson Education Inc., publishing as Addison-Wesley The Acceleration of Gravity As objects fall, they accelerate. The acceleration due to Earth’s gravity is 10 m/s each second, or g = 10 m/s 2. The higher you drop the ball, the greater its velocity will be at impact.

© 2004 Pearson Education Inc., publishing as Addison-Wesley The Acceleration of Gravity (g) Galileo demonstrated that g is the same for all objects, regardless of their mass! This was confirmed by the Apollo astronauts on the Moon, where there is no air resistance.

Acceleration of Gravity Any object which is being acted upon only by the force of gravity is said to be in a state of free fall. There are two important motion characteristics which are true of free-falling objects: –Free-falling objects do not encounter air resistance. –All free-falling objects (on Earth) accelerate downwards at a rate of 9.8 m/s/s (often approximated as 10 m/s/s)

If the velocity and time for a free-falling object being dropped from a position of rest were tabulated, then one would note the following pattern. Time (s)Velocity (m/s)

Free Fall Newton’s 2 nd Law predicts this! a = F m The force of gravity felt by a more massive object is greater

Air Resistance Air resistance is an upward force exerted on an object as it falls by air It is, in essence, a frictional force For simplicity, the amount of air resistance is determined by two factors –The cross-sectional area of the object –The speed of the object

Terminal Velocity Determine the acceleration of this 85 kg skydiver at points A-D. (Hint: F=ma) 9.8 m/s m/s m/s 2 0 m/s 2

Terminal Velocity The terminal velocity of a skydiver in a free-fall position with a semi-closed parachute is about 195 km/h Higher speeds can be attained if the skydiver pulls in his limbs. In this case, the terminal velocity increases to about 320 km/h!

The more compact and dense the object, the higher its terminal velocity will be. Typical examples are the following: raindrop, 25 ft/s, a skydiver was found to be in a range from 53 m/s to 76 m/s

Terminal Velocity Consider a skydiver: 1)At the start of his jump the air resistance is _______ so he ____ downwards. 2) As his speed increases his air resistance will _______ 3) Eventually the air resistance will be big enough to _______ the skydiver’s weight. At this point the forces are balanced so his speed becomes ________ - this is called TERMINAL VELOCITY zero accelerates increase balance constant W RichardsW Richards Worthing High School

How the forces change with time. KEY Gravity (constant value & always present…weight) Air resistance (friction) Net force (acceleration OR changing velocity)

Possible Test Questions: What factor causes terminal velocity to occur? If an object is at terminal velocity, is it speeding up, slowing down, or falling at a constant speed? Describe and explain how forces change on a falling object.

© 2004 Pearson Education Inc., publishing as Addison-Wesley Forces Forces change the motion of objects. momentum – the (mass x velocity) of an object force – anything that can cause a change in an object’s momentum As long as the object’s mass does not change, the force causes a change in velocity, or an…

Momentum Momentum is inertia in motion. It is determined by how big an object is and how fast it is moving. p = m x v (kg x m/s) A stationary object has zero momentum. p = m x v

© 2004 Pearson Education Inc., publishing as Addison-Wesley Is Mass the Same Thing as Weight? mass – the amount of matter in an object weight – a measurement of the force which acts upon an object When in “free-fall,” you are weightless!!

Projectile Motion An object thrown upward at an angle to the ground follows a curved path called a parabola. combines vertical and horizontal motion Orbiting objects- forward motion combines with free fall and object follows a curved path

Projectile Motion Projectile: When a falling object also experiences horizontal motion Horizontal motion does not affect vertical motion

© 2004 Pearson Education Inc., publishing as Addison-Wesley Newton’s Universal Law of Gravitation Isaac Newton discovered that it is gravity which plays the vital role of determining the motion of the planets - concept of action at a distance

© 2004 Pearson Education Inc., publishing as Addison-Wesley Newton’s Universal Law of Gravitation Between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object and inversely proportional to the square of the distance between the centers of the objects.

© 2004 Pearson Education Inc., publishing as Addison-Wesley Newton’s Universal Law of Gravitation G=6.67 x m 3 /(kg s 2 )

© 2004 Pearson Education Inc., publishing as Addison-Wesley How does the acceleration of gravity depend on the mass of a falling object? It does not. All falling objects fall with the same acceleration (on a particular planet). Now see why… F = ma and on Earth acceleration due to gravity denoted “g” so F=mg or g=F/m If mass of earth is M 1 then F g =GM 2 /d 2