Motion  Chapter 1  Joseph F. Alward, PhD  Department of Physics  University of the Pacific

Aristotle (384 - 322 BC)

Galileo Galilei (1564-1642)

Galielo showed Aristotle's ideas on motion were wrong, and got in trouble with the Catholic church for saying that the Earth was not the center of the universe.

   Measuring Distance

One meter = 3.28 feet (ft) ------------------------------------------- One mile = 5280 ft ------------------------------------------- One kilometer = 1000 meters (m)                                                = 1000 m  x  3.28 ft / m                          = 3280 ft                          = about 0.6 mile

  Average Speed

Distance = 300 meters (300 m) Time = 10 seconds (10 s) Average speed = Distance /  Time         ----------------------------------------------- The cheetah averages 70 m/s for 30 seconds.  How far does it travel in those 30 seconds?

 Motion Symbols

d = distance traveled t = time elapsed vave = average velocity

vave = d / t Example: d = 50 m t = 5 s ---------------------- vave = 50 m / 5 s         = 10 m/s

d = vave t Example: vave = 40 m/s t = 3 s --------------------- d = (40 m/s)3 s    = 120 m

   Calculating Distance from Average Speed

Average speed = Distance /  Time      vave = d / t                   Distance = Average speed x Time       d = vave t ------------------------------------------------ The average speed of the cheetah during a 50-second run is 65 m/s. How far does it travel?

  Relative Speed

The speed of the cheetah relative to the ground is 65 m/s. What is the speed of the ground relative to the cheetah?

  Speed versus Velocity

Car is moving at the constant speed of 30 m/s.   Each second it travels 30 m.   Its velocity is not constant.   Why?

   Velocity is Speed with Direction

Velocity is "speed with direction". Velocity is a "vector" a quantity with a directional attribute. "30 m/s due east" is a velocity; it has the two attributes, magnitude, and direction.

  Adding Velocities Using Vectors

Vectors are arrows. Arrows have two attributes:     (1)  length (magnitude)     (2) direction

   Adding Vectors Using the Parallelogram Rule

Put vectors tail-to-tail, sketch the square or rectangle.  The diagonal is the sum.

   Example of Parallelogram Rule

Hypotenuse = Square root of the sum of the squares of the sides:    1002 = 602 + 802

   Using Pythagoras to Add Perpendicular Vectors

Theorem of Pythagoras: The sum of the squares of the sides of a triangle equal the square of the hypotenuse.       2 = 1 + 1

  Changing Velocity Three Ways

Velocity--a vector-- can change three different ways: 1.  Speed changes 2.  Direction changes 3.  Both of the above

   Acceleration

Acceleration  change in speed/ time             a = Dv / t No change in speed. Centripetal acceleration (Circular motion)

  Calculating Accelerations

a = Dv / t   Speed increases from    30 m/s to 70 m/s.

Change in speed = 70 m/s - 30 m/s                    Dv  = 40 m/s ------------------------------------------                      t   =  5 s ------------------------------------------                     a = Dv / t                        = (40 m/s) / 5 s                        = 8 m / s / s                        = 8 m / s2                     a = 8 m / s2

Calculating Accelerations

a = Dv / t    Speed decreases from    70 m/s to 30 m/s.

Change in speed = 30 m/s - 70 m/s                    Dv  = - 40 m/s ------------------------------------------                      t   =  5 s ------------------------------------------                     a = Dv / t                        = (- 40 m/s) / 5 s                        = - 8 m / s / s                        = - 8 m / s2

  Calculating Speeds from Accelerations

a = Dv / t                                (1) Dv = change in speed          (2)

If starting speed is zero, the change in speed equals the speed right now: v = Dv                                    (3) a = v / t                                  (4)   v = a t                                    (5) a = 10 m/s2 (acceleration due to gravity) t = 5 seconds                   v = a t                   (6)

  How Galileo Measured Acceleration Due to Gravity

   Acceleration due to Gravity

g = 10 m/s2    =  Acceleration caused by        Earth's pull ------------------------------------------ 10 seconds, 10 m/s per second (10 m/s2) starting from rest. How far has the rock traveled?

  Distance Traveled by Accelerating Object

g = 10 m/s2 ----------------------------------------- 5 seconds, 10 m/s per second (10 m/s2) starting from rest. How far has the rock traveled? d = 1/2 g t2    = 1/2 (10 m/s2) (5 s)2    = 125 m

  Earth's Pull Accelerates
  Rising or Falling Objects

Change in speed caused by Earth's pull is about 10 m/s for each second. g = 10 m/s2 Speed is subtracted while the object is rising, added when it's falling.

  Air Resistance

Both objects fall the same distance in the same time if there's no air in thecylinder.

  Summary:  Speed versus Velocity

  Summary:  Three Ways to Accelerate

  Acceleration Due to Gravity and Speed