Dynamics Unit 1
Scalars & Vectors Scalar- has magnitude only ! eg. Speed, distance Vector- has magnitude and direction. eg. Velocity, Acceleration Distance - total length of the path travelled by an object in motion Position- is the distance and direction of an object from a particular reference point
Displacement – the change in position of an object When an object changes its position more than once, total displacement is calculated by adding the displacements.
Continued… Adding/Subtracting vectors
Uniform/Non-uniform Motion Uniform – motion of an object at a constant speed in a straight line Non-uniform – motion in which the objects speed changes or the object does not travel in a straight line.
Speed/Velocity/Acceleration Average Speed: Average Velocity: Acceleration:
Information on Linear Motion Graphs Position-Time Graph Slope- represents Velocity Velocity-Time Graph Slope – represents Acceleration Area – represents Displacement Acceleration-Time Graph Area- represents change in velocity
Relationships Among Linear Motion Graphs SLOPE SLOPE AREA AREA
Instructional Objectives: • Students will be able to: • Define Projectile Motion • Distinguish between the different types of projectile motion • Apply the concept to a toy car and measure its velocity
What is a projectile? Projectile -Any object which projected by some means and continues to move due to its own inertia (mass).
Projectile Motion • Two-dimensional motion of an object • Vertical • Horizontal
Projectiles move in TWO dimensions Since a projectile moves in 2-dimensions, it therefore has 2 components just like a resultant vector. • Horizontal and Vertical
Types of Projectile Motion • Horizontal • Motion of a ball rolling freely along a level surface • Horizontal velocity is ALWAYS constant • Vertical • Motion of a freely falling object • Force due to gravity • Vertical component of velocity changes with time • Parabolic • Path traced by an object accelerating only in the vertical direction while moving at constant horizontal velocity
Horizontal “Velocity” Component • NEVER changes, covers equal displacements in equal time periods. This means the initial horizontal velocity equals the final horizontal velocity In other words, the horizontal velocity is CONSTANT. BUT WHY? Gravity DOES NOT work horizontally to increase or decrease the velocity.
Vertical “Velocity” Component • Changes (due to gravity), does NOT cover equal displacements in equal time periods. Both the MAGNITUDE and DIRECTION change. As the projectile moves up the MAGNITUDE DECREASES and its direction is UPWARD. As it moves down the MAGNITUDE INCREASES and the direction is DOWNWARD.
Combining the Components Together, these components produce what is called a trajectory or path. This path is parabolicin nature.
Examples of Projectile Motion • Launching a Cannon ball
Horizontally Launched Projectiles Projectiles which have NO upward trajectory and NO initial VERTICAL velocity.
Horizontally Launched Projectiles To analyze a projectile in 2 dimensions we need 2 equations. One for the “x” direction and one for the “y” direction. And for this we use kinematic #2. Remember, the velocity is CONSTANT horizontally, so that means the acceleration is ZERO! Remember that since the projectile is launched horizontally, the INITIAL VERTICAL VELOCITY is equal to ZERO.
Horizontally Launched Projectiles Example: A plane traveling with a horizontal velocity of 100 m/s is 500 m above the ground. At some point the pilot decides to drop some supplies to designated target below. (a) How long is the drop in the air? (b) How far away from point where it was launched will it land? 1010 m 10.1 seconds
Vertically Launched Projectiles NO Vertical Velocity at the top of the trajectory. Vertical Velocity decreases on the way upward Vertical Velocity increases on the way down, Horizontal Velocity is constant
Vertically Launched Projectiles Since the projectile was launched at a angle, the velocity MUST be broken into components!!! voy vo q vox
Equations • X- Component • Y- Component • Vectors Note: g= 9.8 m/s^2
Vertically Launched Projectiles There are several things you must consider when doing these types of projectiles besides using components. If it begins and ends at ground level, the “y” displacement is ZERO: y = 0
Vertically Launched Projectiles You will still use kinematic #2, but YOU MUST use COMPONENTS in the equation. voy vo q vox
Example A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (a) How long is the ball in the air? (b) How far away does it land? (c) How high does it travel? vo=20.0 m/s q = 53
Example A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (a) How long is the ball in the air? 3.26 s
Example A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (b) How far away does it land? 39.24 m
Example A place kicker kicks a football with a velocity of 20.0 m/s and at an angle of 53 degrees. (c) How high does it travel? CUT YOUR TIME IN HALF! 13.01 m
Factors Affecting Projectile Motion • What two factors would affect projectile motion? • Angle • Initial velocity • Visual Initial Velocity Angle
Example An object is fired from the ground at 100 meters per second at an angle of 30 degrees with the horizontal • Calculate the horizontal and vertical components of the initial velocity • After 2.0 seconds, how far has the object traveled in the horizontal direction? • How high is the object at this point?
Solution • Part a • Part b • Part c
Newton’s Laws • The law of Inertia - an object at rest or in uniform motion will remain at rest or in uniform motion unless acted on by an external force. • F = ma • For every action force on an object (B) due to another object (A), there is a reaction force, equal in magnitude but opposite in direction
Mass Inertial Mass-measure of how strongly the body is accelerated (by A) by a given force. Gravitational Mass -measure of how strongly the body is affected by the force of Gravity
Frames of Reference Inertial frame of reference -Has a constant velocity, meaning moving at a constant speed in a straight line, or it is standing still Non-inertial frame of reference -Does not have a constant velocity, it is accelerating.
Relative Motion • The motion (or way of moving) of an object viewed by an observer Relative Velocity- the velocity of an object relative to a specific frame of reference
General Relationship A relative to C A relative to B B relative to C Note: the outside subscripts on the right side of the equation (A &C) are in the same order as the subscripts on the left side of the equation and the inside subscripts on the right side of the equation are the same (B)
Types of Relative Motion Problems • Relative Motion in 1D • Relative Motion in 2D with perpendicular vectors • Relative Motion in 2D non perpendicular vectors
Quick Practice • A group of teenagers on a ferry walk on the deck with a velocity of 1.1 m/s relative to the deck. The ship is moving forward with a velocity of 2.8 m/s relative to the water. • Determine the velocity of the teenagers relative to the water when they are walking to the bow(front). • Determine the velocity of the teenagers relative to the water when they are walking to the stern
2) A plane is travelling with a velocity relative to the air of 3.5 x102 km/h [N35°W] as it passes over Hamilton. The wind velocity is 62 km/h[S]. • Determine the velocity of the plane relative to the ground. • Determine the displacement of the plane after 1.2 h.
Combining Dynamics and Kinematics Recall:Kinematics – the motion of an object with disregard to the cause Dynamics – The cause of the motion
Forces & FBD’s Common Forces • Gravity ( ) • Normal ( ) • Tension ( ) • Applied ( ) • Friction ( ) Units: Newton's (N) 1N =
Newton’s First Law: (Law of Inertia) If the external net force on an object is zero, the object will remain at rest or continue to move at a constant velocity. Inertia – a measure of an object’s resistance to change in velocity Mass – a measure of the amount of matter in an object
Newton’s Second Law: Newton’s Third Law: For every action force, there exists a simultaneous reaction force that is equal in magnitude but opposite in direction