Introduction to Kinematics Motion, Forces and Energy
Mechanics: The study of motion Kinematics The description of how things move 1-D and 2-D motion Dynamics The study of the forces that cause motion Newton s Laws Energy Momentum http://www.journalism.missouri.edu/images/news/2004/detrick-rollercoaster.jpg
Remember: Before we can study something, scientists need to define what it is they are studying. They determine what belongs in the study boundaries the system all processes, forces, and measurable properties. Anything outside the system s boundaries the surroundings. The surroundings can affect the system and these interactions are studied as well.
Remember: problem solving method 1. Sketch the problem 2. Choose the formula(s) 3. Calculate your Answer 3. Check it!
Kinematics CH 4 Describing motion
What is Motion? any physical movement or change in position or place, relative to a reference point Movement Referenceo int
understanding vocabulary A stationary landmark or location from which we start or make our observations. Reference point
Choose the point of reference or reference frame that is easiest for you to use in solving the problem or answering the question. Make all measurements from that point of reference or reference frame.
understanding vocabulary An unchanging rate of motion. Moving at uniform speed.
understanding vocabulary The rate of change of speed during motion.
Choose the coordinates Establish where 0 is (the origin) Establish directions where the values increase
understanding vocabulary the origin (value of 0) is placed at the reference point. Imaginary line marked off in measured units
Using a coordinate system example - football What origins and direction are used to determine 1 st down? Length of punt?
Motion diagrams A series of images of a moving object that records its position after equal time intervals. At rest Moving at a constant speed 0 1 2 3 4 5 It represents the position, velocity and acceleration of an object Speeding at several up different times. Slowing down
the particle model
What is the motion of the cart in this diagram? Change is position is less per each time interval time in seconds Slowing down (deceleration)
We can use motion diagrams to represent 4 concepts in kinematics: At rest Uniform motion (constant speed) Speeding up (acceleration) Slowing down (deceleration)
Demonstrate uniform and accelerated motion Design it, show it, use evidence to support it.
Measuring motion in 1 and 2 dimensions SCALARS AND VECTORS
understanding vocabulary has magnitude A measurable quantity. Can be positive, negative or zero.
understanding vocabulary has magnitude AND direction A measurable quantity that also includes direction. Can be positive or negative.
Position vector Proportional to the distance of the object from the origin and points from the origin to the location of the object at a particular time. + What is smiley s position vector? + 3 m 0 1 2 4 5 3 meters +
try some. Scalar or Vector? a. 5 m See Answer scalar b. 30 m/sec, East See Answer vector c. 5 mi., North See Answer vector d. 20 degrees Celsius See Answer scalar e. 256 bytes See Answer scalar f. 4000 Calories scalar
Describe the position of the house relative to the bicycle using only scalars. 4 km Describe the position of the house relative to the bicycle using vectors. 4 km, N
Is speed a scalar or vector? 1. What is the bike s speed after 1 hour? 25 mi/hr B C 2. Does the bike speed up or slow down at B? How do you know? Speed up, slope increases 3. What is the speed at B? 50 mi/hr 4. What is the speed at C? 0, it is stopped
Can you control your speed? Another design challenge example
Distance and Direction How far overall?
understanding vocabulary initial time - t i final time - t f t f - t i represents the time interval use the formula: Δt = t f - t i The length of a time span.
remember Motion occurs when an object s position changes during an interval of time. One dimensional motion can be represented by position along a single coordinate axis.
distance vs displacement Distance is a scalar quantity. It is always positive. It refers to how much ground an object has covered during its motion. There is no direction associated with it.
Distance is the length of the actual path taken by an object. Consider travel from point A to point B in diagram below: A d = 20 m B Distance d is a scalar quantity: Contains magnitude only and consists of a number and a unit. ex: 20 m, 40 mi/h, 10 gal
Distance = how far an object has moved. Measured in meters, kilometers (cm or mm) Y Axis X Axis If each mark represents 10 cm, what is the distance between the girl and the ball?
Displacement is the object's change in position. displacement distance
distance vs displacement Displacement is a vector quantity. It is the object's overall change in position. It can be positive or negative depending on your initial point of reference.
As any object moves from one position to another, the length of the straight line drawn from its initial position to the object s final position is called displacement. Displacement doesn t always tell you distance an object moved.
Displacement is the straight-line separation of two points in a specified direction. D = 12 m, 20 o A q B A vector quantity: contains magnitude AND direction. ex: 12 m, 30 0 ; 8 km/h, N
In the diagram below, the origin, or initial position (d o ) is at 0.0 m. The final position (d 1 ) is at 50 m. The distance traveled from the origin is 50 m, but the displacement is 50 m to the right, or can be drawn similar with a green line vector.
Defining the reference point and direction If displacement is positive, the object moves to the right. If the displacement is negative, the object moves to the left.
If the girl walks to the red ball, then walks backwards to the bear, what distance has she traveled? -2 0 6 10 X Axis Displacement = the distance of a body's change in position from a starting point. Her final displacement is.
remember: Displacement (blue line) is how far the object is from its starting point, regardless of how it got there. Distance traveled (dashed line) is measured along the actual path.
Physicists use the tools of math to describe measured or Physics shorthand predicted relationships between physical quantities in a situation. difference or change in x, y t sum or total Equation = a compact statement based on a model of the situation. change in position time interval x = x f - x i Shows how 2 or more variables are thought to be related.
If displacement is the distance and direction between 2 positions = change in position = final position initial position x i initial position Displacement: x = x f x i x f final position
The values of x i and x f are determined by their positions on the axis. While the choice of a reference point for the coordinate system is arbitrary, once chosen, the same point must be used throughout the problem.
Signs of Displacement In physics, the movement from the origin is thought of as positive or negative. In each case, an origin, starting place, or reference point needs to be established. Then, it must be decided which directions are considered positive and which is considered negative. Once a group agrees on that, then you can determine displacement vectors. For example, if we assume that up is positive, then Mt. Elinor, would have an elevation displacement vector of +2,400 ft, based off of the origin of sea level. On the other hand, Death Valley, California is below sea level by 120 ft, so its displacement would be -120 ft compared to sea level.
When would position be but the displacement +?
displacement is written as: Left: Displacement is positive. Right: Displacement is negative.
Check it: In this motion diagram the length of the arrow indicates the change in position of the object, or its. a. Displacement b. Magnitude c. Position d. Resultant
In this image, 7 cm is a. a. Vector b. speed c. Scalar d. interval
Consider a car that travels 8 m, E then 12 m, W. What is the car s displacement? D = 4 m, W D 8 m,e x What is the distance traveled? 20 m!! x = -4 12 m,w x = +8
try a problem A person starts at the 5.0 m mark. They walk to the 12m mark. What is their distance travelled? What is their displacement? They leave the 12m mark and walk to the 1m mark. What is their distance travelled? What is their displacement? What is the total distance travelled? What is the total displacement for the motion?
What about at angles? You drive 3 miles east and then 4 miles north. What is your: Why are you not drawing a picture people? Distance travelled? Displacement?
C 4 mi Distance: AB + BC 3 + 4 = 7 mi B 3 mi A Displacement: measure of the hypotenuse (AB) 2 + (BC) 2 = (AC) 2 (3) 2 + (4) 2 = x 2 9 + 16 = 25 = 5 mi., NE
Try some on your own
How are distance and displacement related to motion? Motion of an object is BOTH a scalar quantity (time) And Vector quantity (displacement)
Quantities in Motion Any motion involves three concepts Displacement Velocity Acceleration These concepts can be used to study objects in motion and called the parameters of the motion.