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Unit 2 Section 1 Notes Motion and Force Introduction to Kinematics
What is Kinematics? –The study of motion: how things move from one place to another, how fast they go, which direction they take, and whether they speed up or slow down.
Reference Frame An object is moving if: its position changes against a background that stays the same –A reference frame is a stationary background. You are constantly moving because the earth is turning; the velocity at the earth’s equator is 1670 km/hr. Why don’t you notice this? –You must be able to compare it to something that isn’t moving; you must have a frame of reference to tell if something is moving.
Talking about Directions Suppose you want to meet a friend at an Ohio State football game. You ask her for directions and she said it was five blocks to the north and then one block east. You follow the directions and there is no football stadium there! How could that happen? She gave the directions from her house and you thought they were from your house.
Reference Points Therefore, the starting point, or reference point, is very important in kinematics. Reference point: the point from which everything is measured –If two people don’t have the same reference point, directions would be meaningless.
Reference Points Your friend’s directions included distance and direction. Without a direction, you would have no idea how to find the stadium and you would just wander around (or check mapquest! ) The combination of distance and direction is called displacement.
Vectors Because displacement includes 2 important pieces of information, distance and direction, it is considered a vector. What is a vector? –A quantity with a number part (called magnitude) and a direction part. –Simply put, a vector has both magnitude and direction. –http://veevr.com/videos/XQfKvGltFhttp://veevr.com/videos/XQfKvGltF
Vectors Example: You might walk down the beach a distance of 250 meters. But if you include the fact that you walk due north, your displacement of 250 meters north would be an example of a vector quantity.
Distance vs. Displacement Distance: a measure of how far something has gone; a scalar quantity (represents size only) Displacement: a measure of where something ends up, relative to where it started; a vector quantity
Distance vs. Displacement Examples The track at Nick’s school is a quarter of a mile long. Nick runs around the track eight times. He has traveled a distance of _____ miles and has a displacement of _____ miles. Edward and his family are sightseeing. They walk two blocks north, four blocks west, and two blocks south. Edward has traveled a distance of _____ blocks and a displacement of _____ blocks.
Distance vs. Displacement Examples The track at Nick’s school is a quarter of a mile long. Nick runs around the track eight times. He has traveled a distance of 2 miles and has a displacement of 0 miles. Edward and his family are sightseeing. They walk two blocks north, four blocks west, and two blocks south. Edward has traveled a distance of 8 blocks and a displacement of 4 blocks.
Distance vs. Displacement Examples A straight drag strip has the starting line at its southern edge and the finish line at its northern edge. It is one mile long. If Cheryl races once down the strip, her distance is _____ mile and her displacement is _____ mile __________. Ava and her friends were walking along a nature trail. They walk three kilometers east and four kilometers north. Their distance traveled is _____ kilometers and their displacement is five kilometers __________.
Distance vs. Displacement Examples A straight drag strip has the starting line at its southern edge and the finish line at its northern edge. It is one mile long. If Cheryl races once down the strip, her distance is one mile and her displacement is one mile north. Ava and her friends were walking along a nature trail. They walk three kilometers east and four kilometers north. Their distance traveled is seven kilometers and their displacement is five kilometers northeast.
Non-linear Motion Think about motion in everyday life: a basketball player moving around the court or a deer moving in the woods. –Because this motion isn’t necessarily in a straight line, it is non-linear. –For this lesson, we will only be working in one dimension.
Speed Speed: describes how fast an object moves –To find speed, you must measure 2 things: Distance traveled by an object Time it takes to travel that distance –SI unit for speed: meters per second (m/s) –Other units for speed: km/h or mi/h or mi/s Or any unit of distance per any unit of time one m/s is equal to mi/h
Average Speed Average speed: since an object normally doesn’t move with constant speed, average speed is often used –Average speed is the: distance traveled by an object divided by the time it takes to travel that distance
Average Speed Equation to calculate average speed: v = d t v is the speed, d is the distance traveled and t is the time. “I feel the need, the need for speed.” —Tom Cruise, Top Gun, 1986
Types of Speed Constant SpeedInstantaneous Speed Instantaneous speed: the speed at a particular moment in time. For example, a car’s speedometer gives the instantaneous speed of the car.
Speed and Velocity Problems What is the speed of a rocket that travels 9000 meters in seconds?
Velocity Velocity includes both speed and direction. –Describes how fast something is actually getting somewhere. –Because velocity includes direction, it is a vector quantity as well. Equation for Velocity: v = d t –v is velocity, d is distance, and t is time What’s the difference between speed and velocity? –Velocity includes speed AND direction; speed is just how fast something is moving.
Speed and Velocity Problems Calculate the velocity of a mountain climber if the climber is moving northeast at a pace of 1.6 km in 1.4 hours.
Distance (Displacement) vs. Time Graphs Distance-Time Graphs: shows relationship between speed, distance, & time –Time, the independent variable, is graphed on the x-axis –Distance (displacement), the dependent variable, is graphed on the y-axis
Distance (Displacement) vs. Time Graphs The speed is calculated by finding the slope of the line. For a car at a constant speed, the distance vs. time graph is a straight line. The distance-time graph of a faster moving object is steeper than the graph of a slower moving object. The distance-time graph of an object at rest is a flat line with a slope of 0.
Distance (Displacement) vs. Time Graphs
Momentum Momentum: Depends on 2 factors: –Mass –Velocity Momentum is the product of the mass and velocity of an object. Equation: p = m·v –SI unit for momentum: kg·m/s
Momentum Momentum has direction: it is the same direction as velocity The greater the mass, the larger the momentum and the greater the velocity, the larger the momentum. –Example: A tractor-trailer has much more momentum than a sports car traveling at the same speed. If an object is NOT moving, its momentum is zero.
Law of Conservation of Momentum Law of Conservation of Momentum: the total amount of momentum in a system is conserved. –In other words, momentum before a crash = momentum after a crash. –If 2 speeding cars collide head on, the cars will continue on in the direction of the car that had the greatest momentum.