Acceleration & Momentum


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  • So for every second the wind starts gusting, the boat is going 4 m/s faster.
  • So for every second the wind starts gusting, the boat is going 4 m/s slow, OR is going 4 m/s faster in the opposite direction.
  • Displacement Graph: AB: Got to Clackamas and realized we'd forgotten Grace. BC: Went back home to pick her up CD: Went to school DF: Stayed at school for the day Speed Graph: AB: accelerated BC: slowed to a stop CD: accelerated (maybe got on freeway) DF: traveled at a constant speed
  • At 30 seconds, car's speed is 20 m/s. Acceleration is 1 m/s/s from 0 to 20 seconds. Deceleration is 1 m/s/s (or -1m/s/s acceleration). Line is curved because acceleration is not constant (slope of line changes throughout).
  • 750 m/s = 900 km/hr = 559 miles per hour kg m/s = SI unit for momentum Practical application: it will take a lot more force (energy) to slow or stop a cargo plane than it would a fly because of the difference in mass.
  • Acceleration & Momentum

    1. 1. Changes in Speed & Direction Acceleration & Momentum
    2. 2. Review - converting metric units <ul><li>To convert WITHIN metric units: </li></ul><ul><ul><li>Move the decimal one place for each box you “jump” into </li></ul></ul><ul><ul><li>Move the decimal in the same direction that you “jump”   </li></ul></ul><ul><li>Example: </li></ul><ul><ul><li>Change .00007623 kilograms into milligrams   </li></ul></ul><ul><ul><li>.00007623 kg </li></ul></ul><ul><ul><li>answer: 76.23 mg </li></ul></ul>1 2 3 4 5 6 milli centi deci meter gram liter deca hecto kilo 0.001 0.01 0.1 1 10 100 1000 1 2 3 4 5 6
    3. 3. Review - converting standard units <ul><li>To convert English to Metric (or metric to English) units: </li></ul><ul><ul><li>Multiply by a conversion factor that will cancel out the original units </li></ul></ul><ul><ul><ul><li>Identify starting & ending units. </li></ul></ul></ul><ul><ul><ul><li>Determine the units that will cancel the original & end with what's needed. </li></ul></ul></ul><ul><ul><ul><li>Find the conversion factor needed (on chart). </li></ul></ul></ul><ul><ul><ul><li>Multiply all top numbers & divide by each bottom number. </li></ul></ul></ul><ul><ul><ul><li>Check units & answer. </li></ul></ul></ul><ul><li>  </li></ul><ul><li>Example: </li></ul><ul><ul><li>Change 76 kilograms into pounds   </li></ul></ul><ul><ul><li>76 kg x = lbs </li></ul></ul>lbs kg 2.2 1 167.2
    4. 4. Review - speed <ul><li>Motion = any change in position & requires a reference point </li></ul><ul><li>Speed is how quickly a change in position happens </li></ul><ul><li>Speed = distance </li></ul><ul><li> time </li></ul><ul><li>  </li></ul>Time in Seconds Distance in Meters
    5. 5. Relative Velocity <ul><li>Velocity = speed + direction (52 m/s South) </li></ul><ul><li>To compare two objects' speeds we do the following: </li></ul><ul><ul><li>When objects travel in the same direction, their relative speed is the difference between their individual speeds. </li></ul></ul><ul><li>  50 mi/h - 40 mi/h = 10 mi/h </li></ul><ul><li> relative velocity = 10 mi/h away from each other </li></ul><ul><ul><li>When they travel in opposite directions, their relative speed is the sum of their individual speeds. </li></ul></ul><ul><li>30 mi/h + 20 mi/h = 50 mi/h </li></ul><ul><li> relative velocity = 50 mi/h away from each other </li></ul>
    6. 6. Relative Velocity Continued <ul><li>Compare these trains' speeds: </li></ul><ul><ul><li>A train is traveling at 120 km/hr down a straight track. A runaway train is 700 km away on a collision course, going 230 km/hr. What is their relative velocity? </li></ul></ul><ul><li>  </li></ul><ul><li>230 km/h + 120 km/h = 350 km/h </li></ul><ul><li> relative velocity = 350 km/h towards each other </li></ul><ul><li>How long do they have to fix this problem before the trains collide? </li></ul>
    7. 7. Acceleration <ul><li>Acceleration is the rate of change in velocity </li></ul><ul><ul><li>in other words, how long it takes an object to: </li></ul></ul><ul><ul><ul><li>speed up </li></ul></ul></ul><ul><ul><ul><li>slow down </li></ul></ul></ul><ul><ul><ul><li>change direction </li></ul></ul></ul><ul><li>To calculate this we use this equation: </li></ul><ul><li>final velocity - starting velocity </li></ul><ul><li>time </li></ul>acceleration =
    8. 8. <ul><li>In other words... </li></ul><ul><li>change in velocity </li></ul><ul><li> time </li></ul><ul><li>Commonly measured in m/s 2 or miles/hour 2 </li></ul><ul><li>Meaning... </li></ul><ul><ul><li>For every one second (or hour or whatever unit of time), the object is either </li></ul></ul><ul><ul><ul><li>speeding up, </li></ul></ul></ul><ul><ul><ul><li>slowing down, or </li></ul></ul></ul><ul><ul><ul><li>changing direction </li></ul></ul></ul><ul><ul><li> a certain rate (speed) </li></ul></ul>acceleration =
    9. 9. <ul><li> final m/s - starting m/s </li></ul><ul><li> time ( s ) taken to change velocity </li></ul><ul><li>m/s 2 = change in velocity per second = m/s per second </li></ul><ul><li>Example: it takes my car 10 seconds to get up to 20 m/s North </li></ul>Units of Acceleration acceleration = = m/s 2 20 m/s 2 m/s 2 North = 10 s 20 m/s  10 s = x = (change in velocity) 10 second acceleration 20 m s 0 m s 20 m s 1 10 s
    10. 10. Positive Acceleration <ul><li>Within 5 seconds, a gust of wind speeds up a west-bound sailboat </li></ul><ul><li>Positive acceleration is always in the SAME DIRECTION as the original motion </li></ul>10 m/s 30 m/s 4 m/s 2 West = 5 s 20 m/s  5 s = x = 5 s 30 m s 10 m s 20 m s 1 5 s
    11. 11. Negative Acceleration <ul><li>Within 5 seconds, a gust of wind slows down a west-bound sailboat </li></ul><ul><li>Negative acceleration is always in the OPPOSITE DIRECTION as the original motion </li></ul>30 m/s 5 m/s - 5 m/s 2 West OR 5 m/s 2 East = 5 s - 25 m/s  5 s = x = 5 s 5 m s 30 m s 20 m s 1 5 s
    12. 12. Graphing Acceleration <ul><li>The graph below describes our trip to school this morning. </li></ul><ul><li>What is happening in each part of the graph? </li></ul><ul><li>Moving Man Illustration </li></ul>Displacement Speed
    13. 13. Calculating Acceleration <ul><li>At 30 seconds, what is the speed of the car? </li></ul><ul><li>What is the car's acceleration at 20 seconds into the trip? </li></ul><ul><li>What is the car's acceleration between 40 & 50 seconds? </li></ul><ul><li>Why is the line from 50 to 90 seconds curved? </li></ul>
    14. 14. Centripetal Acceleration <ul><li>An object moving in a circle is constantly changing direction </li></ul><ul><ul><li> therefore, it is accelerating </li></ul></ul><ul><ul><li>Example: going around a curve in a car </li></ul></ul><ul><ul><ul><li>your body wants to keep going forward (inertia) </li></ul></ul></ul><ul><ul><ul><li>but the seat belt (or car door) pushes you in </li></ul></ul></ul><ul><ul><ul><li>your body is changing direction of motion every second as you go around that curve </li></ul></ul></ul><ul><ul><ul><li>...therefore, you are accelerating, even if your speed remains constant </li></ul></ul></ul><ul><ul><ul><li>video illustrations </li></ul></ul></ul>
    15. 15. Momentum <ul><li>Momentum gives us a measure of an object's inertia (its tendency to keep moving). </li></ul><ul><li> momentum = mass x velocity or p=m • v </li></ul>Example: if a fly and a loaded cargo plane were both flying due East at 750 m/s, what would the momentum of each be? 10 mg x 750 m/s = 7,500 mg • m/s East .00001 kg x 750 m/s = .0075 kg •m/s East 330,000 kg x 750 m/s = 247,500,000 kg•m/s East mass = 10 mg mass = 330,000 kg
    16. 16. <ul><li>Larger mass gives larger momentum </li></ul><ul><li>Greater velocity also increases momentum </li></ul><ul><li>p = m • v </li></ul><ul><li>Which will take longer to stop? </li></ul><ul><li>Which will hit the windshield of the oncoming car that appears out of nowhere with greater force? </li></ul>Example: two flies, both with a mass of 10 grams, are racing Northwest to reach the garbage dump. What would the momentum of each be if Wolfie was going 10 m/s and Nannerl was flying 13 m/s? 10 mg x 10 m/s = 100 mg • m/s NW 10 mg x 13 m/s = 130 mg•m/s NW Wolfie Nannerl mass = 10 mg mass = 10 mg
    17. 17. Conservation of Momentum <ul><li>When two object collide, momentum can be transferred. </li></ul><ul><li>No momentum is created or lost in the process. </li></ul><ul><li>Law of Conservation of Momentum: </li></ul><ul><ul><li>if no other forces act on a set of objects, their total momentum remains the same after they interact </li></ul></ul><ul><ul><li>As the first ball is pulled back and released, it falls and collides with the next ball, transferring its momentum. This happens all down the line until the ball at the ends swings up and returns to again transfer that momentum back again through the balls. </li></ul></ul><ul><ul><li>Other examples: billiards (pool), air hockey, pedestrian hit by car </li></ul></ul>