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MFMcGrawRevised 1/25/2010 Chapter 3 Linear Motion

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MFMcGrawRevised 1/25/2010 Linear Motion Motion is Relative Speed Instantaneous Speed Average Speed Velocity Constant Velocity Changing Velocity Acceleration Acceleration on Galileo’s Inclined Planes Free Fall How Fast How Far How Quickly “How Fast” Changes

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MFMcGrawRevised 1/25/2010 This lecture will help you understand: Motion Is Relative Speed : Average and Instantaneous Velocity Acceleration Free Fall

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MFMcGrawRevised 1/25/2010 Motion Is Relative Motion of objects is always described as relative to something else. For example: You walk on the road relative to Earth, but Earth is moving relative to the Sun. So your motion relative to the Sun is different from your motion relative to Earth.

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MFMcGrawRevised 1/25/2010 Speed Galileo is believed to be the first person to measure speed For most situations we will be using meters / second and not spend a lot of time with the conversion of units. 100 mi/h = 160 km/h = 44 m/s Distance is always measured relative to something. This makes speeds relative Examples: Speed relative to the road Speed of the earth relative to the sun. Instantaneous Speed Average Speed distance Speed = time

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MFMcGrawRevised 1/25/2010 The average speed of driving 30 km in 1 hour is the same as the average speed of driving A.30 km in 1/2 hour. B.30 km in 2 hours. C.60 km in 1/2 hour. D.60 km in 2 hours. Average Speed CHECK YOUR NEIGHBOR

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MFMcGrawRevised 1/25/2010 The average speed of driving 30 km in 1 hour is the same as the average speed of driving A.30 km in 1/2 hour. B.30 km in 2 hours. C.60 km in 1/2 hour. D.60 km in 2 hours. Average Speed CHECK YOUR ANSWER Explanation: Average speed = total distance / time So, average speed = 30 km / 1 h = 30 km/h. Now, if we drive 60 km in 2 hours: Average speed = 60 km / 2 h = 30 km/h Same

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MFMcGrawRevised 1/25/2010 In what order do the balls arrive?

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MFMcGrawRevised 1/25/2010 Answers Ans: C, B, A Until the balls reach line L 1 their conditions are identical. Each ball travels approximately the same distance. The ball with the largest average velocity will arrive first. L1L1 When a ball drops to a lower level its speed increases. Balls B and C both drop the same vertical distance but C spend more time at this higher velocity and therefore has the higher aveage velocity.

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MFMcGrawRevised 1/25/2010 Rank the final velocities

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MFMcGrawRevised 1/25/2010 Answers Ans: B, A=C Until the balls reach line L 1 their velocities are equal. When a ball drops to a lower level its speed increases. When it rises its velocity slows down. L1L1 Ball A remains at a constant speed. Ball C increases its speed and then reduces it back to the same value as Ball A. Ball B increase its velocity and stays at that value through the end of the race.

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MFMcGrawRevised 1/25/2010 Instantaneous Speed Instantaneous speed is the speed at any instant. Example: –When you ride in your car, you may speed up and slow down. –Your instantaneous speed is given by your speedometer.

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MFMcGrawRevised 1/25/2010 Speed and Velocity

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MFMcGrawRevised 1/25/2010 Acceleration Formulated by Galileo based on his experiments with inclined planes. Rate at which velocity changes over time

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MFMcGrawRevised 1/25/2010 Centripetal Force Magnitude of velocity (speed) is constant. Direction of Vel. is changing Centripetal forces are center seeking forces. They are experienced, for example, when an object travels in a circular motion.

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MFMcGrawRevised 1/25/2010 Acceleration In equation form: Unit of acceleration is unit of velocity / unit of time. Example: You car’s speed right now is 40 km/h. Your car’s speed 5 s later is 45 km/h. Your car’s change in speed is 45 – 40 = 5 km/h. Your car’s acceleration is 5 km/h/5 s = 1 km/h/s.

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MFMcGrawRevised 1/25/2010 An automobile is accelerating when it is A.slowing down to a stop. B.rounding a curve at a steady speed. C.Both of the above. D.Neither of the above. Acceleration CHECK YOUR NEIGHBOR

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MFMcGrawRevised 1/25/2010 An automobile is accelerating when it is A.slowing down to a stop. B.rounding a curve at a steady speed. C.Both of the above. D.Neither of the above. Acceleration CHECK YOUR ANSWER Explanation: Change in speed (increase or decrease) is acceleration, so slowing is acceleration. Change in direction is acceleration (even if speed stays the same), so rounding a curve is acceleration.

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MFMcGrawRevised 1/25/2010 Accelerations

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MFMcGrawRevised 1/25/2010 Acceleration

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MFMcGrawRevised 1/25/2010 Acceleration Acceleration on Galileo’s Inclined Planes In which case is the ball experincing the largest acceleration? a.) b.) c.)d.)

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MFMcGrawRevised 1/25/2010 Which has decreasing acceleration? a.)b.)c.)

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MFMcGrawRevised 1/25/2010 Which has increasing velocity? a.)b.)c.)

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MFMcGrawRevised 1/25/2010 Free Fall How Fast? (Velocity) How Far? (Distance) How Quickly “How Fast” Changes? (Accelerations) Free fall – only the force of gravity is acting on the object

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MFMcGrawRevised 1/25/2010 Gravity Note the symmetry (Use g= 10 m/s 2 ) Note the equal time intervals. Magnitude of the descending velocities are equal to the magnitude of the ascending velocities. Directions of the velocities are OPPOSITE. Same time to go up to peak height as it takes to return to the starting level. Note the symmetry (Use g= 10 m/s 2 ) Note the equal time intervals. Magnitude of the descending velocities are equal to the magnitude of the ascending velocities. Directions of the velocities are OPPOSITE. Same time to go up to peak height as it takes to return to the starting level. Conservative Force of Gravity KE to PE to KE 1/2mv 2 -> mgh -> 1/2mv 2 Just a little look ahead. In terms of final velocity at the end of the motion- Launching up at 30m/s or down at –30m/s yields the same final velocity. Of course total flight time is longer for an up launch than a down launch. In terms of final velocity at the end of the motion- Launching up at 30m/s or down at –30m/s yields the same final velocity. Of course total flight time is longer for an up launch than a down launch.

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MFMcGrawRevised 1/25/2010 Free Fall—How Far? The distance covered by an accelerating object starting from rest is So, under free fall, when acceleration is 10 m/s 2, the distance is 5 m/s after 1 s. 20 m/s after 2 s. 45 m/s after 3 s. And so on.

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MFMcGrawRevised 1/25/2010 What are their velocities after 1 second? Remember, velocity has a magnitude and a direction.

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MFMcGrawRevised 1/25/2010 V a = 0 m/s; V a = 5 m/s; V a = -7 m/s

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MFMcGrawRevised 1/25/2010 Summary

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MFMcGrawRevised 1/25/2010 Hewitt Warning The author has a feature called “Next Time Questions.” These are challenging and thought provoking questions but sometimes they can be frustating. One source of this frustration comes from his habit of sometimes including effects that were previously ignored. A second source comes from his use of examples where several forces or effects are carefully balanced and one must predict the affect of upsetting this balance.

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MFMcGrawRevised 1/25/2010 Extra Slides

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