Chapter 3 Linear Motion MFMcGraw Revised 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 MFMcGraw Revised 1/25/2010

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

Average Speed CHECK YOUR NEIGHBOR The average speed of driving 30 km in 1 hour is the same as the average speed of driving 30 km in 1/2 hour. 30 km in 2 hours. 60 km in 1/2 hour. 60 km in 2 hours. MFMcGraw Revised 1/25/2010 6

Average Speed CHECK YOUR ANSWER The average speed of driving 30 km in 1 hour is the same as the average speed of driving 30 km in 1/2 hour. 30 km in 2 hours. 60 km in 1/2 hour. 60 km in 2 hours. Explanation: Average speed = total distance / time So, average speed = 30 km / 1 h = 30 km/h. Same Now, if we drive 60 km in 2 hours: Average speed = 60 km / 2 h = 30 km/h MFMcGraw Revised 1/25/2010 7

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

Answers L1 Ans: C, B, A Until the balls reach line L1 their conditions are identical. Each ball travels approximately the same distance. The ball with the largest average velocity will arrive first. 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. MFMcGraw Revised 1/25/2010

Rank the final velocities MFMcGraw Revised 1/25/2010

Answers Ans: B, A=C Until the balls reach line L1 their velocities are equal. When a ball drops to a lower level its speed increases. When it rises its velocity slows down. L1 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. MFMcGraw Revised 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. MFMcGraw Revised 1/25/2010

Speed and Velocity MFMcGraw Revised 1/25/2010

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

Centripetal Force 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. MFMcGraw Revised 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. MFMcGraw Revised 1/25/2010

Acceleration CHECK YOUR NEIGHBOR An automobile is accelerating when it is slowing down to a stop. rounding a curve at a steady speed. Both of the above. Neither of the above. MFMcGraw Revised 1/25/2010 17

Acceleration CHECK YOUR ANSWER An automobile is accelerating when it is slowing down to a stop. rounding a curve at a steady speed. Both of the above. Neither of the above. 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. Acceleration occurs due to a change in either speed or direction (or both). When a car slows down it changes its speed, so it is accelerating. When a car rounds a curve, although its speed is steady it is accelerating because it is changing direction. MFMcGraw Revised 1/25/2010 18

Accelerations MFMcGraw Revised 1/25/2010

Acceleration MFMcGraw Revised 1/25/2010

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

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

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

Free Fall 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 MFMcGraw Revised 1/25/2010

Gravity 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. Note the symmetry (Use g= 10 m/s2) 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 1/2mv2 -> mgh -> 1/2mv2 Just a little look ahead. MFMcGraw Revised 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/s2, the distance is 5 m/s after 1 s. 20 m/s after 2 s. 45 m/s after 3 s. And so on. MFMcGraw Revised 1/25/2010

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

Va = 0 m/s; Va = 5 m/s; Va = -7 m/s MFMcGraw Revised 1/25/2010

Summary MFMcGraw Revised 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. MFMcGraw Revised 1/25/2010

Extra Slides MFMcGraw Revised 1/25/2010