Chapter 3

MFMcGraw Revised 1/25/2010

Chapter 3

Linear Motion


Linear MotionMotion is RelativeSpeed

Instantaneous SpeedAverage Speed

VelocityConstant VelocityChanging Velocity

AccelerationAcceleration on Galileo’s Inclined

PlanesFree Fall

How FastHow FarHow Quickly “How Fast” Changes


This lecture will help you understand:

• Motion Is Relative• Speed : Average and Instantaneous• Velocity• Acceleration• Free Fall


Motion Is RelativeMotion 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.


SpeedGalileo 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 SpeedAverage Speed

distanceSpeed = -------------- time


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.D. 30 km in 2 hours. E. 60 km in 1/2 hour.F. 60 km in 2 hours.

Average SpeedCHECK YOUR NEIGHBOR


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.D. 30 km in 2 hours. E. 60 km in 1/2 hour.F. 60 km in 2 hours.

Average SpeedCHECK YOUR ANSWER

Explanation:Average speed = total distance / timeSo, 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


In what order do the balls arrive?


AnswersAns: C, B, AUntil 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.

L1

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.


Rank the final velocities


AnswersAns: B, A=CUntil 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.


Instantaneous SpeedInstantaneous 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.


Speed and Velocity


Acceleration

Formulated by Galileo based on his experiments with inclined planes.

Rate at which velocity changes over time


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.


AccelerationIn equation form:

change in velocityAcceleration

time interval

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.


An automobile is accelerating when it isA. slowing down to a stop. D. rounding a curve at a steady speed.E. Both of the above.F. Neither of the above.

AccelerationCHECK YOUR NEIGHBOR


An automobile is accelerating when it isA. slowing down to a stop. D. rounding a curve at a steady speed.E. Both of the above.F. Neither of the above.

AccelerationCHECK 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.


AccelerationsAutomotive Acceleration (g)

Event typical car sports car F-1 race car large truck starting 0.3 - 0.5 > 0.9 1.7 < 0.2 braking 0.8 - 1.0 > 1.3 2 ~ 0.6

cornering 0.6 - 1.0 > 2.5 3 ????

Acceleration and the Human Body

a (g) Event 2.9 sneeze 3.5 cough 3.6 crowd jostle 4.1 slap on back 8.1 hop off step 10.1 plop down in chair 60 chest acceleration limit during car crash at 48 km/h with airbag

70 - 100 crash that killed Diana, Princess of Wales, 1997 150 - 200 head acceleration limit during bicycle crash with helmet

Source: Spine, June 1994


Acceleration


AccelerationAcceleration on Galileo’s Inclined Planes

In which case is the ball experincing the largest acceleration?

a.)

b.)

c.)

d.)


Which has decreasing acceleration?

a.) b.) c.)


Which has increasing velocity?

a.) b.) c.)


Free FallFree 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


Gravity

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.

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.


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.

Distance (1/2) x acceleration x time x time


What are their velocities after 1 second?

Remember, velocity has a magnitude and a direction.


Va = 0 m/s; Va = 5 m/s; Va = -7 m/s


SummaryScalar Vector Units

Distance Displacement m

Speed Velocity m/ s (Magn. of Acceleration) Acceleration (m/ s))/ s = m/ s2


Hewitt WarningThe 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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