01_MotionA_113

8/3/2019 01_MotionA_113

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Motion ± Part 1

Phys 207: University Physics I Instructor : Dr. Demchenko

Pre-requisites: Math 200 (Calculus I)

Highly Recommended : CPS clicker (register at Blackboard)

Recommended: Physics - Vol. 1 by Knight

Drag Racing

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Motion ± Part 1

Syllabus for PHYS207

Class Work (5% or 0%*) ± 2 lowest dropped

Recitation (5%) ± lowest dropped (Meets in Rm. 2305 in Physics

building at intersection of Grace St. & Laurel St.)

Homework (20%) ± due on Wed by 8 am in LC, lowest dropped

Quizzes (20%)± In-class (Thurs) + LC (due Thurs 8 am), lowest dropped

Laboratory (10%) ± lowest dropped

Mid-term exams (20%) ± in-class, closed-book, no calculator

Final exam (20% or 25%*) ± in-class, closed-book, no calculator

*Grading method #2

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Motion ± Part 1

Frequently Asked Questions

1. If your clicker doesn't work, can you still get credit? (a) yes (b) no

2. Have you used LON-CAPA before? (a) yes (b) no

3. Can you use a calculator on quizzes/exams? (a) yes (b) no

4. Will you be given a formula sheet on quizzes/exams? (a) yes (b) no

5. Is the laboratory r equir ed for this course? (a) yes (b) no

6. Can you under very special circumstances make-up a homework,

quiz, lab, or mid-term exam? (a) yes (b) no

ANY QUESTIONS?

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Motion ± Part 1

Motion - Part 1 (one dimension)

2

Tom TomFred

1o, o,2

a t x v t!

Fred speeds up to right and

Tom runs at constant speed

to left. When do they meet?

Graphical Mathematical

Vectorial ³Motion Diagram´

PictorialVerbal

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Motion ± Part 1

Metric (or SI) System

1 meter = 39.4 inches (~3.3 ft)

or 1 inch = 2.54 cm

Metric system is a ³foreign´ language for many people, but we USE³SI´ or ³le Système Internationale d¶Unités´ in physics!

If you don¶t ³think´ in metric, then you must PRACTICE converting

from metric to ³common´ units EVERY time you see a physics

problem.

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Motion ± Part 1

Velocity in Metric & ³Common´ Units

Notice that a ³quick´ conversion between m/s and mph is to simply

double the metric velocity. The conversion is more accurate if you add

another 10% to your answer.

If you are racing on your bike at 10 m/s, what is your speed in mph?

10 m 3600 s 1 mile× ×s 1 hr 1609

22.4 milm

es/hr ¨ ¸ ¨ ¸ ¨ ¸ !© ¹ © ¹ © ¹ª º ª º ª º

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Motion ± Part 1

Speed Conversions [no calculator]

A ppr oximately how fast is 30 m/s in mph? [format = XX]

The fastest recorded baseball pitch is 101 mph by Lynn Nolan Ryan at

Anaheim Stadium on August 20, 1974. A ppr oximately how fast is this

speed in m/s ? [format = XX]

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Motion ± Part 1

Average Velocity/Speed

An object¶s average velocity v equals its net displacement ( x over atime period (t . (Note: Negative velocity is usually left or down.)

An object¶s speed equals the total distance traveled ( s over (t .

(Note: Speed is NEVER negative.)

avet

vx(

!

(( )

sSpeed ave

t

(!

(ave

t a

v(!

(

How fast?

How fast speeding up

or slowing down?

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Motion ± Part 1

In both cases the truck covers the distance in 10 s.

11 ave

70 m

10 s

7 m s

xv

t

( ! !

(

!

&

&

22 ave 60 m

10 s

6 m s

xvt

(

! !(

!

&

&

Average Velocity Examples

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Motion ± Part 1

Average Velocity vs. Average Speed

If you jog 400 m in 200 s and then run back 100 m in 25 s towards thestarting point, what is your average velocity and average speed?

300 m

22

1.3m

5 s

/save

x

t

v(

! ! !

(

4A

0ve

0rage Sp

1eed 2.2 m/s

00 m

225s

s

t

( ! ! !

(

400 m in 200 s

100 m in 25 s( x = 300 m

0 s

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Motion ± Part 1

Average Velocity Calculation

If you drive 100 km in 1 hour on a straight road and then drive back toyour starting point in 2 hours, what is your average velocity in km/h?

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Motion ± Part 1

Average Velocities of Two Balls The figure shows the positions of two balls as they roll left to right at

1 s intervals (called a motion diagram). The average velocity of ball A

is less than that of ball B:

(a) between 1 & 2 s.

(b) between 1 & 2 s and between 2 & 3 s.

(c) between 2 & 3 s and between 3 & 4 s.

(d) None of the above.

Ball A

Ball B

0 s 1 s 2 s 3 s 4 s

0 s 1 s 2 s 3 s 4 s

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Motion ± Part 1

Acceleration

An object¶s average acceleration a equals its CHANGE in velocity (vover a time period (t .

Be CAREFUL about using your "intuition" for acceleration!

If an object is momentarily stopped, then can you say that itsacceleration is zero?

(a) yes (b) no

avet

v x(

!(

( ) s

Speed avet

(!

(ave

t a

v(!

(

How fast?

How fast speeding up

or slowing down?

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Motion ± Part 1

Directions of Velocity & Acceleration

What happens when the velocity v and acceleration a are in the samedirection? Opposite direction?

(a) Object speeds up (b) Object slows down (c) Object tur ns

What is an example of an object with positive velocity and positiveacceler ation?

Can an object have a northward velocity and southward acceleration?

(a) yes (b) no

Is it possible for an object to have "negative" acceleration whileincr easing in speed? (a) yes (b) no

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Motion ± Part 1

Motion Diagram

Choose the correct scenario for the motion diagram.

(a) Bowling ball falling to the floor.

(b) Mars landing vehicle slowing down during a descent.

(c) Man in a parachute falling at constant speed.

(d) None of the above.

0 s

1 s

2 s

3 s

4 s

5 s

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Motion ± Part 1

Motion of Falling Objects

When a bowling ball and basketball are dropped from the same

height, which of the following statements is true? Assume that there

is no air resistance.

(a) Bowling ball speeds up faster and hits the ground first.

(b) Basketball speeds up faster and hits the ground first.

(c) Both objects hit the ground at the same time.

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Motion ± Part 1

Falling Objects

Falling objects speed up by

9.8 m/s ever y second (or 9.8 m/s2)

(Actually, we will use 10 m/s2 in

this course!)

That means the velocity increases

by ~22 mph after each second!

A fte

r 1 second , how fast is the ca

r falling?

Is the car toon corr ect?

Figur e f r om Tipler

³ It goes f r om zer o to 60 mph

in about 3 seconds.´

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Motion ± Part 1

Vertical Motion of Tossed Ball

When throwing a ball straight up, which of the followingstatements is true about its velocity v and acceleration a at the

highest point (apex) in its path?

(a) v = 0 and a = 0(b) v = 0 and a { 0

(c) v { 0 and a = 0

(d) v { 0 and a { 0

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Motion ± Part 1

Vertical Motion of Tossed Ball #2 What are the directions of the ball¶s velocities just befor e and after

reaching the apex?

(a) Up & Up

(b) Down & Down

(c) Up & Down(d) Down & Up

What is the direction of the ball¶s acceleration at the apex?

(a) Up (b) Down (c) Zero

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Motion ± Part 1

Vertical Motion of Ball Thrown Downward

A ball is thrown downwards from a tall building at 5 m/s.

Which statement is TRUE after it is released?

(a) It speeds up by more than 10 m/s every second.

(b) It speeds up by less than 10 m/s every second.(c) It speeds up by 10 m/s every second.

(d) It speeds up by more than 10 m/s in the first second (after

being released) and by 10 m/s each second after that.

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Motion ± Part 1

Vertical Motion of Ball Thrown Downward

A ball is thrown straight down from a tall building at an initialspeed of 5 m/s. (assume no air resistance)

How fast is it traveling at 4 s?

What is its average speed during the 4 s?

How far did it travel during the 4 s?

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Motion ± Part 1

Vertical Motion of Rocket Launched Upward

At time t = 0 a rocket is shot upward from the ground with an initial

velocity of 30 m/s.

How long does it take to reach its greatest height (apex)?

What is the greatest height reached by the rocket?

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Motion ± Part 1

GRAPH of Horizontal Motion Which position-versus-time graph represents the motion shown in the

motion diagram? (assume positive to right and negative to left)

4 s 3 s 2 s 1 s 0 s

0 x (m)

+x ±x

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Motion ± Part 1

Average Velocity

Ave. velocity = SLOPE of

line connecting points

vave23 s2 s1 s0 s

x (m)9 m4 m1 m0 m

1 2 3

t (s)1

9

4

x (m)

vave2

ave t v

x(

! (

2

4 m 1 m

2 s 1 s3 m/savev

! !

What is aver age acceler ation?

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Motion ± Part 1

Instantaneous Velocity

Instantaneous velocity

= SLOPE of tangent

v2

3 s2 s1 s0 s

x (m)9 m4 m1 m0 m

( )t

a t dv

d !

( )t

v t dx

d !

2s( ) 2 2 s 4 m/sv t ! ! !

1 2 3t (s)

1

9

4

x (m)

2

2m

m/s

m/s

2

2

a t

t

t

t

x t

v

!

!

!

v2

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Motion ± Part 1

GRAPHS of x, v, a

Graphs for object with initial position at origin, zero initial velocity,

and constant positive acceleration.

Use calculus to generate graphs by taking derivative (moving to right)

or integrating (moving to left).

t

Take Derivative Integrate

t t

( ) t v t

dx

d ! ( )

t a t

dv

d !

2m x t !

m/s2 v t !

2m/s2 a !

x v a

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Motion ± Part 1

Position and Velocity Graphs

Which velocity-versus-time graph corresponds to the position-versus-

time graph on the left?

(a) (b) (c) (d)

(e) None of the above.

x v v v v

t

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Motion ± Part 1

Acceleration and Velocity Graphs

Which velocity-versus-time graph corresponds to the acceleration-

versus-time graph on the left?

(a) (b) (c) (d)

(e) None of the above.

a v v v v

t

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Motion ± Part 1

Horizontal Acceleration on Incline

The ball rolls up the ramp, and then back down. Which is the correctacceleration graph for horizontal motion? (assume positive x to right)

(b) (c) (d) (e)

a

t

(a)

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Motion ± Part 1

a

v

x

Graphs of Ball¶s Motion

Complete the x, v, a graphs

corresponding to the motion

of the ball shown above.

v

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Motion ± Part 1

Review Graphs of x, v, a

Acceleration = d 2 x/dt 2Velocity = dx/dt Position x

t

x t v

t a

a > 0

a = 0

a < 0

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Motion ± Part 1

Horizontal Acceleration on Incline - AGAIN!

The ball rolls up the ramp, and then back down. Which is the correctacceleration graph for horizontal motion? (assume positive x to right)

(b) (c) (d) (e)

a

t

(a)

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Motion ± Part 1

FORMULAS for 1D Motion (Uniform Acceleration)

0

0 0

212

ave

a

v at

x t x v t at

or

a t

x v

v t

t

!

!

!

( !

TakeDerivative Integrate

( )t

v t dx

d !

( )

t

a t dv

d

!

2

1

t

t

t d v at t ! ´

2

1

t

t x t v t dt !

´

0

22(see Appendix)Eliminate time: 2a x v v( !

0 0at 0; at 0 x x t v v t ! ! ! !

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Motion ± Part 1

Stopping Distance of Car If you brake to stop your car when traveling at 20 m/s, then what is

your stopping TIME if a = ±5 m/s2 ?

What is your stopping DISTANCE?

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Motion ± Part 1

Acceleration of Car

A 1000-kg r acing car is accelerated from rest at a constant rate and

covers a distance of 125 m in 5 s. What is the car¶s acceleration?

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Motion ± Part 1

Example of an Accelerating Car You are driving at a constant velocity and then ³step on it´ at a constant

acceleration of 3 m/s2 after seeing a higher speed limit sign. How far are

you from the sign when you reach 30 m/s after 4 s?

2

0

0

0

0

2

2

12

where 0 m and 3 m/s ,

Solve for : where 4

but v

s 30 m/s

30 m/s 3 m/

is ??

18 ms /4 s s

o oo x t x v t x a

v v t v at v

v t t v a

at ! !

! !

! !

!

!

2

0 0

221 12 2

18 m/s 4 s 3 m/s 96 m4 s x x v t at ! ! !

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Motion ± Part 1

Stopping Distance of Car (again!)

When you are traveling at 30 m/s, how long does it take you to stop if

you slam on the brakes and have an acceleration of ±6 m/s2?

How far did you travel during the stopping time?

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Motion ± Part 1

Example of Falling Brick

The pilot of a helicopter drops a lead brick

from a height of 500 m. How long does ittake to reach the ground? (g~10 m/s2)

Adapted f r om UIUC Physics 111

500 m

0 0 0

0

2 2

2

1 12 2

2 2 500 m

10 m1

/s0 st

x x v t gt x x gt

x x

g

! p !

! ! !

0 0v !

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Motion ± Part 1

Falling Brick, cont.

How fast is the brick moving when it reaches

the ground?

0

2

1000 10 m/s 10 s m/s How fast in mph?

v v gt

v

!

!

!

500 m

00v !

If the brick were dropped from double the height (1 km), instead of

10 s to fall it would take: (assuming no air resistance!)(a) 8 s (b) 14 s (c) 20 s (d) 23.5 s

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Motion ± Part 1

Example of Vertical Rocket Motion

If you shoot a rocket upward with an initial velocity of 40 m/s,

how long does it take to reach the apex and what is that height?

002

40 40 m/s

(from )10 m/

ss

v vt v v at

a

! ! ! !

0 0

22 21 12 2

12

0 m 40 m/s 4 s 10 m/s 4 s

160 m 80 m

OR

80 m

40 m /s + 0 m/s 4 s 80 mave

x x v t at

x v

x

t

! !

! !

( ! ! !

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Motion ± Part 1

Vertical Rocket Motion

What is the total time that the rocket is in the air? (apex time = 4 s)

What is the rocket¶s velocity when it returns to the ground?

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Motion ± Part 1

Appendix: Vertical Motion of Rocket

When is the rocket 50 m above the ground?

0 0

2

2 2

2 2

1

2

1

2

Set 50 m

40 m/s 10 m/s 50 m

5 m/s 40 m/s 50 m 0

x x v t at

t t

t t

! !

!

!

22

Use to solve:

40 40 4 5 504

2 2 5

4 6 4 2.5 1 (going up) or (coming.5 s

Quadrati

6.5 s down)

c Formula

b b act

a

t

s s ! !

! s ! s !

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Motion ± Part 1

Appendix: Motion Formula w/o Time Dependence

Same equation as for Conservation of Energy!!

0

0

0 0

0 0

0 0

0 0 0 0 0

0 0

2

2 22

22

2

12

12

12

1

2

2

v vv v at t

a

x x v t at

v v v v x x v a

a a

a x x v v v v v v v

a x x v v

! !

!

¨ ¸ ¨ ¸! © ¹ © ¹

ª º ª º

!

!

Solve for t

Substitute t

into x(t )

Expression without t 0

222a x v v( !

0

221

2

mgh m v v!

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P 44M ti P t 1

Appendix: Important Length Values

Object meters

Diameter of Nucleus 10 ±15 1 fm

Diameter of Atom 10 ±10 0.1 nm

Paper Thickness (or hair thickness) 0.0001 0.1 mm or 100 Qm

VERY tall person 2 200 cm (6¶ 7´)

Flying Altitude (or Deepest Ocean) 10,000 10 kmEarth Circumference ~4×107 ~40,000 km

Earth to Moon 4×108 400,000 km

Earth to Sun 1.5×1011 150 million km

Radius of solar system 6×1012 6 billion km

To Edge of Visible Universe 1026 10 billion light years

Speed of Light = 3×108 m/s or 300,000 km/s

Light year = 300,000 km/s × (3.15 ×107 s/yr) = 9.5 trillion km

01_MotionA_113

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