Projectile Motion Introduction Section 0 Lecture 1 Slide 1 Lecture 6 Slide 1 INTRODUCTION TO Modern...

Projectile Motion

Introduction Section 0 Lecture 1 Slide 1

Lecture 6 Slide 1

INTRODUCTION TO Modern Physics PHYX 2710

Fall 2004

Physics of Technology—PHYS 1800

Spring 2009

Physics of Technology

PHYS 1800

Lecture 6

Projectile Motion

Projectile Motion


Lecture 6 Slide 2


Fall 2004


Spring 2009

PHYSICS OF TECHNOLOGY Spring 2009 Assignment Sheet

*Homework Handout

Date Day Lecture Chapter Homework Due Jan 5 6 7 9

M T W F*

Class Admin: Intro.Physics Phenomena Problem solving and math Units, Scalars, Vectors, Speed and Velocity

1 App. B, C 1 2

-

Jan 12 14 16

M W F*

Acceleration Free Falling Objects Projectile Motion

2 3 3

1

Jan 19 21 23

M W F*

Martin Luther King Newton’s Laws Mass and Weight

No Class 4 4

2

Jan 26 28 29 30

M W Th F

Motion with Friction Review Test 1 Circular Motion

4 1-4 1-4 5

3

Feb 2 4 6

M W F*

Planetary Motion and Gravity Energy Harmonic Motion

5 6 6

4

Feb 9 11 13

M W F*

Momentum Impulse and Collisions Rotational Motion

7 7 8

5

Feb 16 17 18 19 20

M Tu W H F*

Presidents Day Angular Momentum (Virtual Monday) Review Test 2 Static Fluids, Pressure

No Class 8 5-8 5-8 9

-

Feb 23 25 27

M W F*

Flotation Fluids in Motion Temperature and Heat

9 9 10

6

Mar 2 4 6

M W F*

First Law of Thermodynamics Heat flow and Greenhouse Effect Climate Change

10 10 -

7

Mar 9-13 M-F Spring Break No Classes Mar 16 18 20

M W F*

Heat Engines Power and Refrigeration Electric Charge

11 11 12

8

Mar 23 25 26 27

M W H F*

Electric Fields and Electric Potential Review Test 3 Electric Circuits

12 13 9-12 13

-

Mar 30 Apr 1 3

M W F

Magnetic Force Review Electromagnets Motors and Generators

14 9-12 14

9

Apr 6 8 10

M W F*

Making Waves Sound Waves E-M Waves, Light and Color

15 15 16

10

Apr 13 15 17

M W F*

Mirrors and Reflections Refraction and Lenses Telescopes and Microscopes

17 17 17

11

Apr 20 22 24

M W F

Review Seeing Atoms The really BIG & the really small

1-17 18 (not on test) 21 (not on test)

No test week 12

May 1 F Final Exam: 09:30-11:20am

Projectile Motion


Lecture 6 Slide 3


Fall 2004


Spring 2009


PHYS 1800

Lecture 5

Projectile Motion

Review of Free Fall

Projectile Motion


Lecture 6 Slide 4


Fall 2004


Spring 2009

Describing (Special) Motion

Position—where you are in space (L-meter)

Speed—how fast position is changing with time (LT-1 or m/s)

Acceleration—how fast speed is changing with time (LT-2 or m/s2)

We will focus on a special case of constant acceleration due to gravity, termed FREE FALL.

Projectile Motion


Lecture 6 Slide 5


Fall 2004


Spring 2009

Acceleration

Acceleration is the rate at which velocity changes.– Our bodies don’t feel velocity, if the velocity is constant.– Our bodies feel acceleration.

• A car changing speed or direction.• An elevator speeding up or slowing down.

Acceleration can be either a change in the object’s speed or direction of motion.

t1VV

intervalTime velocityinChange

accelerationAverage 2

2smtVa

In this Chapter acceleration is a constant, a=g=9.8 m/s2

Projectile Motion


Lecture 6 Slide 6


Fall 2004


Spring 2009

Acceleration Due to Gravity

• Earth exerts a gravitational force on objects that is attractive (towards Earth’s surface).

• Near Earth’s surface, this force produces a constant acceleration downward.– To measure this acceleration, we need to slow down the

action.– Galileo was the first to accurately measure this

acceleration due to gravity.– By rolling objects down an inclined plane, he slowed the

motion enough to establish that the gravitational acceleration is uniform, or constant with time.

Projectile Motion


Lecture 6 Slide 7


Fall 2004


Spring 2009


PHYS 1800

Lecture 6

Projectile Motion

Review:Influence of GravityTossing a Ball

Projectile Motion


Lecture 6 Slide 8


Fall 2004


Spring 2009

Tracking a Falling Object

• The distance increases in proportion to the square of the time:

d 1

2at 2

1

210 m/s 1 s 2 5 m

Projectile Motion


Lecture 6 Slide 9


Fall 2004


Spring 2009

Throwing a ball downward

• Let the ball be thrown downward instead of being dropped.– It will have a starting velocity different from zero.– It will reach the ground more rapidly.– It will have a larger velocity when it reaches the ground.

20

0

2

1

222

2222

attvtvv

tvv

d

tvv

tvv

tvv

tvd

t

vvaoratvv

ga

ofoo

ooofofavg

off

Projectile Motion


Lecture 6 Slide 10


Fall 2004


Spring 2009

Beyond Free Fall: Throwing a Ball Upward

What if the ball is thrown upward?Gravitational acceleration is

always directed downward, toward the center of the Earth.

Here, the acceleration is in the opposite direction to the original upward velocity.

Projectile Motion


Lecture 6 Slide 11


Fall 2004


Spring 2009

• Let the initial velocity be 20 m/s upward.– It immediately starts

experiencing a downward acceleration due to gravity, of approximately 10 m/s.

– Every second, the velocity decreases by 10 m/s.

• After 2 s, the ball has reached its highest point.– Its velocity changes direction,

from upward to downward, passing through a value of 0 m/s.

• Now, the downward acceleration increases the downward velocity.

Projectile Motion


Lecture 6 Slide 12


Fall 2004


Spring 2009

What is the ball’s acceleration at the top of

its path (at t=2 s)?

a) zero.b) +10 m/sc) -10 m/sd) +10 m/s2

e) -10 m/s2

Gravity does not “turn off” at the top! The ball’s velocity is still changing, as it changes from going up to going down. For a moment the velocity is zero, but the gravitational acceleration is a constant throughout the path.

Projectile Motion


Lecture 6 Slide 13


Fall 2004


Spring 2009

• The velocity-vs-time plot starts with +20 m/s (upward) at time t=0 and changes at a steady rate of -10 m/s2 (decreasing 10 m/s each second).

• Positive velocities correspond to upward motion; negative velocities correspond to downward motion.

• The slope is constant and negative (for constant downward acceleration).

Projectile Motion


Lecture 6 Slide 14


Fall 2004


Spring 2009


PHYS 1800

Lecture 6

Projectile Motion

Simple Compound Motions—Projectile Motion

Projectile Motion


Lecture 6 Slide 15


Fall 2004


Spring 2009

Does this represent a realistic trajectory?

a) Yes. b) No. c) Maybe.

The coyote would not go straight horizontally, pause, and then fall straight down. There are many examples in movies and on television of unrealistic trajectories.

Can you think of any others?

Projectile Motion


Lecture 6 Slide 16


Fall 2004


Spring 2009

What does the trajectory look like?The acceleration of the horizontal motion is zero (in the absence of air resistance).

The object moves with constant horizontal velocity.It travels equal horizontal distances in equal time intervals.

The acceleration in the vertical direction is constant.

Its vertical velocity increases downward just like the falling ball.In each successive time interval, it falls a greater distance than in the previous time interval.

Projectile Motion


Lecture 6 Slide 17


Fall 2004


Spring 2009

What does the trajectory look like?

The total velocity at any point is found by adding the vertical component of the velocity, at that point, to the horizontal component of the velocity at that point.The horizontal velocity remains constant, because there is no acceleration in that direction.The length of the horizontal velocity vector doesn’t change.The downward (vertical) velocity gets larger and larger, due to the acceleration due to gravity.

Projectile Motion


Lecture 6 Slide 18


Fall 2004


Spring 2009

What does the trajectory look like?

Trajectories for different initial velocities of a ball rolling off a table:

The largest initial velocity is v3.The smallest initial velocity is v1.

The ball travels greater horizontal distances when projected with a larger initial horizontal velocity.

Projectile Motion


Lecture 6 Slide 19


Fall 2004


Spring 2009

Which of these three balls would hit the floor first if all three left the tabletop at the same

time?

a) The ball with initial velocity v1.

b) The ball with initial velocity v2.

c) The ball with initial velocity v3.

d) They would all hit at the same time.

Since all three balls undergo the same downward acceleration, and they all start with a vertical velocity of zero, they would all fall the same distance in the same time!

Projectile Motion


Lecture 6 Slide 20


Fall 2004


Spring 2009

Projectile Motion

• Treating the vertical motion independently of the horizontal motion, and then combining them to find the trajectory, is the secret.– A horizontal glide combines with a vertical plunge to

produce a graceful curve.– The downward gravitational acceleration behaves the

same as for any falling object.– There is no acceleration in the horizontal direction if air

resistance can be ignored.– The projectile moves with constant horizontal velocity

while it is accelerating downward.

Projectile Motion


Lecture 6 Slide 21


Fall 2004


Spring 2009

Hitting a Target

If the rifle is fired directly at the target in a horizontal direction, will the bullet hit the center of the target?

Does the bullet fall during its flight?

Projectile Motion


Lecture 6 Slide 22


Fall 2004


Spring 2009

Hitting a Target

The trajectory depends on the initial velocity. The trajectory depends on the launch angle.

Projectile Motion


Lecture 6 Slide 23


Fall 2004


Spring 2009

Hitting a Target

For the lowest angle, the horizontal velocity is much greater than the initial vertical velocity.The ball does not go very high, so its time

of flight is short.

Projectile Motion


Lecture 6 Slide 24


Fall 2004


Spring 2009

Hitting a Target

For the highest angle, the initial vertical velocity is much greater than the horizontal velocity.The ball goes higher, so its time of flight is

longer, but it does not travel very far horizontally.

Projectile Motion


Lecture 6 Slide 25


Fall 2004


Spring 2009

Hitting a Target

The intermediate angle of 45° divides the initial velocity equally between the vertical and the horizontal.The ball stays in the air longer than at low

angles, but also travels with a greater horizontal velocity than at high angles.

Projectile Motion


Lecture 6 Slide 26


Fall 2004


Spring 2009


Next Lab/Demo: Forces

Thursday 1:30-2:45 ESLC 53

Ch 3

Next Class: Wednesday 10:30-11:20

BUS 318 roomRead Ch 4

Projectile Motion Introduction Section 0 Lecture 1 Slide 1 Lecture 6 Slide 1 INTRODUCTION TO Modern...

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Transcript of Projectile Motion Introduction Section 0 Lecture 1 Slide 1 Lecture 6 Slide 1 INTRODUCTION TO Modern...