PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target...

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PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 4

Transcript of PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target...

Page 1: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

PHYSICS 231

INTRODUCTORY PHYSICS I

Lecture 4

Page 2: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

• Scalars vs. Vectors• Vectors A: (Ax, Ay) or |A| & θ

• Addition/Subtraction

• Projectile Motion• X-direction: ax = 0 (vx = constant)• Y-direction: ay=-g• Parabolic trajectory

Main points of last lecture

Page 3: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 3.4a

h

v0

The X-component of v is smallest (in magnitude) at:a) Ab) Bc) Cd) Same at all points

Page 4: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 3.4b

h

v0

The Y-component of v is smallest (in magnitude) at:a) Ab) Bc) Cd) Same at all points

Page 5: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 3.4c

h

v0

The acceleration is smallest (in magnitude) at:a) Ab) Bc) Cd) Same at all points

Page 6: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Range Formula

• Good for when yf = yi

x = vi,xt

y = vi,yt !1

2gt2= 0

t =2vi,y

g

x =2vi,xvi,y

g=2vi

2cos" sin"

g

x =vi2

gsin2"

Page 7: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Range Formula

• Maximum for θ=45°R =vi2

gsin2!

Page 8: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 3.5a

100 m

A softball leaves a bat with aninitial velocity of 31.33 m/s. Whatis the maximum distance one couldexpect the ball to travel?

Page 9: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 3.6

68 m

A cannon hurls a projectile which hits a target located on acliff D=500 m away in the horizontal direction. The cannonis pointed 50 degrees above the horizontal and the muzzlevelocity is 75 m/s. Find the height h of the cliff?

h

v0

Page 10: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Relative velocity

• Velocity always defined relative to reference frame.

Page 11: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 3.7

a) 5 mphb) 1 mph

An airport walkway moves at 3 mph. A man walks ata leisurely pace of 2 mph.

a) If he walks on the walkway in the same directionas the walkway, what is his speed as seen from theground?

b) If he walks on the walkway in the oppositedirection as the walkway, what is his speed as seenfrom the ground?

Page 12: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Relative velocity in 2-d

• Sum velocities as vectors• velocity relative to

ground= velocity relative to medium + velocity of medium.

vbe = vbr + vre

boat wrtriver

river wrtearth

Boat wrtearth

Page 13: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

2 Cases

pointed perpendicularto stream

travels perpendicularto stream

Page 14: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 3.8

An airplane is capable of moving 200 mph instill air. The plane points directly east, but a50 mph wind from the north distorts hiscourse.

What is the resulting ground speed?What direction does the plane fly relative tothe ground?

206.2 mph14.0 deg. south of east

Page 15: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 3.9

An airplane is capable of moving 200 mph in stillair. A wind blows directly from the North at 50mph. The airplane accounts for the wind (bypointing the plane somewhat into the wind) andflies directly east relative to the ground.

What is the plane’s resulting ground speed?In what direction is the nose of the planepointed?

193.6 mph14.5 deg. north of east

Page 16: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Chapter 4

Forces and Motion

Page 17: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

What is a force?

• Usually a push or pull• A Vector

Fundamental Forces:

1. Strong Nuclear2. Electromagnetic3. Weak Nuclear4. Gravity

Page 18: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Newton’s First Law

• If the net force exerted on an object is zero,its velocity remains constant (both magnitudeand direction).

• Objects at rest feel no net force• Objects moving with constant velocity feel no

net force

• No net force means Σ F = 0

Page 19: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Mass

• A measure of the resistance of an object tochanges in its motion due to a force

• Scalar• SI units are kg

Page 20: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Newton’s Second Law

• Acceleration is proportional to net force andinversely proportional to mass.

rF! = m

ra

Page 21: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Units of Force

• SI unit is Newton (N)

• US Customary unit is pound (lb)• 1 N = 0.225 lb

F = ma

1 N = 1kg !m

s2

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Gravitational Force

Weight = magnitude of Gravitational Force on anobject near the surface of the Earth

Galileo:

weight

mass

!

r a = g

" w = mg

• Weight is different on surface of other planets/moons.

• Mass is same everywhere.

Page 23: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Newton’s Third Law

• Single isolated force cannot exist• For every action there is an equal and opposite

reaction• Action and Reaction Forces act on different

objects

Force on “1” due to “2”

rF12= !

rF21

Page 24: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Action-Reaction Pairs

rn = ! "

rn

Fg= !F

g

'

!

r n =r " n =

Fg =

" F g =

Normal force of table holding up TV

Normal force of TV pushing down on table

Weight of TV (attracted to Earth)

Gravitational force on Earth (attracted to TV)

Page 25: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Defining the Object:Free-body Diagram

• Newton’s Law uses theforces acting ON object

• n and Fg act on object• n’ and Fg’ act on other

objects

Ignore rotational motion for now.Treat object as a particle.

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Definition of Equilibrium

rF! = 0

Object is at rest or movingwith constant velocity

Page 27: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 4.1a

A Ford Pinto is parked in a parking lot

There is no net force on the Pinto

A) TrueB) False

Page 28: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 4.1b

A Ford Pinto is parked in a parking lot

The contact (normal) force acting on the Pinto fromthe parking lot surface ______________ .

A) Points upwardsB) Is zeroC) Points downward

Page 29: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 4.1c

A Ford Pinto drives down a highway on the moonat constant velocity (where there is no airresistance)

The Pinto’s acceleration is __________

A) Less than zeroB) Equal to zeroC) Greater than zero

Page 30: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 4.1d

A Ford Pinto drives down a highway on the moonat constant velocity (where there is no airresistance)

The force acting on the Pinto from the contact withthe highway is vertical.

A) TrueB) False

Page 31: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Mechanical Forces

• Gravity• Normal forces• Strings, ropes and Pulleys• Friction• Springs (later)

Page 32: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Rules for Ropes and Pulleys

• Force from rope points AWAY fromobject• (Rope can only pull)

• Magnitude of the force is Tension• Tension is same everywhere in the rope

• Tension does not change when goingover pulley

Approximations: Neglect mass of rope and pulley, neglect friction in pulley

Page 33: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 4.2

I pull a 5 kg mass up with a rope, so that itaccelerates 2 m/s2. What is the tension in the rope?

T = 59 N

Page 34: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 4.3

a) Find accelerationb) Find T, the tension abovethe bowling ballc) Find T3, the tension in therope between the pailsd) Find force ceiling must exerton pulley

a) a = g/6 = 1.635 m/s2

b) T = 57.2 Nc) T3=24.5 Nd) Fpulley=2T = 114.5 N

Page 35: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 4.4a

2) Which statements are correct?Assume the objects are static.

T1 is _____ T2

cos(10o)=0.985 sin(10o)=0.173

A) Less thanB) Equal toC) Greater than

Page 36: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 4.4b

2) Which statements are correct?Assume the objects are static.

T2 is ______ T3

cos(10o)=0.985 sin(10o)=0.173

A) Less thanB) Equal toC) Greater than

Page 37: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 4.4c

2) Which statements are correct?Assume the objects are static.

cos(10o)=0.985 sin(10o)=0.173

A) Less thanB) Equal toC) Greater than

T1 is _____ Mg

Page 38: PHYSICS 231 INTRODUCTORY PHYSICS IExample 3.6 68 m A cannon hurls a projectile which hits a target located on a cliff D=500 m away in the horizontal direction. The cannon is pointed

Example 4.4d

2) Which statements are correct?Assume the objects are static.

T1+T2 is ______ Mg

cos(10o)=0.985 sin(10o)=0.173

A) Less thanB) Equal toC) Greater than