Physics 1501: Lecture 3, Pg 1 Physics 1501: Lecture 3 Today’s Agenda l Announcements : çLectures posted on: rcote/rcote

Physics 1501: Lecture 3, Pg 1

Physics 1501: Lecture 3Physics 1501: Lecture 3TodayToday’’s Agendas Agenda

Announcements:Lectures posted on: www.phys.uconn.edu/~rcote/Homeworks 01: Homeworks 01: on MasteringPhysicson MasteringPhysics

Due next Monday at11:00AMDue next Monday at11:00AM

You need to register at MasteringPhysics.comYou need to register at MasteringPhysics.com

Labs START next week (Sept. 12)Labs START next week (Sept. 12)


TodayToday’’s Topic :s Topic :

Finish Chapter 2Review of 1-D motionFree Fall

Strategy for Problem Solving

Begin Chapter 3Review of vectors

» Coordinate systems

» Math with vectors

» Unit vectors


Recap of 1-D motionRecap of 1-D motion

For constant acceleration:

From which we know:


Lecture 3, Lecture 3, Act 1Act 1Motion in One DimensionMotion in One Dimension

When throwing a ball straight up, which of the following is When throwing a ball straight up, which of the following is true about its velocity true about its velocity vv and its acceleration and its acceleration aa at the at the highest point in its path?highest point in its path?

(a)(a) BothBoth v = 0v = 0 andand a = 0a = 0..

(b)(b) v v 0 0, but , but a = 0a = 0..

(c) (c) v = 0v = 0, but , but a a 0 0..

y


Lecture 3, Lecture 3, Act 1Act 1SolutionSolution

x

tv

t

Going up the ball has positive velocity, while coming down Going up the ball has positive velocity, while coming down it has negative velocity. At the top the velocity is it has negative velocity. At the top the velocity is momentarily zero.momentarily zero.

Since the velocity is Since the velocity is

continually changing there mustcontinually changing there must

be some acceleration.be some acceleration. In fact the acceleration is caused In fact the acceleration is caused

by gravity ( by gravity (g = 9.81 g = 9.81 m/sm/s22).). (more on gravity in a few lectures)(more on gravity in a few lectures)

The answer is (c) The answer is (c) v = 0v = 0, but , but a a 0 0..

a

t


Free FallFree Fall

When any object is let go it falls toward the ground !! The force that causes the objects to fall is called gravity.

The acceleration caused by gravity is typically written as g

Any object, be it a baseball or an elephant, experiences the same acceleration (g) when it is dropped, thrown, spit, or hurled, i.e. g is a constant.


Gravity facts:Gravity facts:

g does not depend on the nature of the material!Galileo (1564-1642) figured this out without fancy clocks

& rulers!

demo - feather & penny in vacuum

Nominally, g = 9.81 m/s2 At the equator g = 9.78 m/s2

At the North pole g = 9.83 m/s2

More on gravity in a few lectures!


ProblemProblem:: On a bright sunny day you are walking around

the campus watching one of the many construction sites. To lift a bunch of bricks from a central area, they have brought in a helicopter. As the pilot is leaving, she accidentally releases the bricks when they are 1000 m above the ground. The worker below is getting ready to walk away in 10 seconds. Does he live?


Problem Solution Method:Problem Solution Method:Five Steps: (Similar to IDEA)

1) Focus the Problem- Draw a picture – what are we asking for?

2) Describe the physics- What physics ideas are applicable

- What are the relevant variables known and unknown

3) Plan the solution- What are the relevant physics equations

4) Execute the plan- Solve in terms of variables

- Solve in terms of numbers

5) Evaluate the answer- Are the dimensions and units correct?

- Do the numbers make sense?


Problem:Problem:

1. We need to find the time it takes for the brick to hit the ground.

1000 m


Problem:Problem:

2. Free Fall

Constant acceleration at value g

Choose coordinate system

Variables:h – height of helicopter = 1000 m

g – acceleration due to gravity = 9.81 m/s2

t – time to drop – goal

m – mass of brick – unknown

vo – initial velocity = 0 why?

1000 m

y = 0

y


Problem:Problem:

3. Next write position for constant acceleration:

1000 m

y = 0

y

Realize that v0y = 0

Solve for when y=0

• Why ??


Problem:Problem:

y0 = 1000 m

y

y = 0

Solve for t in symbols:

4. Substitute y=0 and vo=0

Solve for t in numbers:


Problem:Problem:

y0 = 1000 m

y

y = 0

5. Does it make sense?

Units worked out to be ‘s’

That’s correct for time

It takes 14.3 s.

That means that the man escapes !!!


Tips:Tips: Read !

Before you start work on a problem, read the problem statement thoroughly. Make sure you understand what information is given, what is asked for, and the meaning of all the terms used in stating the problem.

Watch your units !Always check the units of your answer, and carry the

units along with your numbers during the calculation.


Coordinate Systems / Chapter 3Coordinate Systems / Chapter 3

In 1 dimension, only 1 kind of system, Linear Coordinates (x) +/-

In 2 dimensions there are two commonly used systems,Cartesian Coordinates (x,y)Circular / polar Coordinates (r,)

In 3 dimensions there are three commonly used systems,Cartesian Coordinates (x,y,z)Cylindrical Coordinates (r,,z)Spherical Coordinates (r,)


Vectors (review):Vectors (review): In 1 dimension, we can specify direction with a + or - sign.

In 2 or 3 dimensions, we need more than a sign to specify the direction of something:

To illustrate this, consider the position vector rr in 2 dimensions.

ExampleExample: Where is Boston? Choose origin at New YorkNew York Choose coordinate system Boston is 212 miles northeast of

New York

or

Boston is 150 miles north and

150 miles east of New York

Boston

New York

r r


Vectors...Vectors... There are two common ways of indicating that

something is a vector quantity:

Boldface notation: AA

“Arrow” notation:

A A =

AA

AA


Vectors: definitionVectors: definition

A vector is composed of a magnitude and a directionexamples: displacement, velocity, accelerationmagnitude of A is designated |A|usually carries units

A vector has no particular position

Two vectors are equal if their directions and magnitudes match.

A

B CA = C

A = B, B = C


Vectors and scalars:Vectors and scalars:

A scalar is an ordinary number.a magnitude without a directionmay have units (kg) or be just a numberusually indicated by a regular letter, no bold face and no

arrow on top.

Note: the lack of specific designation of a scalar can lead to confusion

The product of a vector and a scalar is another vector in the same direction but with modified magnitude.

A BA = -0.75 B


Lecture 3, Lecture 3, ACT 2ACT 2Vectors and ScalarsVectors and Scalars

A) my velocity (3 m/s)

C) my destination (the pub - 100,000 m)

B) my acceleration downhill (30 m/s2)

D) my mass (150 kg)

Which of the following is not a vector ?(For bonus points, which answer has a reasonable

magnitude listed ?)

While I conduct my daily run, several quantities describe my condition


Lecture 3, Lecture 3, ACT 1AnswerAnswer

Which of the following is not a vector ?(For bonus points, which answer has a reasonable

magnitude listed ?)

While I conduct my daily run, severalquantities describe my condition

D) my mass (150 kg)

Answer: There is no way to assign a direction to a mass

Can only be a scalar

A) Velocity has direction (3 m/s east)B) Acceleration has directionC) Destination = position and has a direction ( pub is

100,000 m east of my house).


Lecture 3, Lecture 3, ACT 2ACT 2Bonus AnswerBonus Answer

A) my velocity(3 m/s)

C) my destination (the pub - 100,000 m)

B) my acceleration downhill (30 m/s2)

D) my mass (150 kg)

~ 6 mi/hr or 10 min miles

0 to 60 mi/hr in 1 seconds(3 times g)

100 km is about 60 mi

Pounds are a measure of forceOn the earth’s surface, 1 kg weighs

2.2 lbs150 kg weighs about 330 lbs

Answer = (A)


Converting Coordinate SystemsConverting Coordinate Systems In circular coordinates the vector R = (r,)

In Cartesian the vector R = (rx,ry) = (x,y)

We can convert between the two as follows:

• In cylindrical coordinates, r is the same as the magnitude of the vector

rx = x = r cos

ry = y = r sin

arctan( y / x )

y

x

(x,y)

rrry

rx


Vector addition:Vector addition:

The sum of two vectors is another vector.

A = B + C

B

C A

B

C


Vector subtraction:Vector subtraction:

Vector subtraction can be defined in terms of addition.

B - C

B

C

B

-C

B - C

= B + (-1)C


Unit Vectors:Unit Vectors:

A Unit Vector Unit Vector is a vector having length 1 and no units.

It is used to specify a direction. Unit vector uu points in the direction of UU.

Often denoted with a “hat”: uu = û

UU

û û

x

y

z

ii

jj

kk

Useful examples are the cartesian unit vectors [ i, j, ki, j, k ]

point in the direction of the x, y and z axes.

R = rxi + ryj + rzk


Vector addition using components:Vector addition using components:

Consider CC = AA + BB.

(a) CC = (Ax ii + Ay jj ) + (Bx i i + By jj ) = (Ax + Bx )ii + (Ay + By )jj

(b) CC = (Cx ii + Cy jj )

Comparing components of (a) and (b):

Cx = Ax + Bx

Cy = Ay + By

CC

BxAA

ByBB

Ax

Ay


Lecture 3, Lecture 3, ACT 3ACT 3Vector AdditionVector Addition

Vector A = {0,2,1} Vector B = {3,0,2} Vector C = {1,-4,2}

What is the resultant vector, D, from adding A+B+C?

(a)(a) {3,-4,2}{3,-4,2} (b)(b) {4,-2,5}{4,-2,5} (c)(c) {5,-2,4}{5,-2,4}


Lecture 3, Lecture 3, ACT 3ACT 3SolutionSolution

D = (AXi + AYj + AZk) + (BXi + BYj + BZk) + (CXi + CYj + CZk)

= (AX + BX + CX)i + (AY + BY+ CY)j + (AZ + BZ + CZ)k

= (0 + 3 + 1)i + (2 + 0 - 4)j + (1 + 2 + 2)k

= {4,-2,5}

Answer is (b)

Vector A = {0,2,1} Vector B = {3,0,2} Vector C = {1,-4,2}

Physics 1501: Lecture 3, Pg 1 Physics 1501: Lecture 3 Today’s Agenda l Announcements : çLectures posted on: rcote/rcote

Documents