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Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Physics 121.Tuesday January 22, 2008.

Credit: Brookhaven National Laboratory, NY, USAhttp://www.bnl.gov/bnlweb/history/Omega-minus.asp

The bubble chamber picture of the first omega-minus. An incoming K- meson interacts with a proton in the liquid hydrogen of the bubble chamber and produces an omega-minus, a K0 and a K+ meson which all decay into other particles. Neutral particles which produce no tracks in the chamber are shown by dashed lines. The presence and properties of the neutral particles are established by analysis of the tracks of their charged decay products and application of the laws of conservation of mass and energy.

Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Physics 121.Tuesday January 22, 2008.

• Today's topics:

• Physics 121 website, and homework

• Introduction to PRS

• Chapter 2: Describing One Dimensional Motion:

• Position

• Velocity

• Acceleration

Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Physics 121.Course Information.

• Our web site provides up-to-date course information:

• All course handouts are posted in pdf format on our web site.

• The web site contains links to workshop and laboratory information.

• The web site contains a link to our homework system and homeworksolutions (the solutions are password protected).

• The web site contains links to practice exams and their solutions.

• All lecture presentations, including audio recordings, will beavailable on the web site shortly before or after class.

http://teacher.pas.rochester.edu/phy121/Phy121HomePage.html

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Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Physics 121.Course Information.

• Additional comments:

• Homework set # 0 is now available; it is due on Saturday 1/26 at 8.30am. This set is to make you familiar with WeBWorK and does notcount toward your final grade. Make sure you verify that you can login to WeBWorK.

• Homework set # 1 will be available later this week and is due onSaturday 2/2 at 8.30 am. This set will be the first set that countstowards your final grade.

Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Introduction to the Personal Response System(PRS).

Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Describing motion in one dimension.• There are different ways in which

we can describe the motion of anobject.

• In Chapter 2 we will focus ondescribing motion along astraight line, or one-dimensionalmotion.

• The direction of motion is notlimited to the horizontaldirection, but for example canalso be in the vertical direction(e.g. free fall).

• One dimensional motion can besimply translational but may alsoinclude rotational motion.

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Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Describing motion in one dimension.

• When we limit ourselves to puretranslational motion, we ingeneral can describe the motionin terms of three parameters:

• The position x(t): units m.

• The velocity v(t): units m/s.

• The acceleration a(t): units m/s2.

• To specify the position x of anobject we need to define theorigin (the point where x = 0 m)of our coordinate system.

x < 0 x > 0x = 0

Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Position.

• Two terms often confused in indescribing the motion of anobject are:

• Distance traveled: the totaldistance the object moved duringthe motion from its starting pointto its end point. Note: depends onthe exact path followed and isalways positive.

• Displacement: the change in theposition of an object. Note:depends only on its starting pointand its end point.

Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Position.

• Do we understand position versustime graphs and do we reallyunderstand the differencebetween distance traveled anddisplacement?

• Let’s see: Concept Tests 2.1 and2.2.

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Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Velocity.

• All information about the motionof an object is in principlecontained in the time dependenceof its position x(t).

• Often it is useful to talk about thevelocity v of the object, which isdefined as the ratio of the changein position, Δx, and the change intime Δt.

• The velocity calculated in thismanner is the average velocityover the time interval Δt.

Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Velocity.

• Some remarks about velocity:

• Velocity can be positive and negative. In our choice of coordinatesystem, a positive velocity corresponds to motion towards the right,and negative velocity corresponds to motion towards the left.

• The sign of the velocity is does not depend on the sign of the position.

• The speed and velocity of an object are often confused. The speed ofan objective is the magnitude of the velocity of the object. It is thusalways positive!

Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Velocity.

• When the time interval Δtdecreases, the average velocityapproaches the instantaneousvelocity.

• The velocity of the object isrelated to the slope of the positionversus time graph:

• A positive slope correspond to apositive velocity; a negative slopecorresponds to a negativevelocity.

• When the slope increases, thevelocity increases..

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Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Velocity.

• Understanding velocity. Do youget it?

• Concept Tests 2.3, 2.6, and 2.7

Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Acceleration.

• The acceleration of an object isdefined at the ratio of the changeof the velocity of an object, Δv,and the change in time Δt.

• The acceleration calculated inthis manner is the averageacceleration over the timeinterval Δt.

• The acceleration can be positiveor negative depending on whetherΔv > 0 m/s or Δv < 0 m/s.

Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Acceleration.

• Some remarks about acceleration:

• Acceleration can be positive and negative.

• In our every day life, we often use the term acceleration when wespeed up and deceleration when we slow down. This leads to theassumption that a positive acceleration implies an increase in speedwhile a negative acceleration corresponds to a decrease in speed.THIS IS ABSOLUTELY WRONG!!!!!!!!!

• Negative acceleration implies that Δv < 0 m/s. This can be achievedin a number of different ways:

• If v1 = 30 m/s and v2 = 10 m/s: a reduction in speed!

• If v1 = -10 m/s and v2 = -30 m/s: an increase in speed!

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Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Constant acceleration.

• Many important physics effectsinvolve motion with constantacceleration.

• Constant acceleration implies that

• In this case, the velocity willhave a linear dependence ontime:

a =

dv

dt= constant

v(t) = v0

+ a t

Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Constant acceleration.

• When the velocity of an objecthas a linear dependence on t, theposition of the object will have aquadratic dependence on t:

• An important case of constantacceleration, is the verticalmotion of objects under theinfluence of the gravitationalforce.

x(t) = x

0+ v

0t +

1

2a t

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Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Constant acceleration.

• In order to fully define the motionof an object if we know theacceleration, we need to havemore information:

• We need to know v0, which is thevelocity of the object at time t = 0s.

• We need to know x0, which is theposition of the object at time t = 0s.

• Make sure the signs areconsistent!

a =

dv

dt= constant

v(t) = v0

+ a t

x(t) = x

0+ v

0t +

1

2a t

2

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Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Constant gravitational acceleration.• Objects moving in the vertical

direction close to the surface ofthe earth experience a constantgravitational acceleration due tothe gravitational force betweenthe earth and the object.

• In the absence of other forces,such as the drag force due to theair, all objects will experience thesame acceleration, independent oftheir mass or shape.

• The gravitational acceleration isg  = –9.8 m/s2. The minus signindicated that the acceleration isdirected downwards.

Note: many people set g = 9.8 m/s2 and then use -g to represent the gravitational acceleration.

Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Constant gravitational acceleration.

Note: velocity and acceleration donot have to be directed in the samedirection!

Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

Measuring the gravitational acceleration.

• There are many different ways inwhich we can measure thegravitational acceleration. Inorder to describe vertical motionwe usually use y coordinates.

• Let’s consider an object fallingfrom rest, from the origin of ourcoordinate system.

• The initial conditions are suchthat v0 = 0 m/s and y0 = 0 m.

• We conclude that y/t2 equals g/2and measuring the time requiredto fall a distance y allows us tocalculate g. Let’s do it!

a =

dv

dt= - g

v(t) = v0 - g t

y(t) = y

0+ v

0t -

1

2g t

2

Note: in this format, g is assumed to be the magnitude of the gravitational acceleration.

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Frank L. H. Wolfs Department of Physics and Astronomy, University of Rochester

We are done for today!Please review Chapter 3 before the next class.

Sol 5 Postcard from Mars Credit: Mars Exploration Rover Mission, JPL, NASA