DOC PREVIEW
ROCHESTER PHY 121 - Lecture 4 Notes - Motion in Two Dimensions

This preview shows page 1-2-20-21 out of 21 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 21 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.Tuesday, January 29, 2008.This iswhere yourinstructorgrew up.Schiphol(AmsterdamAirport) = cemetery of ships.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.Tuesday, January 29, 2008.• Topics:• Course announcements• Quiz• Motion in two dimensions:• Projectile motion• Problem-solving strategies• Circular motion• Relative motionFrank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.Course announcements.• Workshops started yesterday (Monday January 28, 2008)• The physics laboratories started yesterday (Monday January28, 2008). You are required to complete all fiveexperiments in order to get a grade for Physics 121. If youcomplete less than five experiments you will get anincomplete (on average 15% of the Physics 121 students getan incomplete as a results of missing laboratoryexperiments).• Homework set # 1 (the first one to count towards your finalgrade) is available and is due on Saturday morning at 8.30am. Let’s have a quick look at using spreadsheets!Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.Course announcements.• There will be no lecture on Thursday January 31.• Anyone who did not take the Diagnostic Test on Tuesday1/22 needs to make up this test on Thursday morning 1/31 at9.40 am in Hoyt (it will take 45 minutes to complete thisDiagnostic Test).Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterPhysics 121.Quiz Lecture 4.• The quiz today will have 4 questions.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterMotion in two dimensions.• When an object moves in twodimensions, we can consider thetwo components of its motionseparately.• For example, in the case ofprojectile motion, thegravitational acceleration onlyinfluences the motion in thevertical direction.• In the absence of an externalforce, there is no acceleration inthe horizontal direction, and thevelocity in that direction is thusconstant.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterMotion in two dimensions:projectile motion.• To study projectile motion wedecompose the motion into itstwo components:• Vertical motion:• Defines how long it will take forthe projectile to hit the ground• Horizontal motion:• During this time interval, thedistance traveled by the projectileist =2v0sin!0gx = v0cos!0( )2v0sin!0g"#$%&'=v02gsin 2!0= RFrank L. H. Wolfs Department of Physics and Astronomy, University of RochesterMotion in two dimensions:projectile motion.• The equation of the range showsthat the range has a maximumwhen sin(2θ) = 1 or θ = 45°.• The range for smaller and largerangles will be smaller.• The difference between forexample the 30° and 60°trajectories shown in the Figure isthe time of flight.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterMotion in two dimensions:projectile motion: problem solving.• Choose your coordinate systemsuch that one of the axes isdirected in the direction of thegravitational acceleration.• Where do you choose the originof your coordinate system?• Determine the initial conditions(e.g. x and y components of thevelocity at time t = 0 s, the x andy positions at time t = 0 s).• Calculate the time to reach theground, tgr.• The displacement in thehorizontal direction is v0tgr.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterMotion in two dimensions:projectile motion: problem solving.• The critical component of mostproblems is the definition of theboundary conditions (forexample, the horizontal andvertical components of theposition and the velocity).• The problems may differ in whatyou are being asked to do (forexample, determine the range ofthe projectile, its time of flight,etc.)Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterMotion in two dimensions:projectile motion: problem solving.• In general you should work with variablesas long as you can.• Consider the trajectory problem shownin the Figure:• Starting point: x0 = 0 m, y0 = h• Starting velocity: vx0 = v0 cos(θ), vy0 = v0 sin(θ)• To calculate the range we first calculate the time t it takes to reach theground (this is just one-dimensional motion in the vertical direction)• The range R is equal to vx0 t = vx0 {vy0 + √( vy02 + 2hg)}/g• Check your units• Now substitute your numbers to get a numerical answer!Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterCircular motion.• The circular motion of an objectwith period T can be described bythe following equations:x(t) = r0 cos(2π t/T)y(t) = r0 sin(2π t/T)• The motion described by theseequations is motion with constantspeed, v0 = 2π r0/T, in a circle ofradius r0.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterCircular motion.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterCircular motion.• The components of the velocityand acceleration can be obtainedby differentiating x(t) and y(t)with respect to time.• This procedure will produce ofcourse the same results as thegraphical analysis.• Important facts to remember:• The acceleration vector pointstowards the center of the circle.• The magnitude of the accelerationis v02/r0.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterRelative motion.• The velocity of an objectmeasured by an observer dependsnot only on the motion of theobject, but also on the motion ofthe observer.• Examples:• Rain appears to fall at angle θwhen the observer is moving inthe horizontal directions.• The relative velocity of twodrivers going at 55 mph in thesame direction is 0 mph.Frank L. H. Wolfs Department of Physics and Astronomy, University of RochesterRelative motion in 1D.• Consider two different observersA and B looking at the same car.• The position observations madeby these observers are related inthe following manner:XCA = XBA + XCB• The velocities of the caraccording to the two


View Full Document

ROCHESTER PHY 121 - Lecture 4 Notes - Motion in Two Dimensions

Download Lecture 4 Notes - Motion in Two Dimensions
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Lecture 4 Notes - Motion in Two Dimensions and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Lecture 4 Notes - Motion in Two Dimensions 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?