Physics 1110: Mechanics Announcements: Tutorials Thursday and Friday in G2B60, G2B75, & G2B77 Students on wait list should attend lectures and tutorials. CAPA assignments are in bins in G2B hallway. No school on Monday in honor of MLK. Web page: http://www.colorado.edu/physics/phys1110/ 1
Thinking about motion Our first project is to observe and think about motion We see many examples of motion in the world around us. We are going to try to break down exactly what we mean by motion. 2
Motion diagram If you imagine filming a long jump and then putting all of the frames together you might get If you imagine doing the same thing while I walk across the stage and then drawing it you might get a motion diagram..... 3
Clicker question 1 Set frequency to BA If instead of walking across the stage I stroll the first half and run the second half (in the same direction as before) what will the motion diagram look like? A. B. C.................. 4
Particle model...... Although a person is an extended object, for now we model everything as a particle. 0 1 2 3 4 5 Looking at the diagram can one tell the direction of motion? We need to label the points to know the order of events (which gives us the direction of motion). 5
Measuring position We have the positions of the professor at 6 different times r 4 0 1 2 3 4 5 To complete this picture we need a coordinate system x A coordinate system needs an origin. This is arbitrary but the starting location is a good choice A coordinate system needs axes. With only 1 dimension, we just need one axis. r r 4 A position vector gives a location relative to the origin One example is the position vector 6
Vectors Vectors have magnitude and direction velocity, acceleration, displacement, force Scalars only have magnitude speed, temperature, mass, volume Vector quantities are indicated by an arrow above them: r Can use arrow to represent direction & magnitude 7
Graphical vector addition C A+ B A B Want to find where and Start with A B A Place the tail of at the tip of : C A+ Draw an arrow from tail of to tip of : This is B Vector subtraction is done by adding the negative. The negative of a vector has the same length but opposite direction. A B A B A B C A+ B A B A + ( B) B A B A 8
Clicker question 2 X, Y, Z Q. Three vectors, are shown. Which answer represents the vector? S X + Y + Z S Set frequency to BA X X Y Y Z Z (A) (B) (C) (D) (E) None of these. 9
Canyon Follow the HOP to the 29 th Street Mall r 0 r 2 r 1 0 Folsom Δr 1 2 Colorado Origin at Duane physics Start at Geology building Down to Arapahoe and then the mall Position vectors for each point Displacement vectors between points Note that r and so 0 + Δr r 1 Δr r 1 r0 Position vectors give the location of points from an origin. Displacement vectors go from a start point to an end point (and so they don t depend on the origin location). 10
Distance versus Displacement Canyon 0 Folsom 1 Δr 2 Colorado The displacement vector between point 0 and point 2 is Δr Since it is a vector, it has a magnitude and direction. We also define the distance as the ground covered by the actual route. r 2 r 0 The distance is a scalar. It does not give a direction. 11
Defining velocity Back to the position of the professor at 6 different times Δ Δ Δ Δ 1 2 r 3 4 r 0 r A displacement vector gives the change in position: This occurs over some time interval: r Δt Δr t f t i Δr x r f r i An object s speed tells how fast it is moving and is a scalar average speed distance traveled time interval of travel An object s velocity tells us the speed and direction of motion average velocity displacement time interval v avg Δr Δt 12
Adding velocity to motion diagrams Note that the velocity vector points in the same direction as the displacement vector. v 0 v 1 v 2 v 3 v 4 Δr Δt If all of the time intervals in a motion diagram are the same (as we have specified so far) then the velocity vector length is proportional to the displacement vector length. So the vectors connecting points are also velocity vectors: The length of the velocity vector tells us the average speed between the two points v avg x 13
Clicker question 3 Set frequency to BA Q. A particle moves from position 1 to position 2 during the time interval Δt. Which vector shows the particle s average velocity? The velocity vector points in the direction of motion (also the direction of the displacement vector) 14
Acceleration Velocity is the rate of change of position: Acceleration is the rate of change of velocity: v 0 v 1 v 2 v 3 v 4 a 0 0 a 1 0 2 Let s figure out acceleration between each velocity pair. v 1 v0 v2 v1 v4 v3 To be more clear write as Δv v avg Δ r Δt a 3 0 Δv v 3 v2 v 3 v 2 0 r f r i t f t i a avg Δ v Δt a Δv Can think of as: v + Δv 2 v 3 v + Δv 2 v 3 v f v i t f t i v 3 v 2 15