PHY 121 Ch 2 Lecture

# PHY 121 Ch 2 Lecture - How to draw motion diagrams Drawing...

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1 How to draw motion diagrams ! v ! v ! v ! v ! a ! a ! a Drawing good motion diagrams is critical for problem solving in physics. This method is better than the one discussed in your textbook, and we will use it for the rest of the semester. 1. Use dots to indicate the object’s position at equal time intervals. Usually ~10 dots is sufficient. 2. Draw the velocity vector from one dot to the next. 3. Calculate the acceleration vector for every two consecutive velocities, and place it betweeen the velocities. 4. For rectilinear motion offset the acceleration vector a bit for clarity.

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2 One dimensional motion One-dimensional motion is motion along a line x >0 0 x <0 y >0 0 y <0
3 Graphs x 0 8 4 0 -4 Position (m) 12 10 8 6 4 2 0 Time (s)

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4 What is the motion diagram? 120 80 40 0 Position (m) 12 10 8 6 4 2 0 Time (s) x 0
5 What is the motion diagram? x 0 200 150 100 50 0 Position (m) 12 10 8 6 4 2 0 Time (s)

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6 What is the motion diagram? -20 0 20 Position (m) 12 10 8 6 4 2 0 Time (s) x 0
7 Figurative art vs. abstract art • A motion diagram is a figurative representation of motion: it shows reality as in a photograph. • A graph is an abstract representation of motion. It requires interpretation. • If the motion diagram is a curve, the object moves along a curve. • If the graph is a curve, the object might still move along a straight line!

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8 Uniform motion: the graph is a straight line x 0 8 4 0 -4 Position (m) 12 10 8 6 4 2 0 Time (s) Equal displacements in equal times.
9 Average velocity 8 6 4 2 0 -2 -4 s (m) 12 10 8 6 4 2 0 t (s) v av, x = x 2 ! x 1 t 2 ! t 1 = " x " t = 4m 4s = 1 m/s ! x = " 0m ! t = 8s " x

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10 Average velocity is a vector component v av, x = ! x ! t = x 2 " x 1 t 2 " t 1 = ( ! r 2 " ! r 1 ) x t 2 " t 1 The average velocity v av- x is the x -component of the average velocity vector ! v av = ! ! r ! t = ! r 2 " ! r 1 t 2 " t 1 Using this notation Notice that the velocity that appears in motion diagrams is in reality an average velocity between two successive points.
11 Sign of the average velocity •The average velocity is positive if the object is moving in the direction of the + x axis. •The average velocity is negative if the object is moving in the direction of the - x axis. v av, x = ! x ! t = x 2 " x 1 t 2 " t 1 = ( ! r 2 " ! r 1 ) x t 2 " t 1

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12 Negative average velocity v av, x = x 2 ! x 1 t 2 ! t 1 = " x " t = ! 4m 4s = ! 1 m/s ! x = " 14m " ( " 10m) ! t = 10s " 6s -16 -14 -12 -10 -8 -6 -4 s (m) 12 10 8 6 4 2 0 t (s) x
13 Average velocity in uniform motion The average velocity is always the same, independent of the times t 1 and t 2 . 8 6 4 2 0 -2 -4 s (m) 12 10 8 6 4 2 0 t (s) x

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14 Average velocity in accelerated motion The average velocity depends on the times t 1 and t 2 . 140 120 100 80 60 40 20 0 s (m) 12 10 8 6 4 2 0 t (s) x
15 “At” versus “between” quantities • Position is an “at” quantity: we talk about the position of an object at a particular time t. • Average velocity is a “between” quantity, for we say: “what is the average velocity between times t 1 and t 2 ?

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16 Velocity as an “at” quantity • It would be nice to define a velocity at a particular time t . This would help us understand statements such as “when throwing a ball upwards, the velocity is zero at the highest point”.
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