Main points of today s lecture: Example: addition of velocities Trajectories of objects in 2 dimensions: Physic 231 Lecture 5 ( )

Transcription

1 Main points of toda s lecture: Eample: addition of elocities Trajectories of objects in dimensions: Phsic 31 Lecture 5 ( ) t g gt t t gt o 1 1 downwards 9.8 m/s g Δ Δ Δ + Δ

2 Motion under Earth s graitational attraction Near the Earth s surface, all objects are accelerated b grait downwards with an acceleration of g9.8 m/s. g 9.8 m/s downwards gt 1 Δ 1 Δ t gt gδ ( + ) o t A timed drop can proide one measurement of g.

3 Eample 1 At t Luc throws a ball straight upwards with a elocit of 3 m/s. It rises a distance h and then falls downward where Luc catches it. 1) When does the ball stop? ) How high does it go? g 9.8 m/s gt 1 Δ 1 Δ t gt gδ downwards ( + ) o t 3 m/s t? h?

4 Eample At t Luc throws a ball straight upwards with a elocit of 3 m/s. It rises a distance h and then falls downward where Luc catches it. 1) When does the ball return to Luc s hand? ) What is its elocit when Luc catches it? a) 3 m/s b) 6 m/s c) 3 m/s d) 6 m/s g 9.8 m/s gt 1 Δ 1 Δ t gt gδ downwards ( + ) o t 3 m/s Δ t??

5 (m) Trajector of Luc's ball Δt t (s) t ma 1 Δ t gt (t ma +Δt) (t ma -Δt) It takes the same time to go up as down. Smmetries of trajector Δt (m/s) elocit of Luc's ball Δt t (s) t ma Δt gt (t ma +Δt) -(t ma- -Δt) Speed Δt before the maimum is the same as the speed Δt after the maimum height The acceleration remains g because the slope remains g eerwhere!!!

6 Clicker quiz Where does the acceleration anish on this trajector? a) at s b) at 6 s c) at s and 6 s. d) at 3 s e) neer (m) Trajector of Luc's ball Δt Δt t ma t (s)

7 Conceptual Reading Quiz If ou drop an object in the absence of air resistance, it accelerates downward at 9.8 m/s. If instead ou throw it downward, its downward acceleration after release is: a) less than 9.8 m/s. b) 9.8 m/s. c) more than 9.8 m/s. It ain't what ou don't know that gets ou into trouble. It's what ou know for sure that just ain't so. Mark Twain

8 A Reading Quiz What goes in the blank? A is the of the ector a) Magnitude b) - component c) direction d) size e) displacement

9 Two dimensional coordinate sstems 3 1 (, ) ( f, f ) 1 3 An position can be unique epressed in terms of its point (,) on the two dimensional grid. The displacement of a person or object from (, ) to ( f, f ) can be drawn as an arrow. This is the graphical representation of the displacement ector. The length of the ector (arrow) is the distance moed if the displacement is in a straight line. The direction of the ector (arrow) indicates the direction of the displacement.

10 Graphical representation has the displacement ector as an arrow starting at (, ) and ending at ( f, f ). It is defined b its length and direction 3 1 (, ) 1 3 Vector representations ( f, f ) These are all equialent! One can also represent a ector b its components in a Cartesian coordinate sstem. The Cartesian components of the displacement ector are: component: Δr component: Δr Δ Alternatiel, we can write them in terms of the length of the displacement ector and its angle with respect some fied ais, e.g. the ais. It doesn t matter where ou place the ector. Δ Δ θ Δ f f

11 A! A B the Pthagorean theorem, the length of this ector is: A + The angle θ can be obtained from arious trigonometric relations: sin and θ A A ( θ ) ;cos( θ ) tan A A ( θ ) A A More about ectors A A ; A Vector addition: Place the tail of one ector (B) on the head of the other (A). Draw the sum ector (C) from the tail of the first ector to the head of the second. A! C!! B B! A! It doesn t matter which order ou do it. Addition b components: C A +B C A +B

12 Addition of components Consider the addition of two ectors both graphicall and b components.! A C!! B B A C A + B C A + B A B

13 Other ector properties/operations Inerse: -A is drawn in the opposite direction as A. The - component of -A is A and the component is A. Obiousl, RA+ (-A ) A-A, both from the drawing and also b adding components. A! A! Subtracting ectors can be done b subtracting components. If RB-A, then R B -A and R B -A. Graphicall: R! A! A! B!

14 Eample What are the - and -components of this ector? a. 3, -1 b. 3, -4 b. 4,3 d. 4, -3 e. -3, -4