New Topic PHYS 11: Pg 2

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2 New Topic PHYS 11: Pg 2

3 Instantaneous velocity is the slope of the position-vs-time curve PHYS 11: Pg 3

4 Displacement (not position!) is the area under the velocity-vs-time curve How would I calculate the average speed between tf and ti? PHYS 11: Pg 4

5 Acceleration vs velocity is similar to velocity vs position PHYS 11: Pg 5

6 Sketch the velocity graph associated with this acceleration graph: Assuming that the initial velocity is zero, how far does the object travel? Write an equation for the position as a function of time: Between t = 0 and 1 s Between t = 1 and 2 s Between t = 2 and 3 s PHYS 11: Pg 6

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11 Upload to your page and tag with phys21bio does this matches your FB persona? Go to phys21bio wall and upload directly only friends of phys21bio can view your postings (unless you tag yourself on the image). your images to fast, easy, can do this right in class, from your cellphone. Fill in the subject line (can be as long as you like) This will be the figure caption. Nothing you put in the body will be transmitted. PHYS 11: Pg 11

12 New Topic PHYS 11: Chap. 2, Pg 12

13 Scalars are numbers with units. Vectors have both magnitude and direction In 1-D, we could specify direction with a + or - sign In 2-D or 3-D, we need more than a sign to specify direction To illustrate, consider the position vector in 2 dimensions Philadelphia Washington Phys 11: chap 2, Pg 13

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15 Phys 11: chap 2, Pg 15

16 Tip-to-tail method C = A + B We can arrange the vectors any way we want, as long as we maintain their length and direction! Parallelogram method C = A + B

17 (r x,r y ) r y Components can be expressed as: r x = r cos θ r y = r sin θ θ = arctan (r y / r x ) θ r x

18 Expressing vectors in a coordinate system is a generic method for vector manipulation. The number of component depends on spatial dimension! PHYS 11: Pg 18

19 Components depend on the choice of the coordinate system. Can add vectors graphically (tip to tail) Can also add vectors by adding the components How to choose the coordinate system? the right coordinate makes the problem easier. PHYS 11: Pg 19

20 1) they are perpendicular to each other 2) they are parallel and in the same direction 3) they are parallel but in the opposite direction 4) they are at 45 to each other 5) they can be at any angle to each other

21 Given that A + B = C, and that lal + lbl = lcl, how are vectors A and B oriented with respect to each other? 1) they are perpendicular to each other 2) they are parallel and in the same direction 3) they are parallel but in the opposite direction 4) they are at 45 to each other 5) they can be at any angle to each other The only time vector magnitudes will simply add together is when the direction does not have to be taken into account (i.e. the direction is the same for both vectors). In that case, there is no angle between them to worry about. So vectors A and B must be pointing in the same direction.

22 1) 0 2) 18 3) 37 4) 64 5) 100

23 You are adding vectors of length 20 and 40 units. What is the only possible resultant magnitude that you can obtain out of the following choices?

24 dv/dt = a So how does the velocity vector change? v new = v old + a dt v old + a dt v new PHYS 11: Pg 24

25 Ponderable PHYS 11: Pg 25

26 Help 1. Gather: What s going on here, draw a picture, What physics concepts do you need? 2. Organize: Translate words into physics terms, write down some equations you think you ll need. Decide what is known and unknown in the problem 3. Analyze: Use equations to solve for unknown variable 4. Learn: Insert numbers into solved equations. Does the answer make sense? Why was this problem assigned? 5 Phys 11: chap 2, Pg 26

27 The two masses in the figure slide on frictionless wires. They are connected by a pivoting rigid rod of length L. Prove that v 2x = - v 1y tanθ Phys 11: chap 2, Pg 27

28 A ball is released at a height of 1.0 m on a frictionless 30 slope. At the bottom, it turns smoothly onto a 60 slope going back up. What maximum height does it reach on the right side? Phys 11: chap 2, Pg 28

29 Ball A rolls along a frictionless, horizontal surface at a speed of 1.0 m/s. Ball B is released from rest at the top of a 2.0-m-long, 10 ramp at the exact instant ball A passes by. Will B overtake A before reaching the bottom of the ramp? If so, at what position? (Before doing the mathematics, it s worth sketching position graphs and showing that you re trying to find where the two graphs intersect.) Phys 11: chap 2, Pg 29

30 Bouncing ball Cello bow Walking Phys 11: chap 2, Pg 30