1. Physics 101: Lecture 27, Pg 1 More Constant Acceleration and Relative Velocity Physics 101: Lecture 07 Exam I Exam 1 is one week from Monday Today is the last lecture for Exam 1 material No circular motion on exam 1 – different from past years! I will hold a special office hour 10-11 Friday in 235 Loomis

2. Physics 101: Lecture 27, Pg 2 Some Charts

3. Physics 101: Lecture 27, Pg 3 Top Ten Comments… You don’t need to spend as much time explaining basic algebra… …please explain how to do the math equations more. I LOVE PHYSICS!!! CHEERS!!! The quizzes are just so confusing… If you could increase the volume of the microphone that would be GREAT Physics fills me with glee. I enjoy the demonstrations. Nervous for the first exam. Please assign us more practice problems… 7

4. Physics 101: Lecture 27, Pg 4 Extra Problems Ch 2 Problems: 1,5,7,11,13,17,29,49,69 Ch 3 Problems: 5,13,33,47,57,65,67 Ch 4 MC all, Problems: 1, 3,5,9, 17,19,23,25,27,35,41,53,55

5. Physics 101: Lecture 27, Pg 5 Last Time l X and Y directions are Independent! è Position, velocity and acceleration are vectors  F = m a applies in both x and y direction l Projectile Motion è a x = 0 in horizontal direction è a y = g in vertical direction 8

6. Physics 101: Lecture 27, Pg 6 Today l More 2-D Examples l Newton’s 3 rd Law Review l Relative Motion 10

7. Physics 101: Lecture 27, Pg 7 Pulley, Incline and 2 blocks T m2gm2g m1gm1g T N y x A block of mass m 1 = 2.6 kg rests upon a frictionless incline as shown and is connected to mass m 1 via a flexible cord over an ideal pulley. What is the acceleration of block m 1 if m 2 = 2.0 kg? X – direction  F x = m a x : Block 1: T – m 1 g sin(30) = m 1 a 1x T = m 1 g sin(30) + m 1 a 1x y x Y – direction F y = m a y : Block 2: T – m 2 g = m 2 a 2y Note: a 1x = - a 2y Combine T – m 2 g = m 2 a 2y m 1 g sin(30) + m 1 a 1x – m 2 g = m 2 a 2y m 1 g sin(30) + m 1 a 1x – m 2 g = -m 2 a 1x m 1 a 1x +m 2 a 1x = m 2 g - m 1 g sin(30) (m 1 +m 2 ) a 1x = g (m 2 - m 1 sin(30)) 17 1.49 m/s 2

8. Physics 101: Lecture 27, Pg 8 Newton’s Third Law è For every action, there is an equal and opposite reaction. Finger pushes on box F finger  box = force exerted on box by finger F finger  box F box  finger Box pushes on finger F box  finger = force exerted on finger by box Third Law: F box  finger = - F finger  box 17

9. Physics 101: Lecture 27, Pg 9 2) Compare the magnitudes of the acceleration you experience, a A, to the magnitude of the acceleration of the spacecraft, a S, while you are pushing: 1. a A = a S 2. a A > a S 3. a A < a S Newton’s 3 rd Law Suppose you are an astronaut in outer space giving a brief push to a spacecraft whose mass is bigger than your own. 1) Compare the magnitude of the force you exert on the spacecraft, F S, to the magnitude of the force exerted by the spacecraft on you, F A, while you are pushing: 1. F A = F S 2. F A > F S 3. F A < F S correct a=F/m F same  lower mass give larger a Third Law! 20

10. Physics 101: Lecture 27, Pg 10 Newton’s 3 rd Example A rope attached to box 1 is accelerating it to the right at a rate of 3 m/s 2. Friction keeps block 2 on top of block 1 w/o slipping. What is the tension in the rope? M1M1 M2M2 T x y W1W1 N2N2 NTNT f 12 T X-direction: F = ma Block 2: f 21 = m 2 a 2 Block 1: T – f 12 = m 1 a 1 N3L says |f 12 | = |f 21 | Combine: T - m 2 a 2 = m 1 a 1 T = m 1 a 1 + m 2 a 2 = (m 1 +m 2 ) a Same as if had one block M = m 1 +m 2 !!!! 23 f 21 N1N1 W2W2

11. Physics 101: Lecture 27, Pg 11 Relative Velocity You are on a train traveling 40 mph North. If you walk 5 mph toward the front of the train, what is your speed relative to the ground? A) 45 mphB) 40 mphC) 35 mph 40 mph N + 5 mph N = 45 mph N 25 40 5 45

12. Physics 101: Lecture 27, Pg 12 Relative Velocity You are on a train traveling 40 mph North. If you walk 5 mph toward the rear of the train, what is your speed relative to the ground? A) 45 mphB) 40 mphC) 35 mph 40 mph N - 5 mph N = 35 mph N 27 40 5 35

13. Physics 101: Lecture 27, Pg 13 Relative Velocity You are on a train traveling 40 mph North. If you walk 5 mph sideways across the car, what is your speed relative to the ground? A) 40 mph 40 mph N + 5 mph W = 41 mph N 30 40 5

14. Physics 101: Lecture 27, Pg 14 Relative Velocity l Sometimes your velocity is known relative to a reference frame that is moving relative to the earth. è Example 1: A person moving relative to a train, which is moving relative to the ground. è Example 2: a plane moving relative to air, which is then moving relative to the ground. l These velocities are related by vector addition : »v ac is the velocity of the object relative to the ground »v ab is the velocity of the object relative to a moving reference frame »v bc is the velocity of the moving reference frame relative to the ground 32

15. Physics 101: Lecture 27, Pg 15 Tractor Demo 1 Which direction should I point the tractor to get it across the table fastest? A) 30 degrees left B) Straight across C) 30 degrees right 34 1 2 3

16. Physics 101: Lecture 27, Pg 16 Tractor Demo (moving table) l Which direction should I point the tractor to get it across the table fastest? A) 30 degrees left B) Straight across C) 30 degrees right 37 1 2 3

17. Physics 101: Lecture 27, Pg 17 Three swimmers can swim equally fast relative to the water. They have a race to see who can swim across a river in the least time. Relative to the water, Beth (B) swims perpendicular to the flow, Ann (A) swims upstream, and Carly (C) swims downstream. Which swimmer wins the race? A) Ann B) Beth C) Carly Preflight 7.1 correct A B C 39 t = d / v y Ann v y = v cos(  ) Beth v y = v Carly v y = v cos(  ) x y

18. Physics 101: Lecture 27, Pg 18 Three swimmers can swim equally fast relative to the water. They have a race to see who can swim across a river in the least time. Relative to the water, Beth (B) swims perpendicular to the flow, Ann (A) swims upstream, and Carly (C) swims downstream. Who gets across second Ann or Carly? A) Ann B) Same C) Carly ACT A B C 42 t = d / v y Ann v y = v cos(  ) Beth v y = v Carly v y = v cos(  )  x y

19. Physics 101: Lecture 27, Pg 19 What angle should Ann take to get directly to the other side if she can swim 5 mph relative to the water, and the river is flowing at 3 mph? Swimmer Example A B C 48 V Ann,ground = V ann,water +V water,ground x y x-direction 0 = V x,Ann,Water + 3 0 = -V Ann,Water sin(  ) + 3 5 sin(  ) = 3 sin(  ) = 3/5 

20. Physics 101: Lecture 27, Pg 20 A B C x y Think of a swimming pool on a cruise ship When swimming to the other side of the pool, you don’t worry about the motion of the ship ! Demo - bulldozer HW: swimmer

21. Physics 101: Lecture 27, Pg 21 Summary of Concepts l X and Y directions are Independent! è Position, velocity and acceleration are vectors l F = m a applies in both x and y direction l Newton’s 3 rd Law l Relative Motion (Add vector components)