This Week. Next Week

Transcription

1 This Week Errors Lecture (in the lab) Next Week Tutorial and Test 1 (chapters 1 and ) Questions for tutorial 1 Cutnell edition 8 Ch 1: 6 Ch 1: 53 Ch : 10 Ch : 54 Cutnell edition 7 Ch 1: 54 Ch 1: 47 Ch : 8 Ch : 47 1 Chapter : Kinematics in One Dimension Will cover motion in a straight line with constant acceleration: Displacement not always the same as distance travelled Speed, velocity, acceleration Equations of motion in one dimension Free fall under gravity - which way is up? Graphical representation

2 Displacement, average speed, velocity Car starts at x o at time t o, reaches x at time t Average speed = Distance Elapsed time = x x 0 t t 0 Distance travelled = x - x o Displacement,!x =x x 0 Average velocity = Displacement Elapsed time =!x t t 0 3 Displacement and distance not necessarily the same Example: Car travels 50 km to east, then 0 km to west in 1 hour. Distance travelled = = 70 km Average speed = 70 km/h 30 km 0 km 50 km Displacement = 30 km to the east Average velocity = 30 km/h to east 4

3 Example: A car makes a trip due north for 3/4 of the time and due south for 1/4 of the time. The average northward velocity has a magnitude of 7 m/s. The average southward velocity has a magnitude of 17 m/s. What is the average velocity for the entire trip? Put T = time for the entire trip. x 1 = (3T/4) x (7 m/s) x = (T/4) x (17 m/s) Average velocity = Displacement/Time Net displacement = (x 1 x )/T, to the north = 3! 7/4 17/4 m/s = 16 m/s, to the north 5 Clicker Questions: Focus on Concepts, Question Three runners start at the same place. Shaun runs 4.0 km due east and then runs 1.0 km due west. Mark runs 3.0 km due east. Jeff runs.0 km due west and then runs 5.0 km due east. Which of the following is true concerning the displacement of each runner? A) Shaun s displacement equals Mark s displacement, but Jeff s displacement is different. B) Shaun, Mark, and Jeff have the same displacements. C) Shaun s displacement equals Jeff s displacement, but Mark s displacement is different. D) Shaun, Mark, and Jeff have different displacements. E) Mark s displacement equals Jeff s displacement, but Shaun s displacement is different. Answer B) 6

4 Clicker Question: Focus on Concepts, Question 4 A cyclist races around a circular track and covers the same number of metres per second everywhere. Which one of the following is true? A) Neither the speed nor the velocity of the cyclist is constant. B) The velocity of the cyclist is constant. C) The speed of the cyclist is constant. D) The speed and the velocity of the cyclist are constant. Hint: velocity has a magnitude (speed) and a direction Answer C) 7 Clicker Question: Focus on Concepts, Question 5 A boat moves 3.0 km due north and then moves 1.0 km due south. The time for this trip is half an hour. What is the average velocity of the boat? A) 8.0 km/h B).0 km/h, due south C) 4.0 km/h, due north D) 4.0 km/h E) 8.0 km/h, due north Answer C) 8

5 Instantaneous Velocity The velocity measured during a vanishingly small time interval. That is, the velocity at a particular instant in time.!x v = lim!t 0!t This differs from the average velocity because the average is measured over an extended time during which the object may be changing velocity. 9 Acceleration Average acceleration = Change in velocity Elapsed time!v Instantaneous acceleration = lim!t 0!t = v v 0 t t 0 Any change of velocity, including slowing down, is an acceleration. 10

6 Average acceleration ā = 9 0 = 9 km/h per second 1 0 = 9000 =.5 m/s 3600 ā = = 9 km/h per second 11 Clicker Question: Focus on Concepts, Question 6 The velocity of a train is 80.0 km/h, due west. One and a half hours later its velocity is 65.0 km/h, due west. What is the train s average acceleration? A) 43.3 km/h, due east B) 53.3 km/h, due east C) 10.0 km/h, due east D) 10.0 km/h, due west E) 43.3 km/h, due west Answer C) 1

7 Two cars are moving in a straight section of a highway. The acceleration of the first car is greater than the acceleration of the second car and both accelerations have the same direction. Which one of the following is true? Clicker Question a) The velocity of the first car is always greater than the velocity of the second car. b) The velocity of the second car is always greater than the velocity of the first car. c) In the same time interval, the velocity of the first car changes by a greater amount than the velocity of the second car. d) In the same time interval, the velocity of the second car changes by a greater amount than the velocity of the first car. Answer C) 13 Equations of Motion Consider an object that has speed v 0 at time t = 0. It is accelerated in a straight line at a constant rate to speed v at time t. Acceleration: a = v v 0, so v = v 0 + at (1) t Average speed: v = x x 0 t = v + v 0 = v 0 + at + v 0 x x 0 = v 0 t + 1 at () 14

8 From previous page: v = x x 0 t = v + v 0 = v 0 + at + v 0 (1) x x 0 = 1 (v + v 0)t And: v v 0 = at (3) Multiply (v v 0 ) (v + v 0) = at (x x 0) t (3) v + v 0 = x x 0 t v v 0 = a(x x 0 ) (4) 15 The famous four formulae v = v 0 + at x x 0 = v 0 t + 1 at (1) () x x 0 = 1 (v + v 0)t (3) v v 0 = a(x x 0 ) (4) You will definitely need to know these! 16

9 Example: A runner accelerates to a velocity of 5.36 m/s due west in 3 seconds. His average acceleration is m/s, also directed due west. What was his velocity when he began accelerating? Take quantities pointing to the east (right) as positive. So: v 0 =? v = 5.36 m/s a = m/s t = 3s v v 0 = at (1) v 0 = v at = 5.36 ( 0.640) 3 = 3.44 m/s Answer: 3.44 m/s due west. 17 Clicker Question: Focus on Concepts, Question 4 The graph accompanying this problem shows a three-part motion. For each of the three parts, A, B, and C, identify the direction of the motion. A positive velocity denotes motion to the right. A) A left, B right, C right B) A right, B left, C right C) A right, B right, C left D) A right, B left, C left E) A left, B right, C left Answer B) 18

10 Clicker Question A runner runs half the remaining distance to the finish line every ten seconds. She runs in a straight line and does not ever reverse her direction. Does her acceleration have a constant magnitude? Hint Suppose she starts at L from finish, covers a distance L in the first 10 s. Average speed is v 1 = L/10. In the second 10 s, she covers a distance L/. Average speed is v = L/0, and so on.. Average acceleration is (change in speed)/time!is it same from v 1 to v as it is from v to v 3 in the next 10 s? Answer C) a) the acceleration is constant b) the acceleration increases c) the acceleration decreases 19 Example: A car accelerates from rest to a final speed in two stages. Each stage takes the same time T. In stage 1, the car s acceleration is a = 3.0 m/s and ends at speed v 1. At the end of stage, the car is travelling.5 times as fast as at the end of stage 1. The acceleration is a. Question: what is the acceleration during stage? a = 3 m/s a =? v 0 T v 1 T 1 v =.5v 1 Hints: What is v 1 in terms of a and T? What is the final speed in terms of v 1, a and T? 0