Physics 1010: The Physics of Everyday Life. TODAY More Acceleration Newton s Second Law Gravity

Transcription

1 Physics 11: The Physics of Everyday Life TODAY More Acceleration Newton s Second Law Gravity 1

2 Help, Office and Tutorial Hours TUTORIALS (G1B75/77/79) Isidoros: 12:32:3 Thursday (same as office hours) Shaun: 1:12:5 Monday Joseph: 4:5: Monday, 2:4: Friday HELP (G1B9) Mark (exams overall):??? Ye (Clickers): 3:5: Friday Yin (Homework): 2:3: Monday and Friday Times may still change, depending on demand 2

3 Review Acceleration is to velocity as velocity is to position Acceleration is Change in velocity divided by elapsed Slope on velocity versus graph Acceleration is proportional to force (F = ma) 3

4 Newton s second law: Force = mass x acceleration F=ma Force and acceleration are both VECTORS Acceleration and force are always IN THE SAME DIRECTION (velocity and force do not have to be) The mass tells us the ratio 4

5 ACCELERATION The car is subjected to a constant force in the direction away from the motion detector. Sketch your predictions for the velocity and acceleration of the cart moving toward the motion detector, slowing down at a steady rate, and then reversing direction and speeding up. (Start your graph after the push that gets the cart moving.) v start Velocity 5 feet 5 Acceleration 5

6 ACCELERATION Sketch your predictions for the velocity and acceleration of the cart moving toward the motion detector, slowing down at a steady rate, and then reversing direction and speeding up. Velocity Acceleration Velocity C A #1 Velocity Acceleration Velocity B D #1 E none of the above Acceleration #1 Acceleration #1 6

7 ACCELERATION The car accelerates always away from the motion detector, even though it initially moves towards the motion detector. v start 5 feet 5 Velocity D #1 A constant force is pointing down the slope (away from the detector) so a constant acceleration is also pointing down the slope (away from detector) Acceleration #1 ANSWER IS D 7

8 Newton s second law: Force = mass x acceleration F=ma Force and acceleration are both VECTORS Acceleration and force are always IN THE SAME DIRECTION (velocity and force do not have to be) The mass tells us the ratio 8

9 From acceleration and velocity we can find the position Acceleration (a) = change in velocity elapsed Velocity = Starting velocity change in velocity Velocity = Starting velocity acceleration x V(t) = v initial at Position = initial position (average velocity) x v average = (v initial v final )/2 = (v initial v initial at)/2 = v initial (1/2) at x = x initial v average t = x initial (v initial (1/2) at) t x(t) = x initial v initial t (1/2) at 2 To succeed in this course you have to be able to do this algebra. 9

10 ACCELERATION For a = 1. m/s 2, plot the distance against for the first two seconds. Assume the body starts from rest at x=. x(t) = x initial v initial t (1/2) at 2 We often leave out the (t), so we write x = x initial v initial t (1/2) at 2 We also often write x initial as x, meaning x(t=) 1

11 ACCELERATION For a = 1. m/s 2, plot the distance against for the first two seconds. Assume the body starts from rest at x=. x = x v t (1/2) at 2 distance distance A B distance distance C D 11

12 We can plot the formula to see what the motion looks like x = x initial v initial t (1/2) at 2 x initial =, a=1; from rest means v initial = x = (1/2) t 2 Table t x x t 12

13 We can plot the formula to see what the motion looks like x = x initial v initial t (1/2) at 2 x initial =, a=1; from rest means v initial = x = (1/2) t 2 Table t x x Answer is A t 13

14 The Formula, Graph, and Physical Motion are all interconnected Graph: shows picture of physical motion in one instant Formula: Relates Position to average velocity Velocity to acceleration Position to acceleration Plotting the formula gives instant visualization of the motion! 14

15 ACCELERATION Sketch Position vs. graph for the car moving towards the motion detector and slowing down at a steady rate. (Velocity and acceleration graphs shown.) Velocity 5 feet 5 Acceleration Position? 15

16 ACCELERATION Sketch Position vs. graph for the car moving towards the motion detector and slowing down at a steady rate. (Velocity and acceleration graphs shown.) Position a) 5 feet Position c) 5 Position b) Position d) 16

17 ACCELERATION Sketch Position vs. graph for the car moving towards the motion detector and slowing down at a steady rate. (Velocity and acceleration graphs shown.) Velocity 5 feet The correct answer is d 5 Acceleration Position d) 17

18 GRAVITY GALILEO Droped balls of different weight from tower of Pisa; balls reach the ground at the same NEWTON Saw apple falling, deduced Universal Law of Gravitation 18

19 GRAVITY F ON CAR What causes the acceleration? There is a net force on the car. SOMETHING is exerting a force on the car Gravity Car accelerates in same direction as net force: F net = mass x acceleration F net = F on car = mass of car x acceleration of car 19

20 We figure out the force of gravity by dropping stuff I drop heavy metal ball and light wooden ball when standing on top of desk. a. the light ball will hit the ground first. b. they will hit the ground together. c. the heavy ball will hit the ground first. d. neither will fall, they will stay suspended in mid air e. they will both fall up and hit the ceiling. 2

21 Dropping stuff I drop heavy metal ball and light foam ball when standing on top of desk. a. the light ball will hit the ground first b. they will hit the ground together c. the heavy ball will hit the ground first. d. neither will fall, they will stay suspended in mid air e. they will both fall up and hit the ceiling. 21

22 Dropping stuff I drop heavy metal ball and light foam ball when standing on top of desk. a. the light ball will hit the ground first b. they will hit the ground together c. the heavy ball will hit the ground first. d. neither will fall, they will stay suspended in mid air e. they will both fall up and hit the ceiling. Gravity must pull harder on larger mass. Metal Foam rubber a gravity F gravity on foam rubber ball F gravity 22

23 Since acceleration is the same, force must be proportional to mass F metal ball = M metal ball x a metal ball F foam ball = M foam ball x a foam ball a foam ball = a metal ball = univeral constant For metal ball, foam ball, anything F gravity = M x a gravity We use g = a gravity On the earth, g = 9.8 m/s 2 23

24 We can calculate the acceleration due to gravity from an experiment Don t forget to choose a positive direction! x = x initial v initial t (1/2) gt 2 v initial = x = x initial (1/2) gt 2 x x initial = (1/2) gt 2 gt 2 = 2(x x initial ) t 2 = 2(x x initial )/g 24

25 After 1s, the ball will have droped by: t 2 = 2(x x initial )/g A B C D 25

26 After 2s, the ball will have droped by: t 2 = 2(x x initial )/g A B C D 26

27 Summary Gravitational force is proportional to mass Gravitational acceleration on earth is downward and 9.8 m/s 2 in magnitude Acceleration = net force/mass 27