PHYS 100: Lecture 5. F F ma NEWTON S SECOND LAW. N Mg. Physics 100 Lecture 5, Slide 1

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1 PHYS 100: Lecture 5 NEWTON S SECOND LAW T v N u ma tot i θ Physics 100 Lecture 5, Slide 1

2 usic Who is the Artist? A) David Benoit B) Oscar Peterson C) Thelonius onk D) Dr. John E) ose Allison classics SORRY.. DON T HAVE Y POD TODAY! y theme for today was to have been ardi Gras! Which of the above piano players is most closely associated with New Orleans? Physics 100 Lecture 5, Slide 2

3 How To Learn Lectures Study the Lecture slides after lecture. Ask yourself: What was the Point of the lecture? Try to understand the logic of what was asked. Homework Do nteractive Examples first: Use as much HELP as you need! Do the ollow-ups: they test whether you understand what you just did! Your initial score on the delayed feedback questions is your first indicator of your understanding. f you do not answer those correctly, try to understand why! Discussion Study the solutions after discussion. What was the point of asking those questions? KEYS OR PROBLE SOLVNG AVOD EQUATON HUNTNG THNK RST!! What concepts apply to the problem? What are the relevant variables? Which are known? Which are unknown? Develop a plan (first in English) Write down equations for relevant variables Solve Physics 100 Lecture 5, Slide 3

4 THE BG DEAS NOTE: THE BG DEAS ARE ALWAYS GVEN THE LAST SLDE 1. An object accelerates only when the total force on it is non-zero. 2. The weight of an object is always equal to 3. The Normal orce and Tension forces must be determined from ma Physics 100 Lecture 5, Slide 4

5 Thrown Ball A ball is thrown straight up in the air. Take up to be the positive direction What are the velocity (v) and acceleration (a) of the ball at its highest point? (A) v 0 a > 0 (B) v 0 a < 0 (C) v 0 a 0 (D) v 0 a 0 (E) v 0 a 0 + v Just before the ball reaches its highest point: what is its velocity? v 1 Just after the ball reaches its highest point: what is its velocity? v 2 Just as the ball reaches its highest point: what is its velocity? v 0 Just as the ball reaches its highest point: what is its acceleration? dv a a v v dt 2 v 1 v 2 -v 1 a + Physics 100 Lecture 5, Slide 5

6 A ball is thrown straight up in the air. CheckPoint 1 How many forces are acting on the ball at its highest point? (A) 0 (B) 1 (C) 2 (D) 3 (E) Greater than 3 You said: The ball is not moving at its highest point so there are no forces acting on the ball at that moment. weight is the only force acting on the ball the gravitational force and the force exerted to throw it into the air We know a g throughout the flight of the ball! The net force at all times then must be given by: ma mg (the weight!!) A B C D E Physics 100 Lecture 5, Slide 6

7 Pulling a block n both cases shown, forces of equal magnitude,, are exerted on identical blocks supported by a frictionless floor. n Case, the force is applied at an angle θ wrt horizontal while in Case, the force is applied horizontally. Compare a to a : (A) a < a θ (B) a a Case Case (C) a > a WHAT DO YOU KNOW?? WHAT DO YOU DO RST? Draw ree Body Diagram!! tot i ma θ i) Σ xi ma x ii) Σ yi ma y APPLY NEWTON S SECOND LAW N HORZONTAL DRECTON cosθ a a cosθ a a cosθ a a Physics 100 Lecture 5, Slide 7

8 Pulling a block n both cases shown, forces of equal magnitude,, are exerted on identical blocks supported by a frictionless floor. n Case, the force is applied at an angle θ wrt horizontal while in Case, the force is applied horizontally. Compare to : (A) < N θ (B) Case Case (C) > WHAT DO YOU KNOW?? tot i ma WHAT DO YOU DO RST? Draw ree Body Diagram!! θ APPLY NEWTON S SECOND LAW N VERTCAL DRECTON sinθ + N sinθ N N sinθ Physics 100 Lecture 5, Slide 8

9 CheckPoint 2 n both cases shown, forces of equal magnitude,, are exerted on identical blocks. The forces are directed parallel to the frictionless surfaces Compare a to a : (A) (B) (C) a < a a a a > a You said: Case 1 has gravity acting against it at angle theta while case 2 is acting at a 90 degree angle. n case 1 part of the force is used to counteract that of gravity while case 2 all of the force is used to move the box Acceleration orce/mass, so since the blocks have the same mass and each block has the same force acting upon it, the acceleration is equal. t takes a greater acceleration to push the object up a incline than to push it straight across a surface A B C Physics 100 Lecture 5, Slide 9

10 CheckPoint 2 n both cases shown, forces of equal magnitude,, are exerted on identical blocks. The forces are directed parallel to the frictionless surfaces Compare a to a : (A) (B) (C) a < a a a a > a WHAT DO YOU DO RST? Draw ree Body Diagram!! Same kind of forces, but differences in orientation will cause differences in magnitude! APPLY NEWTON S SECOND LAW N DRECTON O ACCELERATON θ sinθ a g sinθ a a a y a a a g sinθ Physics 100 Lecture 5, Slide 10 x

11 ollow-up n both cases shown, forces of equal magnitude,, are exerted on identical blocks. The forces are directed parallel to the frictionless surfaces Compare to : (A) (B) (C) < > WHAT DO YOU DO RST? Draw ree Body Diagram!! θ APPLY NEWTON S SECOND LAW PERPENDCULAR TO THE PLANE cos θ 0 cosθ 0 N N cosθ Physics 100 Lecture 5, Slide 11

12 Elevators Both elevators shown carry identical crates and are moving down. n Case, the elevator is moving at constant velocity v, while in Case the elevator is moving at constant velocity 2v. Compare to : 2v (A) < (B) (C) > WHAT DO YOU DO RST? Draw ree Body Diagram!! 2v APPLY NEWTON S SECOND LAW N VERTCAL DRECTON (a 0!!) 0 0 N N Physics 100 Lecture 5, Slide 12

13 CheckPoint 3 Both elevators shown carry identical crates and are moving down. n Case, the elevator is slowing down, while in Case the elevator is speeding up. Compare to : (A) < (B) (C) > You said: The acceleration is positive in case two where it is negative in case one, the overall force of case two is greater. would say the normal forces are equal in both cases because its pushing against identical crates. N1 has more force opposing the fall, this is why it is slowing down. N2 has less force opposing the fall, this is why it speeds up A B C Physics 100 Lecture 5, Slide 13

14 CheckPoint 3 Both elevators shown carry identical crates and are moving down. n Case, the elevator is slowing down, while in Case the elevator is speeding up. Compare to : (A) < (B) (C) > WHAT DO YOU DO RST? Draw ree Body Diagram!! WHAT S ACCELERATON?? a a APPLY NEWTON S SECOND LAW N VERTCAL DRECTON (take direction of a to be positive) N a a N ( g + a ) N ( g a ) N > N Physics 100 Lecture 5, Slide 14

15 ollow Up Both elevators shown carry identical crates and are moving up. n Case, the elevator is slowing down, while in Case the elevator is speeding up. Compare to : v v (A) < (B) (C) > WHAT DO YOU DO RST? Draw ree Body Diagram!! v v WHAT S ACCELERATON?? a a APPLY NEWTON S SECOND LAW N VERTCAL DRECTON (take direction of a to be positive) N N a N a g a ) N g + a ) ( N < ( N Physics 100 Lecture 5, Slide 15

16 CheckPoint 4 n both cases shown identical signs are suspended from the ceiling. One string is used in Case, while two strings, each making an angle of θ 20 o with the horizontal, are used in Case. Compare T to T L : (A) T < T L (B) T T L (C) T > T L You said: n case, the tension equals to the mass of the object (except the signs are different). n case, the x and the y components of the tensions have to be considered in order to find the value of TL or TR. LET S DO THE EXPERENT!! The similarity in angles calls for the tension to be equal. the sum of TL and TR will equal T since both cases are at equilibrium, therefore T must be greater than TL A B C Physics 100 Lecture 5, Slide 16

17 CheckPoint 4 n both cases shown identical signs are suspended from the ceiling. One string is used in Case, while two strings, each making an angle of θ 20 o with the horizontal, are used in Case. Compare T to T L : (A) T < T L (B) T T L (C) T > T L WHAT DO YOU DO RST? Draw ree Body Diagram!! T APPLY NEWTON S SECOND LAW N VERTCAL DRECTON (Symmetry of Case insures a x 0) (i.e., T L T R ) T T L T 2sinθ 2T L sinθ T L 2sinθ T L > T if sinθ < 1/2 i.e., θ < 30 o Physics 100 Lecture 5, Slide 17