Mechanics Lecture 4, Slide 1 Classical Mechanics Lecture 4 Homework 3 and Midterm Exam 1 Today's Concepts: Newton’s Laws a) Acceleration is caused by forces b) Force changes momentum c) Forces always come in pairs d) Good reference frames

Homework 3 Mechanics Lecture 4, Slide 2 Average=84.5%

Midterm exam 1 Distribution Mechanics Lecture 4, Slide 3 Average=9.2 Take-home exam due Friday Feb 20 Only need to do problems that were missed! Will receive ¾ credit for corrected problems

Midterm exam 1 Problem Difficulty Mechanics Lecture 4, Slide 4 p01p02p03p04p05p06p07p08p09p10p11p12p13p14p15p16p17p18p19p

Midterm “Take-home” due on Friday Feb 20 Mechanics Lecture 4, Slide 5  Meet with Instructor or TA if desired  Prepare notes/Review before taking exam  Practice solving homework/sample exam problems  Take exam in timed situation  Answer questions that were incorrect:  Letter response in spaces provided.  Written response for each answer.  Brief justification for answer to conceptual questions (1,2,3,7,9,15,20)  Show all steps in responses requiring calculations. State input data and relevant equations. Simulate Real Exam Situation

Course Schedule: February Mechanics Lecture 4, Slide 6

Course Schedule: March Mechanics Lecture 4, Slide 7

Discussion Sections? Mechanics Lecture 4, Slide 8 Enter your available times

Sir Isaac Newton and his 3 Laws Mechanics Lecture 4, Slide 9

Main Points Mechanics Lecture 4, Slide 10

Main Points Mechanics Lecture 4, Slide 11

Main Points Mechanics Lecture 4, Slide 12

Lecture Thoughts Mechanics Lecture 4, Slide 13

Mechanics Lecture 4, Slide 14 Let’s start with Newton’s 2 nd Law

Mechanics Lecture 4, Slide 15 Acceleration is caused by force. A bigger mass makes this harder Newton’s 2 nd Law

Mechanics Lecture 4, Slide 16 Force is a vector. Acceleration vector is parallel to (same direction) as (Net) force vector. Force is a Vector Quantity

Mechanics Lecture 4, Slide 17 Acceleration is caused by force. A bigger mass makes this harder Newton’s 2 nd Law

Pre-lecture Question 1 A. B. C. D. E. Mechanics Lecture 4, Slide 18

Pre-lecture Question 1 Mechanics Lecture 4, Slide 19

Unit of Force Mechanics Lecture 4, Slide 20 Kinematics units Dynamics unit

Momentum Mechanics Lecture 4, Slide 21

Spaceship example Mechanics Lecture 4, Slide 22

Newton’s First law Mechanics Lecture 4, Slide 23

Inertial Reference Frame Mechanics Lecture 4, Slide 24

Newton’s 3 rd Law Mechanics Lecture 4, Slide 25

Newton’s 3 rd Law Mechanics Lecture 4, Slide 26 The motion of an object is affected by only the forces acting upon it.

Prelecture Question 2 A. B. C. D. E. Mechanics Lecture 4, Slide 27

Prelecture Question 2 Mechanics Lecture 4, Slide 28

Checkpoint 1 A. B. C. D. Mechanics Lecture 4, Slide 29 The net force on a box is in the positive x direction. Which of the following statements best describes the motion of the box : A) Its velocity is parallel to the x axis B) Its acceleration parallel to the x axis C) Both its velocity and its acceleration are parallel to the x axis D) Neither its velocity or its acceleration need be parallel to the x axis

Mechanics Lecture 4, Slide 30 B) Net force causes acceleration, but it does not necessarily say anything about the direction of the velocity. CheckPoint The net force on a box is in the positive x direction. Which of the following statements best describes the motion of the box : A) Its velocity is parallel to the x axis B) Its acceleration parallel to the x axis C) Both its velocity and its acceleration are parallel to the x axis D) Neither its velocity or its acceleration need be parallel to the x axis

Force on Two Masses A. B. C. Mechanics Lecture 4, Slide 31 A force F is applied to a small block, that pushes a larger block. The two blocks accelerate to the right. Compare the NET FORCE on the block with mass M, to the net force on the block with mass 5M. A) F M < F 5M B) F M = F 5M C) F M > F 5M M F a 5M5M

Mechanics Lecture 4, Slide 32 Force on Two Masses M F a Net Force Same acceleration, so larger mass has larger net force. 5M5M A force F is applied to a small block, that pushes a larger block. The two blocks accelerate to the right. Compare the NET FORCE on the block with mass M, to the net force on the block with mass 5M. A) F M < F 5M B) F M = F 5M C) F M > F 5M

Mechanics Lecture 4, Slide 33

Mechanics Lecture 4, Slide 34

Checkpoint A. B. C. D. Mechanics Lecture 4, Slide 35 You are driving a car with constant speed around a horizontal circular track. The net force acting on your car A) Points radially inward toward the center of the circular track B) Points radially outward, away from the center of the circular track C) Points forward in the same direction your car is moving D) Points backward, opposite to the direction your car is moving E) Is zero.

Mechanics Lecture 4, Slide 36 CheckPoint

Mechanics Lecture 4, Slide 37 A) Force is in the same direction as acceleration (in this case, centripetal). CheckPoint Responses You are driving a car with constant speed around a horizontal circular track. The net force acting on your car A) Points radically inward toward the center of the circular track B) Points radically outward, away from the center of the circular track C) Points forward in the same direction your car is moving D) Points backward, opposite to the direction your car is moving E) Is zero.

Mechanics Lecture 4, Slide 38 * They can have also have tangential acceleration if their speed is not constant Aside: Centripetal acceleration and force 1) Objects moving in a circle always have a component of acceleration, called centripetal, which is toward the center of the circle.* 2) Centripetal acceleration must be caused by a force:  Friction, gravity – whatever force keeps it moving in a circle.  This force is often called the “centripetal force” 3) There is no “new” kind of force here. 4) There is no such thing as centrifugal force.

Mechanics Lecture 4, Slide 39 Oooomf Momentum

Mechanics Lecture 4, Slide 40 Momentum

Mechanics Lecture 4, Slide 41 Momentum & Force

Checkpoint Momentum Mechanics Lecture 4, Slide 42 You are driving a car with constant speed around a horizontal circular track. The momentum of your car A. B. C. D. E.

Mechanics Lecture 4, Slide 43 C) It points in the same direction as v, which is forward CheckPoint Responses You are driving a car with constant speed around a horizontal circular track. The momentum of your car

Mechanics Lecture 4, Slide 44 Momentum & Centripetal Acceleration

Mechanics Lecture 4, Slide 45 Momentum & Centripetal Acceleration

Mechanics Lecture 4, Slide 46 Ice-puckFake Forces: Coriolis (YouTube) Newton’s 1 st Law

Mechanics Lecture 4, Slide 47 Forces come in pairs! Fire-cart Newton’s 3 rd Law

Mechanics Lecture 4, Slide 48 Newton’s 3 rd Law Concerns I would ask you to briefly explain why when the person is pushing the box does his force on the box not per se cancel with the force the box exerts on him and the box remain motionless? Is not acting on the box

Clicker Question A. B. C. Mechanics Lecture 4, Slide 49 A small guy and a large football player moving at the same speed collide head-on. Which person experiences the larger force during the collision? A) The small guy. B) The football player. C) They experience the same force.

Mechanics Lecture 4, Slide 50

Main Points Mechanics Lecture 4, Slide 51

Main Points Mechanics Lecture 4, Slide 52

Main Points Mechanics Lecture 4, Slide 53

Midterm “Take-home” due on Friday Feb 20 Mechanics Lecture 4, Slide 54  Prepare notes  Meet with Instructor or TA if desired  Take exam in timed situation  Answer questions that were incorrect:  Letter response in spaces provided.  Written response for each answer.  Brief justification for answer to conceptual questions (1,2,3,7,9,15,20)  Show all steps in responses requiring calculations. State input data and relevant equations.

Midterm exam 1 Distribution Mechanics Lecture 4, Slide 55 Average=9.2 Take-home exam due Friday Feb 20 Only need to do problems that were missed! Will receive ¾ credit for corrected problems

Midterm exam 1 Problem Difficulty Mechanics Lecture 4, Slide 56 p01p02p03p04p05p06p07p08p09p10p11p12p13p14p15p16p17p18p19p

Exam Problems Mechanics Lecture 4, Slide 57 26/39 correct 30/39 correct 23/39 correct

Exam Problems Mechanics Lecture 4, Slide 58 23/39 correct

Exam Problems Mechanics Lecture 4, Slide 59 6/39 correct

Exam Problems Mechanics Lecture 4, Slide 60 16/39 correct

Exam Problems Mechanics Lecture 4, Slide 61 15/39 correct 10/39 correct

Exam Problems Mechanics Lecture 4, Slide 62 19/39 correct 13/39 correct

Exam Problems Mechanics Lecture 4, Slide 63 17/39 correct

Exam Problems Mechanics Lecture 4, Slide 64 17/39 correct 11/39 correct

Exam Problems Mechanics Lecture 4, Slide 65 24/39 correct

Exam Problems Mechanics Lecture 4, Slide 66 18/39 correct

Exam Problems Mechanics Lecture 4, Slide 67 11/39 correct 10/39 correct

Exam Problems Mechanics Lecture 4, Slide 68 12/39 correct 31/39 correct

How difficult was the exam overall? A. Most difficult exam that you ever encountered. B. Moderately Difficult C. Fairly Easy D. Easiest Exam that you ever encountered. Mechanics Lecture 4, Slide 69

How much time should we have had to complete all problems? A. 50 minutes B. 75 minutes C. 90 minutes D. 120 minutes Mechanics Lecture 4, Slide 70

Given sufficient time I could have correctly completed “most” of the problems A. True B. False Mechanics Lecture 4, Slide 71

What percentage of the questions were “fair”? A. 100% B. >80% C. >60% D. >30% E. 0% Mechanics Lecture 4, Slide 72