Lecture 10Textbook ChaptersExample with pulleySlide 4Another example with a pulleySlide 6Problem recast as 1D motionSlide 8Slide 9Analyzing motion plotsChapter 2Slide 12Chapter 3Slide 14Chapter 4Slide 16Chapter 5Chapter 5 & 6Chapter 6Chapter 7Conceptual ProblemGraphing problemSlide 23Slide 24Sample ProblemSlide 26Slide 27Slide 28Exercise: Newton’s 2nd LawExercise: SolutionAnother question to ponderSlide 32Sample exam problemSlide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Slide 41Slide 42Slide 43RecapPhysics 207: Lecture 9, Pg 1Lecture 10Today:Today: Review sessionAssignment: For Monday, Read through Chapter 8 There will be a reading quiz posted at Mastering Physics.Exam Thursday, Oct. 6th from 7:15-8:45 PM Chapters 1-6,7One 8½ X 11 hand written note sheet and a calculator (for trig.)Physics 207: Lecture 9, Pg 2Textbook ChaptersChapter 1 Concept of MotionChapter 2 1D KinematicsChapter 3 Vector and Coordinate SystemsChapter 4 Dynamics I, Two-dimensional motionChapter 5 Forces and Free Body DiagramsChapter 6 Force and Newton’s 1st and 2nd Laws Chapter 7 Newton’s 3rd Law Exam will reflect most key points (but not all) 25-30% of the exam will be more conceptual 70-75% of the exam is problem solvingPhysics 207: Lecture 9, Pg 3Example with pulleyA mass M is held in place by a force F. Find the tension in each segment of the massless ropes and the magnitude of F. Assume the pulleys are massless and frictionless.•The action of a massless frictionless pulley is to change the direction of a tension.•This is an example of static equilibrium.MT5T4T3T2T1FPhysics 207: Lecture 9, Pg 4Example with pulleyA mass M is held in place by a force F. Find the tension in each segment of the rope and the magnitude of F. Assume the pulleys are massless and frictionless. Assume the rope is massless.•The action of a massless frictionless pulley is to change the direction of a tension.•Here F = T1 = T2 = T3 = T•Equilibrium means F = 0 for x, y & z•For example: y-dir ma = 0 = T2 + T3 – T5 and ma = 0 = T5 – Mg •So T5 = Mg = T2 + T3 = 2 F T = Mg/2 MT5T4T3T2T1FPhysics 207: Lecture 9, Pg 5Another example with a pulleyThree blocks are connected on the table as shown. The table is frictionless & the masses are m1 = 4.0 kg, m2 = 1.0 kg and m3 = 2.0 kg. (A) 3 Free Body Diagramsm1T1m2m3m2gNm3gm1gT3T1Physics 207: Lecture 9, Pg 6Another example with a pulleyThree blocks are connected on the table as shown. The table is frictionless & the masses are m1 = 4.0 kg, m2 = 1.0 kg and m3 = 2.0 kg. (1) m1 a1y= -m1g + T1(2) m2 a2yx= -T1 + T3(3) m3 a3y= -m3g + T3Let a = a1y= a12y= - a3y or m3 a= m3g - T3Add (1) & (2) (m1 +m2)a = -m1g + T3Now add (3)(m1 +m2+m3)a = -m1g + m3 ga = (-m1g + m3 g)/(m1 +m2+m3)= -20 / 7 m/s2 m1T1m2m3m2gNm3gm1gT3T1T1T3Physics 207: Lecture 9, Pg 7Problem recast as 1D motionThree blocks are connected on the table as shown. The center table has a coefficient of kinetic friction of K=0.40, the masses are m1 = 4.0 kg, m2 = 1.0 kg and m3 = 2.0 kg. m1m2m3m2gNm3gm1gT3T1frictionlessfrictionlessm1g > m3g and m1g > (km2g + m3g) and friction opposes motion (starting with v = 0)so ff is to the right and a is to the left (negative)ffPhysics 207: Lecture 9, Pg 8Another example with a pulleyThree blocks are connected on the table as shown. The table has a coefficient of kinetic friction of K=0.40, the masses are m1 = 4.0 kg, m2 = 1.0 kg and m3 = 2.0 kg. (A) FBD (except for friction) (B) So what about friction ?m1T1m2m3m2gNm3gm1gT3T1Physics 207: Lecture 9, Pg 9Problem recast as 1D motionThree blocks are connected on the table as shown. The center table has a coefficient of kinetic friction of K=0.40, the masses are m1 = 4.0 kg, m2 = 1.0 kg and m3 = 2.0 kg. m1m2m3m2gNm3gm1gT3T1frictionlessfrictionlessx-dir: 1. Fx = m2a = k m2g - T1 + T3 m3a = m3g - T3 m1a = m1g + T1 Add all three: (m1 + m2 + m3) a = k m2gm3g – m1g ffT3T1Physics 207: Lecture 9, Pg 10Analyzing motion plotsThe graph is a plot of velocity versus time for an object. Which of the following statements is correct?A The acceleration of the object is zero.B The acceleration of the object is constant.C The acceleration of the object is positive and increasing in magnitude.D The acceleration of the object is negative and decreasing in magnitude.E The acceleration of the object is positive and decreasing in magnitude.VelocityTimePhysics 207: Lecture 9, Pg 11Chapter 2Physics 207: Lecture 9, Pg 12Chapter 2Also average speed and average velocityPhysics 207: Lecture 9, Pg 13Chapter 3Physics 207: Lecture 9, Pg 14Chapter 3Physics 207: Lecture 9, Pg 15Chapter 4Physics 207: Lecture 9, Pg 16Chapter 4Physics 207: Lecture 9, Pg 17Chapter 5Physics 207: Lecture 9, Pg 18Chapter 5 & 6Physics 207: Lecture 9, Pg 19Chapter 6Note: Drag in air is proportional to v2Physics 207: Lecture 9, Pg 20Chapter 7Physics 207: Lecture 9, Pg 21Conceptual ProblemThe pictures below depict cannonballs of identical mass which are launched upwards and forward. The cannonballs are launched at various angles above the horizontal, and with various velocities, but all have the same vertical component of velocity.Physics 207: Lecture 9, Pg 22Graphing problemThe figure shows a plot of velocity vs. time for an object moving along the x-axis. Which of the following statements is true?(A) The average acceleration over the 11.0 second interval is -0.36 m/s2(B) The instantaneous acceleration at t = 5.0 s is -4.0 m/s2 (C) Both A and B are correct.(D) Neither A nor B are correct.Note:x ≠ ½ aavg t2Physics 207: Lecture 9, Pg 23Conceptual ProblemA block is pushed up a 20º ramp by a 15 N force which may be applied either horizontally (P1) or parallel to the ramp (P2). How does the magnitude of the normal force N depend on the direction of P? (A) N will be smaller if P is horizontal than if it is parallel the ramp. (B) N will be larger if P is horizontal than if it is parallel to the ramp. (C) N will be the same in both cases. (D) The answer will depend on the coefficient of friction. 20°Physics 207: Lecture 9, Pg 24Conceptual ProblemA cart on a roller-coaster rolls down the track shown below. As the cart rolls beyond the point shown, what happens to its speed and acceleration in the direction of motion?A. Both decrease.B. The speed decreases, but the acceleration increases.C. Both remain constant.D. The speed increases, but acceleration
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