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Your Comments A. Why do keep having prelectures due the day after a test? B. Do we have to go to discussion this week or is it optional? Because some people are saying you don't have to go. C. do physics teachers get mad when they watch Wile E. Coyote and Roadrunner defy physics time after time? The suspended beam problem is confusing, I don't understand what is meant by 'inside the footprint'. My biggest confusion is where to set up the axis of rotation when using torque. Is there a trick to it? When are we going to learn something practical? With chemistry, you can make crystal meth. The whole idea seems vague to me. A few explanations here and there should fix the loose knots Due to my previous minimal participation, my previous test kinda sucked. Therefore, see you in class tomorrow. Oh, by they way, do explain the two signs problem. Preferably with numbers, not purely conceptual. I notice Selen sometimes says "preflight" instead of "prelecture", Are you a pilot? If so, that's awesome! Hey, tall, blonde, tan girl (who usually sits on the right side of the class). My name is xxxx xxxx. I don't know your name, but I think you're very pretty. Mechanics Lecture 18, Slide 1
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Today’s Concepts: a) Static Equilibrium b) Potential Energy & Stability Physics 211 Lecture 18 Mechanics Lecture 18, Slide 2
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Clicker Question A (static) mobile hangs as shown below. The rods are massless and have lengths as indicated. The mass of the ball at the bottom right is 1 kg. What is the total mass of the mobile? A) 4 kg B) 5 kg C) 6 kg D) 7 kg E) 8 kg 1 kg 1 m3 m 1 m2 m Mechanics Lecture 18, Slide 3
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Clicker Question In which of the static cases shown below is the tension in the supporting wire bigger? In both cases M is the same, and the blue strut is massless. A) Case 1 B) Case 2 C) Same Mechanics Lecture 18, Slide 4 M 30 0 L/2 T2T2 Case 2 M 30 0 L T1T1 Case 1
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M L T1T1 d1d1 Balancing Torques It’s the same. Why? Mechanics Lecture 18, Slide 5 M T2T2 d2d2 Case 2 L/2
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CheckPoint In which of the static cases shown below is the tension in the supporting wire bigger? In both cases the red strut has the same mass and length. A) Case 1 B) Case 2 C) Same Mechanics Lecture 18, Slide 6 30 0 L/2 T2T2 Case 2 30 0 T1T1 L M Case 1
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CheckPoint In which of the static cases shown below is the tension in the supporting wire bigger? In both cases the red strut has the same mass and length. A) Case 1 B) Case 2 C) Same A) The level arm is longer. B) Case 2 is closer to the point of rotation. This is like pushing a door from the center. C) The beam is the same length and weight so the tension will be the same regardless of where the rope is.. Mechanics Lecture 18, Slide 7
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CM Mg T1T1 T2T2 T 1 T 2 T Same distance from CM: T Mg/2 So: Mechanics Lecture 18, Slide 8 T 1 T 2 Mg Balance forces: Homework Problem
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Mechanics Lecture 18, Slide 9 Homework Problem
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These are the quantities we want to find: Mechanics Lecture 18, Slide 10 d Mg y x T1T1 M A CM
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What is the moment of inertia of the beam about the rotation axis shown by the blue dot? A) B) C) L Clicker Question Mechanics Lecture 18, Slide 11 d M
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The center of mass of the beam accelerates downward. Use this fact to figure out how T 1 compares to weight of the beam? A) T 1 Mg B) T 1 Mg C) T 1 Mg Clicker Question Mechanics Lecture 18, Slide 12 T1T1 Mg y x A CM d M
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The center of mass of the beam accelerates downward. How is this acceleration related to the angular acceleration of the beam? A) A CM d B) A CM d / C) A CM / d Clicker Question Mechanics Lecture 18, Slide 13 T1T1 Mg y x d M A CM
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Apply Plug this into the expression for T 1 A CM d Use A CM d to find Mechanics Lecture 18, Slide 14 T1T1 Mg y x d M A CM
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Conserve energy: CM demos After the right string is cut, the meterstick swings down to where it is vertical for an instant before it swings back up in the other direction. What is the angular speed when the meter stick is vertical? Mechanics Lecture 18, Slide 15 M y x d T
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y x Applying Mg d A CM 2 d Centripetal acceleration Mechanics Lecture 18, Slide 16 T
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Another HW problem: We will now work out the general case Mechanics Lecture 18, Slide 17
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General Case of a Person on a Ladder Bill (mass m ) is climbing a ladder (length L, mass M ) that leans against a smooth wall (no friction between wall and ladder). A frictional force f between the ladder and the floor keeps it from slipping. The angle between the ladder and the wall is . How does f depend on the angle of the ladder and Bill’s distance up the ladder? L m f y x M Bill Mechanics Lecture 18, Slide 18
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Balance forces: x:F wall f y:N Mg mg Balance torques: Mg mg L/2 f y x N F wall d axis Mechanics Lecture 18, Slide 19
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f d M m Lets try it out Climbing further up the ladder makes it more likely to slip: Making the ladder more vertical makes it less likely to slip: This is the General Expression: Mechanics Lecture 18, Slide 20
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Moving the bottom of the ladder further from the wall makes it more likely to slip: If its just a ladder… Mechanics Lecture 18, Slide 21 “For the ladder example in the prelecture, what if the center of mass of the ladder was not in the middle of the ladder??”
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In the two cases shown below identical ladders are leaning against frictionless walls. In which case is the force of friction between the ladder and the ground the biggest? A) Case 1B) Case 2C) Same CheckPoint Case 1 Case 2 Mechanics Lecture 18, Slide 22
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In the two cases shown below identical ladders are leaning against frictionless walls. In which case is the force of friction between the ladder and the ground the biggest? A) Case 1 B) Case 2 C) Same Case 1Case 2 A) Since case 1 is further down on the wall, it is closer to sliding down. B) more of the weight of the ladder is pressed against the ground in case 2 Mechanics Lecture 18, Slide 23 CheckPoint
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Suppose you hang one end of a beam from the ceiling by a rope and the bottom of the beam rests on a frictionless sheet of ice. The center of mass of the beam is marked with an black spot. Which of the following configurations best represents the equilibrium condition of this setup? A) B) C) Mechanics Lecture 18, Slide 24
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CheckPoint Which of the following configurations best represents the equilibrium condition of this setup? A) B) C) B) CoM is directly beneath point of attachment. C) CM gets as low as it can. Mechanics Lecture 18, Slide 25
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Mechanics Lecture 18, Slide 26 “How come in previous problems that involve finding the maximum acceleration a truck can have before the crate starts to slip doesn't require calculating torque?”
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footprint Stability & Potential Energy Mechanics Lecture 18, Slide 27 I don't understand what is meant by 'inside the footprint'.
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