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Phys. 121: Tuesday, 09 Sep. ● Reading: finish ch. 6 by Thursday. ● Written HW 3: Due Thursday. ● Mastering Phys.: Second assignment is due tonight. Third assignment due in one week. ● Office hours (tentative): Mon. 10-11:45, Tues. 11-12, or by appointment. ● Clicker update: The Academic Center for Technology (Distance Ed.) has agreed to share their supply with us. If you still need a clicker, please bring your I.D. to Speare 14 between 3-5 pm today or from 8-10 am tomorrow. (Return these to ME at the end of the semester, and not the library - thanks!)

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Newton's First Law of Motion An object in uniform straight-line motion at constant velocity will remain in that state of motion unless acted upon by a non-zero total outside force. In particular, an object at rest will remain at rest unless acted upon by a net force. (At some level, this is just the DEFINITION of what a “force” is. But we'll see in Newton's 2 nd law that there's more to it.)

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This equation is exactly true, always! p = m v for objects moving slowly compared with the speed of light. is called the momentum of the object. So Newton's 2 nd law says: forces change momentum. SI unit of force: “Newtons” (N)

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This is the “usual” case: does not apply to anything whose mass is changing, however.

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If mass is changing, Newton's second law becomes:... which shows that a force can be necessary even to move at constant velocity! (Example: train car in the rain, gaining mass from the rainwater.)

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As a vector formula, this gives 2 equations in 1 (or 3-in-1 in 3 dimensions). We will use it over and over again! Strategy: draw a force diagram for the relevant object(s). Construct a coordinate system which simplifies things as much as possible.

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The x and y components of the motion behave independently! We can look at each vector component of the motion separately from the other(s).

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Example: Find the tension in the elevator cable if its acceleration is known (to be 0, or to be 1.0 m/s ² downward, or 1.0 m/s ² upward).

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CLICKERS: the net (total) horizontal force on the 3 kg block is.... a) Less than 2 N b) Exactly equal to 2N c) Greater than 2 N

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Example: Normal force perpendicular to surface: net force does NOT vanish here, so skier accelerates!

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Clickers: Diego wants to shoot a tranquilizer dart at a rabid smart monkey, who lets go when he sees the dart fire. Where should Diego aim the dart? a) A fixed bit above the target b) Above the target; farther above if the target is farther away c) Right at the target d) A fixed bit below the target e) Below the target; farther below if the target is farther away

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This is the magnitude of a for purely circular motion. The direction is toward the center of the circle! Again, this is merely a description of a type of motion. We'll see why something might move in circular motion beginning with chapter 5.

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The inward force for an object in circular motion is called the centripetal force. Here, it is provided by the ground pushing on the car's tires sideways.

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Clickers: Space station occupants feel weightless because... a) they are outside the pull of Earth's gravity b) the atmosphere acts like a big pillow, cushioning their weight c) their weight on the station is balanced by the station's weight on them, by Newton's 3 rd law d) their weight is opposed by Earth's normal force e) their weight is just enough to move them in the circle made by their orbit

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Roller coaster occupants don't fall out (even with seat belts off!) for the same reason orbiting satellites don't hit the ground: because they're moving.

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The inward force for an object in circular motion is called the centripetal force. Here, it is provided by the ground pushing on the car's tires sideways.

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Wait: then what is centrifugal force? That term is only used when acting as if the car is in an inertial reference frame (it is NOT); then a force must be invented to “push” the occupants outward (their natural motion would be a straight line). (We won't use it in this class.)

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Clickers: A ball is whirled around on a string in a vertical circle (gravity points down), at constant speed. If the string breaks, where will the ball most likely be at that moment? a) Top of the circle b) Bottom of the circle c) On the circle's side d) All positions are equally likely e) That's impossible; the string will NEVER break. F X X

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Tension in Massless Cables or Strings Once things have stopped stretching, tension pulls BOTH directions on the interior bits of the string or cable. Upward tension and downward tension at each point are equal but opposite (Newton's Third Law). Tension for a massless (meaning much less mass than the load placed on it) vertical cable or string is CONSTANT with varying height.

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Clickers: how should tension in a heavy rope or chain vertically suspended behave? a) It should be equal upward and downward at each point, but should decrease with altitude b) It should be equal upward and downward at each point, but should increase with altitude c) It should be equal upward and downward at each point and constant with altitude d) It should be stronger downward than upward at each point e) It should be stronger upward than downward at each point

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Clickers: A given force F pulls straight down. What value for the angle minimizes the force on each anchor point (R and L)? a) 0 degrees b) Between 0 and 45 degrees c) Between 45 and 90 degrees d) Exactly 90 degrees e) Need more information to tell. F X X R L (This angle) (equal to this)

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CHAPTER 6 : CIRCULAR MOTION AND OTHER APPLICATIONS OF NEWTON’S LAWS

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