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In reference to Newton’s 3 rd Law

In reference to Newton’s 3 rd Law. "Professor Goddard does not know the relation between action and reaction and the need to have something better than a vacuum against which to react. He seems to lack the basic knowledge ladled out daily in high schools." New York Times editorial, 1921 ,

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In reference to Newton’s 3 rd Law

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  1. In reference to Newton’s 3rd Law "Professor Goddard does not know the relation between action and reaction and the need to have something better than a vacuum against which to react. He seems to lack the basic knowledge ladled out daily in high schools." New York Times editorial, 1921, about Robert Goddard's revolutionary rocket work. "Correction: It is now definitely established that a rocket can function in a vacuum. The 'Times' regrets the error." New York Times editorial, July 1969.

  2. Lecture 7 • Goals: • Identify the types of forces • Use a Free Body Diagram to solve 1D and 2D problems with forces in equilibrium and non-equilibrium (i.e., acceleration) using Newton’ 1st and 2nd laws. • Distinguish static and kinetic coefficients of friction • Differentiate between Newton’s 1st, 2nd and 3rd Laws Assignment: HW4, (Chapters 6 & 7) Read Chapter 7 1st Exam Thursday, Oct. 7 from 7:15-8:45 PM Chapters 1-7

  3. Example Non-contact Forces FB,G All objects having mass exhibit a mutually attractive force (i.e., gravity) that is distance dependent At the Earth’s surface this variation is small so little “g” (the associated acceleration) is typically set to 9.80 or 10. m/s2

  4. Contact (i.e., normal) Forces FB,T Certain forces act to keep an object in place. These have what ever force needed to balance all others (until a breaking point).

  5. No net force  No acceleration FB,G (Force vectors are not always drawn at contact points) y FB,T Normal force is always  to a surface

  6. No net force  No acceleration • If zero velocity then “static equilibrium” • If non-zero velocity then “dynamic equilibrium” • Forces are vectors

  7. High Tension Height Time • A crane is lowering a load of bricks on a pallet. A plot of the position vs. time is • There are no frictional forces • Compare the tension in the crane’s wire (T) at the point it contacts the pallet to the weight (W) of the load (bricks + pallet) A: T > W B: T = W C: T< W D: don’t know

  8. Analyzing Forces: Free Body Diagram Eat at Mickey’s A heavy sign is hung between two poles by a rope at each corner extending to the poles. A hanging sign is an example of static equilibrium (depends on observer) What are the forces on the sign and how are they related if the sign is stationary (or moving with constant velocity) in an inertial reference frame ?

  9. Free Body Diagram T2 T1 Eat at Mickey’s Step one: Define the system q2 q1 T2 T1 q2 q1 mg mg Step two: Sketch in force vectors Step three: Apply Newton’s 2nd Law (Resolve vectors into appropriate components)

  10. Free Body Diagram T1 T2 q2 q1 Eat at Bucky’s mg Vertical : y-direction 0 = -mg + T1 sinq1 + T2 sinq2 Horizontal : x-direction 0 = -T1 cosq1 + T2 cosq2

  11. Scale Problem ? 1.0 kg • You are given a 1.0 kg mass and you hang it directly on a fish scale and it reads 10 N (g is 10 m/s2). • Now you use this mass in a second experiment in which the 1.0 kg mass hangs from a massless string passing over a massless, frictionless pulley and is anchored to the floor. The pulley is attached to the fish scale. • What does the string do? • What does the pulley do? • What does the scale now read? 10 N 1.0 kg

  12. Pushing and Pulling Forces • String or ropes are examples of things that can pull • You arm is an example of an object that can push or push

  13. Examples of Contact Forces:A spring can push

  14. A spring can pull

  15. Ropes provide tension (a pull) In physics we often use a “massless” rope with opposing tensions of equal magnitude

  16. Moving forces around string T1 -T1 • Massless strings: Translate forces and reverse their direction but do not change their magnitude (we really need Newton’s 3rd of action/reaction to justify) • Massless, frictionless pulleys: Reorient force direction but do not change their magnitude T2 T1 -T1 -T2 | T1 | = | -T1 | = | T2 | = | T2 |

  17. Scale Problem ? 1.0 kg • You are given a 1.0 kg mass and you hang it directly on a fish scale and it reads 10 N (g is 10 m/s2). • Now you use this mass in a second experiment in which the 1.0 kg mass hangs from a massless string passing over a massless, frictionless pulley and is anchored to the floor. The pulley is attached to the fish scale. • What force does the fish scale now read? 10 N 1.0 kg

  18. What will the scale read? A 5 N B 10 N C 15 N D 20 N E something else

  19. Scale Problem ? • Step 1: Identify the system(s). In this case it is probably best to treat each object as a distinct element and draw three force body diagrams. • One around the scale • One around the massless pulley (even though massless we can treat is as an “object”) • One around the hanging mass • Step 2: Draw the three FBGs. (Because this is a now a one-dimensional problem we need only consider forces in the y-direction.) 1.0 kg

  20. Scale Problem ? ? 1.0 kg 1.0 kg T ’ 3: 1: 2: • SFy = 0 in all cases 1: 0 = -2T + T ’ 2: 0 = T – mg  T = mg 3: 0 = T” – W – T’ (not useful here) • Substituting 2 into 1 yields T ’ = 2mg = 20 N (We start with 10 N but end with 20 N) T” T -T -T W -T ’ -mg

  21. A “special” contact force: Friction • What does it do? • It opposes motion (velocity, actual or that which would occur if friction were absent!) • How do we characterize this in terms we have learned? • Friction results in a force in a direction opposite to the direction of motion (actual or, if static, then “inferred”)! j N FAPPLIED i ma fFRICTION mg

  22. Friction... • Friction is caused by the “microscopic” interactions between the two surfaces:

  23. Static and Kinetic Friction • Friction exists between objects and its behavior has been modeled. At Static Equilibrium: A block, mass m, with a horizontal force F applied, Direction: A force vector  to the normal force vector N and the vector is opposite to the direction of acceleration if m were 0. Magnitude:fis proportional to the applied forces such that fs≤ms N ms called the “coefficient of static friction”

  24. Friction... N F ma fF mg • Force of friction acts to oppose motion: • Parallel to a surface • Perpendicular to a Normal force. j i

  25. Sliding Friction: Quantitatively • Direction: A force vector  to the normal force vector N and the vector is opposite to the velocity. • Magnitude: fkis proportional to the magnitude of N • fk= kN ( = Kmg in the previous example) • The constant k is called the “coefficient of kinetic friction” • Logic dictates that S > Kfor any system

  26. Static Friction with a bicycle wheel • You are pedaling hard and the bicycle is speeding up. What is the direction of the frictional force? • You are breaking and the bicycle is slowing down What is the direction of the frictional force?

  27. Recap • Assignment: Soon….HW4 (Chapters 6 & 7, due 10/5) • Read through first half of Chapter 7

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