1 / 30

Lecture 7

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’ 1 st and 2 nd laws. Distinguish static and kinetic coefficients of friction.

alessa
Download Presentation

Lecture 7

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 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 1st Exam Thursday, Oct. 6 from 7:15-8:45 PM Chapters 1-7(light)

  2. Chaps. 5, 6 & 7What causes motion?(actually changes in motion)What kinds of forces are there ?How are forces & changes in motion related?

  3. Newton’s First Law andIRFs An object subject to no external forces moves with constant velocity if viewed from aninertial reference frame (IRF). If no net force acting on an object, there is no acceleration. • The above statement can be used to define inertial reference frames.

  4. IRFs • An IRF is a reference frame that is not accelerating (or rotating) with respect to the “fixed stars”. • If one IRF exists, infinitely many exist since they are related by any arbitrary constant velocity vector! • In many cases (i.e., Chapters 5, 6 & 7) the surface of the Earth may be viewed as an IRF

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

  6. Newton’s Second Law The acceleration of an object is directly proportional to the net force acting upon it. The constant of proportionality is the mass. • This is a vector expression: Fx, Fy, Fz • Units The metric unit of force is kg m/s2 = Newtons (N) The English unit of force is Pounds (lb)

  7. 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

  8. Contact (e.g., “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). Here: A contact force from the table opposes gravity, Normal force is perpendicular to the surface.

  9. 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

  10. 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

  11. Important notes • Many contact forces are conditional and, more importantly, they are not necessarily constant • We have general idea of forces from everyday life. • In physics the definition must be precise. • Aforce is an action which causes a body to accelerate. (Newton’s Second Law) • On a microscopic level, all forces are non-contact

  12. Analyzing Forces: Free Body Diagram Eat at Bucky’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 ?

  13. Free Body Diagram T2 T1 Eat at Bucky’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)

  14. 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

  15. Scale Problem ? 5.0 kg • You are given a 5.0 kg mass and you hang it directly on a fish scale and it reads 50 N (g is 10 m/s2). • Now you use this mass in a second experiment in which the 5.0 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? 50 N 5.0 kg

  16. 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

  17. Examples of Contact Forces:A spring can push

  18. A spring can pull

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

  20. 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 |

  21. Scale Problem ? 5.0 kg • You are given a 5.0 kg mass and you hang it directly on a fish scale and it reads 50 N (g is 10 m/s2). • Now you use this mass in a second experiment in which the 5.0 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? 50 N 5.0 kg

  22. What will the scale read? A 25 N B 50 N C 75 N D 100 N E something else

  23. 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.) 5.0 kg

  24. Scale Problem ? ? 1.0 kg 5.0 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 = 100 N (We start with 50 N but end with 100 N) T” T -T -T W -T ’ -mg

  25. Home Exercise,Newton’s 2nd Law • P + C < W • P + C > W • P = C • P + C = W

  26. 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

  27. If no acceleration • No net force • So frictional force just equals applied force • Key point: It is conditional! j N FAPPLIED i fFRICTION mg

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

  29. Friction: Static friction FBD N F m1 fs mg Static equilibrium: A block with a horizontal force F applied, As F increases so does fs S Fx = 0 = -F + fs fs = F S Fy = 0 = - N + mg  N = mg

  30. Recap • Assignment: Soon….HW4 (Chapters 6 & 7, due 10/4) • Read through first half of Chapter 7

More Related