How are forces & changes in motion related?

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1 Lecture 7 l Goals: v Identify the types of forces v 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. v Distinguish static and kinetic coefficients of friction 1 st Exam Thursday, Oct. 6 from 7:15-8:45 PM Chapters 1-7(light) Physics 207: Lecture 7, Pg 1 Chaps. 5, 6 & 7 What causes motion? (actually changes in motion) What kinds of forces are there? How are forces & changes in motion related? Physics 207: Lecture 7, Pg 2 Page 1

2 Newton s First Law and IRFs An object subject to no external forces moves with constant velocity if viewed from an inertial reference frame (IRF). If no net force acting on an object, there is no acceleration. l The above statement can be used to define inertial reference frames. Physics 207: Lecture 7, Pg 3 IRFs v An IRF is a reference frame that is not accelerating (or rotating) with respect to the fixed stars. v If one IRF exists, infinitely many exist since they are related by any arbitrary constant velocity vector! v In many cases (i.e., Chapters 5, 6 & 7) the surface of the Earth may be viewed as an IRF Physics 207: Lecture 7, Pg 4 Page 2

3 No net force No acceleration r F = r r Fnet = 0 a = 0 l If zero velocity then static equilibrium l If non-zero velocity then dynamic equilibrium l Forces are vectors r r r r r F Fnet = F1 + F2 + F3 + K Physics 207: Lecture 7, Pg 5 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. l This is a vector expression: F x, F y, F z l Units The metric unit of force is kg m/s 2 = Newtons (N) The English unit of force is Pounds (lb) Physics 207: Lecture 7, Pg 6 Page 3

4 Example Non-contact Forces 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/s 2 F B,G Physics 207: Lecture 7, Pg 7 Contact (e.g., normal ) Forces 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. F B,T Physics 207: Lecture 7, Pg 8 Page 4

5 y r r F = F F x F y No net force No acceleration = 0 = 0 net r = ma = 0 F B,T Normal force is always to a surface F B,G (Force vectors are not always drawn at contact points) = mg + N = 0 F y N = mg Physics 207: Lecture 7, Pg 9 High Tension l A crane is lowering a load of bricks on a pallet. A plot of the position vs. time is l There are no frictional forces l 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) Height Time A: T > W B: T = W C: T< W D: don t know Physics 207: Lecture 7, Pg 10 Page 5

6 Important notes l Many contact forces are conditional and, more importantly, they are not necessarily constant l We have general idea of forces from everyday life. l In physics the definition must be precise. v A force is an action which causes a body to accelerate. (Newton s Second Law) l On a microscopic level, all forces are non-contact Physics 207: Lecture 7, Pg 11 Analyzing Forces: Free Body Diagram A heavy sign is hung between two poles by a rope at each corner extending to the poles. Eat at Bucky s 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? Physics 207: Lecture 7, Pg 12 Page 6

7 Free Body Diagram Step one: Define the system T 1 T 2 θ 1 θ 2 Eat at Bucky s T 1 T 2 mg θ 1 θ 2 Step two: Sketch in force vectors Step three: Apply Newton s 2 nd Law (Resolve vectors into appropriate components) mg Physics 207: Lecture 7, Pg 13 Free Body Diagram T 1 T 2 θ 1 θ 2 Eat at Bucky s mg Vertical : y-direction 0 = -mg + T 1 sinθ 1 + T 2 sinθ 2 Horizontal : x-direction 0 = -T 1 cosθ 1 + T 2 cosθ 2 Physics 207: Lecture 7, Pg 14 Page 7

8 Scale Problem l 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/s 2 ). 50 N 5.0 kg l 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. l What does the string do? l What does the pulley do? l What does the scale now read? 5.0 kg? Physics 207: Lecture 7, Pg 15 Pushing and Pulling Forces l String or ropes are examples of things that can pull l You arm is an example of an object that can push or push Physics 207: Lecture 7, Pg 16 Page 8

9 Examples of Contact Forces: A spring can push Physics 207: Lecture 7, Pg 17 A spring can pull Physics 207: Lecture 7, Pg 18 Page 9

10 Ropes provide tension (a pull) In physics we often use a massless rope with opposing tensions of equal magnitude Physics 207: Lecture 7, Pg 19 Moving forces around l Massless strings: Translate forces and reverse their direction but do not change their magnitude (we really need Newton s 3 rd of action/reaction to justify) string T 1 -T 1 l Massless, frictionless pulleys: Reorient force direction but do not change their magnitude T 1 -T 1 T 2 -T2 T 1 = -T 1 = T 2 = T 2 Physics 207: Lecture 7, Pg 20 Page 10

11 Scale Problem l 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/s 2 ). 50 N 5.0 kg l 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.? l What force does the fish scale now read? 5.0 kg Physics 207: Lecture 7, Pg 21 What will the scale read? A 25 N B 50 N C 75 N D 100 N E something else Physics 207: Lecture 7, Pg 22 Page 11

12 Scale Problem l 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. v One around the scale v One around the massless pulley (even though massless we can treat is as an object ) v One around the hanging mass? l 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 Physics 207: Lecture 7, Pg 23 Scale Problem T 3: T 2: 1: T W? 1.0 kg -T -mg -T -T l Σ F y = 0 in all cases 1: 0 = -2T + T 2: 0 = T mg T = mg 3: 0 = T W T (not useful here) l Substituting 2 into 1 yields T = 2mg = 100 N (We start with 50 N but end with 100 N) 5.0 kg Physics 207: Lecture 7, Pg 24? Page 12

13 Home Exercise, Newton s 2 nd Law P is the upward force being exerted on the crate by the person C is the contact or normal force on the crate by the floor, and Wis the weight (force of the earth on the crate). A. P + C < W B. P + C > W C. P = C D. P + C = W Physics 207: Lecture 7, Pg 25 A special contact force: Friction l What does it do? v It opposes motion (velocity, actual or that which would occur if friction were absent!) l How do we characterize this in terms we have learned? v Friction results in a force in a direction opposite to the direction of motion (actual or, if static, then inferred )! N j F APPLIED ma i f FRICTION mg Physics 207: Lecture 7, Pg 26 Page 13

14 If no acceleration l No net force l So frictional force just equals applied force l Key point: It is conditional! N j F APPLIED i f FRICTION mg Physics 207: Lecture 7, Pg 27 Friction... l Friction is caused by the microscopic interactions between the two surfaces: Physics 207: Lecture 7, Pg 28 Page 14

15 Friction: Static friction Static equilibrium: A block with a horizontal force F applied, Σ F x = 0 = -F + f s f s = F FBD Σ F y = 0 = - N + mg N = mg As F increases so does f s F mg N m 1 f s Physics 207: Lecture 7, Pg 29 Recap l Assignment: Soon.HW4 (Chapters 6 & 7, due 10/4) l Read through first half of Chapter 7 Physics 207: Lecture 7, Pg 30 Page 15

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