1. Physics 215 – Fall 2014Lecture 06-11 Welcome back to Physics 215 Today’s agenda: Weight, elevators, and normal forces Static and kinetic friction Tension

2. Physics 215 – Fall 2014Lecture 06-12 Current homework assignment HW5: –Knight textbook Ch.6: 38, 42, 56, 58 –Ch.7: 46, 54 –due Friday, Oct. 3 rd in recitation

3. Physics 215 – Fall 2014Lecture 06-13 Summary To solve problems in mechanics, identify all forces and draw free body diagrams for all objects If more than one object, use Newton’s Third law to reduce number of independent forces Use Newton’s Second law for all components of net force on each object Choose component directions to simplify equations

4. Physics 215 – Fall 2014Lecture 06-14 Weight, mass, and acceleration What does a weighing scale ``weigh’’? Does it depend on your frame of reference? Consider elevators….

5. Physics 215 – Fall 2014Lecture 06-15 A person is standing on a bathroom scale while riding an express elevator in a tall office building. When the elevator is at rest, the scale reads about 160 lbs. While the elevator is moving, the reading is frequently changing, with values ranging anywhere from about 120 lbs to about 200 lbs. At a moment when the scale shows the maximum reading (i.e., 200 lbs) the elevator 1.must be going up 2.must be going down 3.could be going up or going down 4.I’m not sure.

6. Physics 215 – Fall 2014Lecture 06-16 Motion of elevator (if a < 0 ) Moving upward and slowing down, OR Moving downward and speeding up. Motion of elevator (if a > 0 ) Moving upward and speeding up, OR Moving downward and slowing down.

7. Physics 215 – Fall 2014Lecture 06-17 A person is standing on a bathroom scale while riding an express elevator in a tall office building. When the elevator is at rest, the scale reads about 160 lbs. While the elevator is accelerating, a different reading is observed, with values ranging anywhere from about 120 lbs to about 200 lbs. At a moment when the scale shows the maximum reading (i.e., 200 lbs) the acceleration of the elevator is approximately 1.1 m/s 2 2.2.5 m/s 2 3.5 m/s 2 4.12.5 m/s 2

8. Physics 215 – Fall 2014Lecture 06-18 Conclusions Scale reads magnitude of normal force |N PS | Reading on scale does not depend on velocity (principle of relativity again!) Depends on acceleration only * a > 0  normal force bigger * a < 0  normal force smaller

9. Physics 215 – Fall 2014Lecture 06-19 Reminder of free-fall experiment Objects fall even when there is no atmosphere (i.e., weight force is not due to air pressure). When there is no “air drag” things fall “equally fast.” i.e. same acceleration From Newton’s 2 nd law, a = W/m is independent of m -- means W = mg The weight (i.e., the force that makes objects in free fall accelerate downward) is proportional to mass.

10. Physics 215 – Fall 2014Lecture 06-110 Inertial and gravitational mass Newton’s second law: F = m I a For an object in “free fall” W = m G g If a independent of m I, must have m I = m G  Principle of equivalence

11. Physics 215 – Fall 2014Lecture 06-111 Forces of friction There are two types of situations in which frictional forces occur: –Two objects “stick to each other” while at rest relative to one another (static friction). –Two objects “rub against each other” while moving relative to each other (kinetic friction). We will use a macroscopic description of friction that was obtained by experiment.

12. Physics 215 – Fall 2014Lecture 06-112 Friction demo Static friction: depends on surface and normal force for pulled block Kinetic friction: generally less than maximal static friction

13. Physics 215 – Fall 2014Lecture 06-113 The maximum magnitude of the force of static friction between two objects The actual magnitude of the force of static friction is generally less than the maximum value. depends on the type of surfaces of the objects depends on the normal force that the objects exert on each other does not depend on the surface area where the two objects are touching

14. Physics 215 – Fall 2014Lecture 06-114 1.0 N3.12 N 2.8 N4.24 N A 2.4-kg block of wood is at rest on a concrete floor. (Using g = 10 m/s 2, its weight force is about 24 N.) No other object is in contact with the block. If the coefficient of static friction is  s = 0.5, the frictional force on the block is:

15. Physics 215 – Fall 2014Lecture 06-115 1.0 N3.12 N 2.8 N4.24 N A 2.4-kg block of wood is at rest on a concrete floor. (Using g = 10 m/s 2, its weight force is about 24 N.) Somebody is pulling on a rope that is attached to the block, such that the rope is exerting a horizontal force of 8 N on the block. If the coefficient of static friction is  s = 0.5, the frictional force on the block is:

16. Physics 215 – Fall 2014Lecture 06-116 1.No, the lighter car would start sliding at a less steep incline. 2.It doesn’t matter. The lighter car would start sliding at an incline of the same angle. 3.Yes, you could park a lighter car on a steeper hill without sliding. Having no choice, you have parked your old heavy car on an icy hill, but you are worried that it will start to slide down the hill. Would a lighter car be less likely to slide when you park it on that icy hill?

17. Physics 215 – Fall 2014Lecture 06-117 Block on incline revisited W F N 

18. Physics 215 – Fall 2014Lecture 06-118 Initially at rest What is the largest angle before the block slips? Resolve perpendicular to plane  N = Wcos  Resolve parallel  F = Wsin  Since F ≤  s N, we have Wsin  ≤  s Wcos  i.e. tan  ≤  s

19. Physics 215 – Fall 2014Lecture 06-119 The magnitude of the force of kinetic friction between two objects depends on the type of surfaces of the objects depends on the normal force that the objects exert on each other does not depend on the surface area where the two objects are touching does not depend on the speed with which one object is moving relative to the other What if  > tan -1  s ?

20. Physics 215 – Fall 2014Lecture 06-120 What if  > tan -1  s ? Block begins to slide Resolve along plane: Wsin  -   Wcos  = ma Or: a = g(sin  -   cos  )

21. Physics 215 – Fall 2014Lecture 06-121 Summary of friction 2 laws of friction: static and kinetic Static friction tends to oppose motion and is governed by inequality F s ≤  s N Kinetic friction is given by equality F K =  K N

22. Physics 215 – Fall 2014Lecture 06-122 Tension For an ideal string or rope connecting two objects: does not stretch  inextensible has zero mass Let’s look at an example of a cart connected to a falling mass by an ideal string...

23. Physics 215 – Fall 2014Lecture 06-123 1.less than 2.equal to 3.greater than the (upward) tension force on the lower block by the rope. 4.Answer depends on which block is heavier. Two blocks are connected by a heavy rope. A hand pulls block A in such a way that the blocks move upward at increasing speed. The (downward) tension force on the upper block by the rope is What if the mass of the rope/string is not zero?

24. Physics 215 – Fall 2014Lecture 06-124 Hand pulls block A so blocks move up at increasing speed.

25. Physics 215 – Fall 2014Lecture 06-125 Notice: for m R = 0, the tension forces exerted at either end are the same. The term “tension in the string” is therefore often used as a short-hand for the tension forces exerted on or by the string at either end.

26. Physics 215 – Fall 2014Lecture 06-126 1.equal to 1.0 N (i.e. the weight of A), 2.between 1.0 N and 1.5 N, 3.equal to 1.5 N (i.e. the weight of C), or 4.equal to 2.5 N (i.e. the sum of their weights)? Blocks A and C are initially held in place as shown. After the blocks are released, block A will accelerate up and block C will accelerate down. The magnitudes of their accelerations are the same. Will the tension in the string be

27. Physics 215 – Fall 2014Lecture 06-127 Reading assignment Tension, pulleys Chapters 6, 7 in textbook Start circular motion Ch. 8 in textbook