Welcome back to Physics 211

1. Welcome back to Physics 211 Today’s agenda: Free fall and weight Elevators and normal forces Static and kinetic friction

2. Reminder • Homework due this week: • Wednesday, Tutorial HW Forces, p. 31 – 34 • Friday noon, MPHW3 (motion and forces)

3. Weight, mass and acceleration What does a weighing scale ``weigh’’ ? Does it depend on your frame of reference ? Consider elevators ….

4. 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.

5. Cinema Classics Person on scale in elevator

6. Free body diagram for person

7. Motion of elevator (if a = ) Moving upward and slowing down, OR Moving downward and speeding up. Motion of elevator (if a = ) Moving upward and speeding up, OR Moving downward and slowing down.

8. 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/s2 2. 2.5 m/s2 3. 5 m/s2 4. 12.5 m/s2

9. Conclusions • Scale reads magnitude of normal force |NPS| • 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

10. Galileo and the Leaning Tower of Pisa • Conjectured on the basis of expt that all bodies fall at same rate • Neglect air resistance • Repeat here with vacuum tube • Feather and cue ball

11. Conclusions from 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 2nd 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.

12. Inertial and gravitational mass • Newton’s second law: F = mIa • For an object in “free fall” W=mG g • If a independent of mI must have mI=mG Principle of equivalence

13. 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 which was obtained by experiment.

14. The maximum magnitude of the forceofstatic 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 The actual magnitude of the force of static friction is generally less than the maximum value.

15. A 2.4-kg block of wood is at rest on a concrete floor. (Using g = 10 m/s2, its weight force is about 24 N.) No other object is in contact with the block. If the coefficient of static friction is ms = 0.5, the frictional force on the block is: 1. 0 N 3. 12 N 2. 8 N 4. 24 N

16. A 2.4-kg block of wood is at rest on a concrete floor. (Using g = 10 m/s2, 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 ms = 0.5, the frictional force on the block is: 1. 0 N 3. 12 N 2. 8 N 4. 24 N

17. The maximum magnitude of the forceofstatic 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 The actual magnitude of the force of static friction is generally less than the maximum value.

18. A small wooden block is placed on top of a larger wooden block. A person starts pulling on a thin string attached to the lower block, such that both blocks accelerate to the right. The upper block does not slip with respect to the lower block. The frictional force ontheupper block is 1. a force of static friction to the right 2. a force of static friction to the left 3. a force of kinetic friction to the right 4. a force of kinetic friction to the left

19. Do forces of friction always “oppose” motion?

20. 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? 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.

21. The magnitude of the forceofkinetic 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

22. You are pushing a wooden crate across the floor at constant speed. You decide to turn the crate on end, reducing by half the surface area in contact with the floor. In the new orientation, to push the same crate across the same floor with the same speed, the force that you apply must be about 1. one fourth 2. half as great 3. the same 4. twice as great as the force required before you changed the crate’s orientation.

23. You are pushing a wooden crate across the floor at constant speed. You then decide to push the crate across the same floor at twice the speed. Once the crate has reached the greater speed, the force that you continue to apply must be about 1. half as great 2. the same 3. twice as great 4. four times as great as the force required to push the cart at the slower speed.

24. Block on plane revisited F N W q

25. Initially at rest • What is largest angle before slips ? Resolve perpendicular to plane  N=Wcosq resolve parallel  F=Wsinq since F <= mN we have Wsinq <= mWcosq ie tanq <= m

26. Angle > tan-1m • Resolve along plane Wsinq-mKWcosq=a Or a=g(sinq-mKcosq)

27. Summary of friction • 2 laws of friction: static and kinetic • Static: friction tends to oppose motion and is governed by inequality Fs <=msN • Kinetic friction is given by equality FK=mKN