1. Physics 101: Lecture 27, Pg 1 Forces: Equilibrium Examples Physics 101: Lecture 02 l Today’s lecture will cover Textbook Sections 2.1-2.7 No LAB preflights Physics 101 URL: http://online.physics.uiuc.edu/ courses/phys101/fall07

2. Physics 101: Lecture 27, Pg 2Overview l Last Week è Newton’s Laws of Motion » Inertia »  F=ma( a =  F/m ) » Forces come in pairs è Free Body Diagrams » Draw coordinate axis, each direction is independent. » Simple Picture » Identify/draw all forces  Friction F f   s N( N = normal force ) è Gravity W = mg( g=9.8m/s 2 ) l Today: Forces on objects at rest è Contact Force---Springs è Contact Force---Tension è 2-D Examples 05

3. Physics 101: Lecture 27, Pg 3 Example Solution 1. Draw Free Body Diagram Of What? What forces do I include? 2. Write  F = ma Separate x and y directions What m and a? 3. Solve 07

4. Physics 101: Lecture 27, Pg 4 Book Pushed Across Table Calculate force of hand to keep the book sliding at a constant speed, if the mass of the book is 1 Kg,  k = 0.75. Physics y x 09

5. Physics 101: Lecture 27, Pg 5 Contact Force: Springs l Force exerted by a spring is directly proportional to its displacement (stretched or compressed). F spring = k x l Example: When a 5 Kg mass is suspended from a spring, the spring stretches 8 cm. If it is hung by two identical springs, they will stretch A) 4 cmB) 8 cmC) 16 cm y x 14

6. Physics 101: Lecture 27, Pg 6 Contact Force: Tension l Tension in an Ideal String: è Magnitude of tension is equal everywhere. è Direction is parallel to string (only pulls) l Example : Determine force applied to string to suspend 45 kg mass hanging over pulley: Answer: è FBD è  F = ma 15

7. Physics 101: Lecture 27, Pg 7 Pulley ACT l Two boxes are connected by a string over a frictionless pulley. In equilibrium, box 2 is lower than box 1. Compare the weight of the two boxes. A) Box 1 is heavier B) Box 2 is heavier C) They have the same weight 1 2 1 T m1gm1g 2 T m2gm2g 19

8. Physics 101: Lecture 27, Pg 8 Tension Example: l Determine the force exerted by the hand to suspend the 45 kg mass as shown in the picture. y x 24 A) 220 NB) 440 NC) 660 N D) 880 NE) 1100 N

9. Physics 101: Lecture 27, Pg 9 Tension ACT II l Determine the force exerted by the ceiling to suspend pulley holding the 45 kg mass as shown in the picture. y x 28 A) 220 NB) 440 NC) 660 N D) 880 NE) 1100 N

10. Physics 101: Lecture 27, Pg 10 Springs Preflight What does scale 1 read? A) 225 NB) 550 NC) 1100 N 30 1

11. Physics 101: Lecture 27, Pg 11 Springs ACT Scale 1 reads 550 Newtons. What is the reading on scale 2? A) 225 NB) 550 NC) 1100 N 32 12

12. Physics 101: Lecture 27, Pg 12 Forces in 2 Dimensions: Ramp l Calculate tension in the rope necessary to keep the 5 kg block from sliding down a frictionless incline of 20 degrees. 34 y x  y x

13. Physics 101: Lecture 27, Pg 13 Normal Force ACT What is the normal force of ramp on block? A) F N > mg B) F N = mg C) F N < mg 42 

14. Physics 101: Lecture 27, Pg 14 Force at Angle Example A person is pushing a 15 kg block across a floor with  k = 0.4 at a constant speed. If she is pushing down at an angle of 25 degrees, what is the magnitude of her force on the block? y x  48

15. Physics 101: Lecture 27, Pg 15Summary l Contact Force: Spring è Can push or pull, force proportional to displacement è F = k x l Contact Force: Tension è Always Pulls, tension equal everywhere è Force parallel to string l Two Dimensional Examples è Choose coordinate system è Analyze each direction is independent Next time: Sections 3.1-3.3