Equilibrium Using Newton’s second law Mass, weight, and apparent weight

1. Chapter 5 Applying Newton’s Laws • Equilibrium • Using Newton’s second law • Mass, weight, and apparent weight • Static and kinetic friction • Applying Newton’s third law Topics: Sample question: Before his parachute opens, why does this skydiver fall at a constant speed? And why does he suddenly slow down when his parachute opens? Slide 5-1

2. Reading Quiz 1. What is the difference, or is there a difference, between mass and weight? Slide 5-2

3. Reading Quiz 2. What is apparent weight? Slide 5-3

4. Reading Quiz 3. The coefficient of static friction is A. smaller than the coefficient of kinetic friction. B. equal to the coefficient of kinetic friction. C. larger than the coefficient of kinetic friction. D. not discussed in this chapter. Slide 5-4

5. Answer 3. The coefficient of static friction is C. larger than the coefficient of kinetic friction. Slide 5-5

6. Reading Quiz 4. The force of friction is described by A. the law of friction. C. a model of friction. B. the theory of friction. D. the friction hypothesis. Slide 5-6

7. Answer 4. The force of friction is described by C. a model of friction. Slide 5-7

8. Equilibrium An object is in equilibrium when the net force acting on it is zero. In component form, this is The net force on each man in the tower is zero. Slide 5-8

9. Slide 5-9

10. Example • A 100 kg block with a weight of 980 N hangs on a rope. Find the tension in the rope if • the block is stationary. • it’s moving upward at a steady speed of 5 m/s. Slide 5-10

11. Example A wooden box, with a mass of 22 kg, is pulled at a constant speed with a rope that makes an angle of 25° with the wooden floor. What is the tension in the rope? Slide 5-11

12. Checking Understanding A rod is suspended by a string as shown. The lower end of the rod slides on a frictionless surface. Which figure correctly shows the equilibrium position of the rod? Slide 5-12

13. Answer A rod is suspended by a string as shown. The lower end of the rod slides on a frictionless surface. Which figure correctly shows the equilibrium position of the rod? Slide 5-13

14. Example A ball weighing 50 N is pulled back by a rope to an angle of 20°. What is the tension in the pulling rope? Slide 5-14

15. Using Newton’s Second Law Slide 5-15

16. Example A sled with a mass of 20 kg slides along frictionless ice at 4.5 m/s. It then crosses a rough patch of snow which exerts a friction force of 12 N. How far does it slide on the snow before coming to rest? Slide 5-16

17. Example Macie pulls a 40 kg rolling trunk by a strap angled at 30° from the horizontal. She pulls with a force of 40 N, and there is a 30 N rolling friction force acting on trunk. What is the trunk’s acceleration? Slide 5-17

18. Example Find the x- and y-components of w in each of these three coordinate systems. Slide 5-18

19. Example A 75 kg skier starts down a 50-m-high, 10° slope on frictionless skis. What is his speed at the bottom? Slide 5-19

20. Example Burglars are trying to haul a 1000 kg safe up a frictionless ramp to their getaway truck. The ramp is tilted at angle θ. What is the tension in the rope if the safe is at rest? If the safe is moving up the ramp at a steady 1 m/s? If the safe is accelerating up the ramp at 1 m/s2? Do these answers have the expected behavior in the limit θ → 0° and θ → 90°? Slide 5-20

21. Example The same burglars push the 1000 kg safe up a 20° frictionless slope with a horizontal force of 4000 N. What is the safe’s acceleration? Slide 5-21

22. Mass and Weight –w = may = m(–g) w = mg Slide 5-22

23. Apparent Weight Slide 5-23

24. Example A 50 kg student gets in a 1000 kg elevator at rest. As the elevator begins to move, she has an apparent weight of 600 N for the first 3 s. How far has the elevator moved, and in which direction, at the end of 3 s? Slide 5-24

25. Static Friction fs max = µsn Slide 5-25

26. Kinetic Friction fk = µkn Slide 5-26

27. Working with Friction Forces Slide 5-27

28. Example A car traveling at 20 m/s stops in a distance of 50 m. Assume that the deceleration is constant. The coefficients of friction between a passenger and the seat are μs = 0.5 and μk = 0.3. Will a 70 kg passenger slide off the seat if not wearing a seat belt? Slide 5-28

29. Applying Newton’s Third Law: Interacting Objects Acceleration Constraints Slide 5-29

30. Slide 5-30

31. Example Block A has a mass of 1 kg; block B’s mass is 4 kg. They are pushed with a force of magnitude 10 N. a) What is the acceleration of the blocks? b) With what force does A push on B? B push on A? Slide 5-31

32. Checking Understanding Which pair of forces is an action/reaction pair? • The string tension and the friction force acting on A. • The normal force on A due to B and the weight of A. • The normal force on A due to B and the weight of B. • The friction force acting on A and the friction force acting on B. Slide 5-32

33. Answer Which pair of forces is an action/reaction pair? D. The friction force acting on A and the friction force acting on B. Slide 5-33

34. Example What is the acceleration of block B? Slide 5-34

35. Ropes and Pulleys Slide 5-35

36. Example Block A, with mass 4.0 kg, sits on a frictionless table. Block B, with mass 2.0 kg, hangs from a rope connected through a pulley to block A. What is the acceleration of block A? Slide 5-36