1. Physics 203 – College Physics I Department of Physics – The Citadel Physics 203 College Physics I Fall 2012 S. A. Yost Chapter 4 Newton’s Laws – Part 3

2. Physics 203 – College Physics I Department of Physics – The Citadel Weight and Normal Force If you stand on a scale, what force does a scale measure? (N or W) It measures the normal force between you and the scale. This equals the weight by Newton’s second law – provided you are in an inertial reference frame. NWNW N + W = 0

3. Physics 203 – College Physics I Department of Physics – The Citadel Weight in an Elevator An elevator accelerates upward at 2.2 m/s 2. What does the passenger apparently weigh, as measured by the scale in the elevator, if his mass is 100 kg? a = 2.2 m/s 2

4. Physics 203 – College Physics I Department of Physics – The Citadel Weight in an Elevator a = 2.2 m/s 2 NWNW A net force on the passenger causes the upward acceleration: F = N – W = ma. W = mg. N = ma + W = m(a+g) = (100 kg)(12.0 m/s 2 ) = 1200 N.

5. Physics 203 – College Physics I Department of Physics – The Citadel Tension Pulling on a rope applies tension. The force always acts along the rope if it is free to bend.

6. Physics 203 – College Physics I Department of Physics – The Citadel Measuring Tension The magnitude of the tension in the rope shown is the magnitude of the force F pulling on it, which is also what would be reading on the balance.. F FF

7. Physics 203 – College Physics I Department of Physics – The Citadel Example: Gymnast on Rings What is the tension in each rope supporting a 150 lb gymnast if they make the angle of  relative to horizontal? Evaluate the tension at  = 30 o. FgFgFgFg T1T1T1T1 T2T2T2T2

8. Physics 203 – College Physics I Department of Physics – The Citadel Example: Gymnast on Rings x: T 1x + T 2x = 0 y: T 1y + T 2y – F g = 0 T 1 cos  – T 2 cos  = 0 T 1 = T 2  T 2 T sin  = F g = 150 lb T = 75 lb / sin . At 30 o, T = 150 lb. FgFgFgFg T1T1T1T1 T2T2T2T2

9. Physics 203 – College Physics I Department of Physics – The Citadel Pulleys Pulleys can be used to redirect tension. Tension always follows the string. If the pulley does not resist the motion of the string, it is said to be frictionless. If the pulley is frictionless, and massless then the magnitude of the tension is the same on both sides. Otherwise, T 1  T 2. T1T1 T2T2 T 1 = T 2

10. Physics 203 – College Physics I Department of Physics – The Citadel Gymnast on Pulley The gymnast weighs 150 lb. What is the tension on the rope? T 1 + T 2 = F g = 150 lb T 1 = T 2 = 75 lb T1T1T1T1 T2T2T2T2 FgFgFgFg

11. Physics 203 – College Physics I Department of Physics – The Citadel Atwood Machine If the blocks have masses m 1 = 6.0 kg and m 2 = 4.0 kg, what is the acceleration of the blocks? Assume the pulley is massless and frictionless, and neglect the mass of the string. m 1 m2m2 What is the tension in the string?

12. Physics 203 – College Physics I Department of Physics – The Citadel Inclined Plane A block slides down the inclined plane shown, starting at the top. How long does it take to reach the bottom? 5 m 3 m 4 m

13. Physics 203 – College Physics I Department of Physics – The Citadel Inclined Plane F net = ma F net = mg sin  = 3/5 mg a = 3/5 g = 5.88 m/s 2 Time to reach bottom… x = ½ a t 2 5 m = (2.94 m/s 2 ) t 2 t = 1.3 s. N F net  y x sin  = 3/5 mgmg  a = g/5 = 1.96 m/s 2

14. Physics 203 – College Physics I Department of Physics – The Citadel Friction If I push on an object and it doesn’t move, it means another force is pushing back to balance my force: static friction. FpFp FfFfFfFf F p = F f

15. Physics 203 – College Physics I Department of Physics – The Citadel Friction At some point, if I push hard enough the object will start to move. This limit to the amount of force friction can supply turns out to be proportional to the normal force. FpFp N FfFfFfFf F f max =  s N F p = F f  s coefficient of static friction

16. Physics 203 – College Physics I Department of Physics – The Citadel Friction Once the object is moving, the friction is called kinetic friction, and is again proportional to the normal force, but with a smaller coefficient. FpFp N FfFfFfFf F f max =  k N coefficient of kinetic friction  k <  s

17. Physics 203 – College Physics I Department of Physics – The Citadel Friction Is the amount of friction affected whether I put the object on its long side or short side? No Is the amount of friction affected by how fast I push the object? No FpFp FpFp

18. Physics 203 – College Physics I Department of Physics – The Citadel Friction Suppose the coefficients of kinetic and static friction are  k = 0.7 and  s = 0.8, and the box weighs 700 N. It is at rest on a table. a)If I push with a force of 400 N, what is the force of friction? F f = 400 N. FpFp FfFfFfFf F p <  s F N = 560 N

19. Physics 203 – College Physics I Department of Physics – The Citadel Friction b)If I push with a force of 600 N, what is the force of friction? F p >  s N = 560 N. c)If I then reduce my force to 400 N, what is the force of friction? F f = 490 N until it stops. mg=700 N mg=700 N FpFp FfFfFfFf F f =  k N = 490 N  k = 0.7  s = 0.8

20. Physics 203 – College Physics I Department of Physics – The Citadel Inclined Plane with Friction If the board is tilted until the box just starts to slide, at an angle  = 37 o. What is the coefficient of static friction?  FfFfFfFf mgmg N

21. Physics 203 – College Physics I Department of Physics – The Citadel Inclined Plane with Friction It is convenient to pick axes so that two of the forces align with them. Decompose the weight into x and y components. The forces balance. x: F f = mg sin  y: N = mg cos   s  = F f /N = tan  = 0.75  FfFfFfFf mgmg N  x x mg sin  mg cos   = 37 o

22. Physics 203 – College Physics I Department of Physics – The Citadel Two Blocks Two blocks of mass 5.0 kg each are being pulled at a constant speed by a 2.0 N force. What is the tension T in the rope connecting them? 5 kg T 2.0 N

23. Physics 203 – College Physics I Department of Physics – The Citadel T F p = 2.0 N F f Two Blocks F p = T + F f T = F f F p = 2.0 N = 2T T = 1.0 N 5 kg T F f

24. Physics 203 – College Physics I Department of Physics – The Citadel Two Blocks What pulling force must be applied to accelerate the blocks at a rate of 0.2 g, and what is the tension in the rope? 5 kg T 2.0 N

25. Physics 203 – College Physics I Department of Physics – The Citadel T F p F f Two Blocks F f = 1.0 N again. F p – T – F f = ma T – F f = ma Add: F p – 2F f = 2 ma F p = 2 ma + 2F f = 2 N + 2N = 4 N. 5 kg T F f T = F f + ma = F p /2 = 2 N.