Physics Lecture 12. P. Gutierrez. Department of Physics & Astronomy University of Oklahoma

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1 Physics 2514 Lecture 12 P. Gutierrez Department of Physics & Astronomy University of Oklahoma P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

2 Goal Goals for today s lecture: Application of Newton s second law. Equilibrium Static and Dynamic. Define weight. Introduce friction Static and Dynamic P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

3 Clicker An elevator suspended by a cable is moving upward and slowing to a stop. Which free-body diagram is correct? P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

4 Equilibrium Newton s Second Law. An object of mass m subjected to forces F 1, F 2,... will undergo an acceleration a given by a = F net m where F net = n i=1 F i is the vector sum of all forces acting on the object. The acceleration vector a points in the same direction as the force vector F net. Condition for equilibrium. F i = 0 a = 0 i P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

5 Equilibrium Newton s Second Law. An object of mass m subjected to forces F 1, F 2,... will undergo an acceleration a given by a = F net m where F net = n i=1 F i is the vector sum of all forces acting on the object. The acceleration vector a points in the same direction as the force vector F net. Condition for equilibrium. F i = 0 a = 0 i P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

6 Equilibrium Newton s Second Law. An object of mass m subjected to forces F 1, F 2,... will undergo an acceleration a given by a = F net m where F net = n i=1 F i is the vector sum of all forces acting on the object. The acceleration vector a points in the same direction as the force vector F net. Condition for equilibrium. F i = 0 a = 0 i P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

7 Equilibrium Equilibrium i F i = 0. Static equilibrium system is at rest. Dynamic equilibrium system moves with a constant velocity; a = 0. P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

8 Example An accident victim with a broken leg is placed in traction. The patient wears a special boot with a pulley attached to the sole. The foot and boot together have a mass of 4.0 kg and the doctor decides to hang a 6.0 kg mass from the rope. The boot is held suspended by the ropes and does not touch the bed. P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

9 Example What is the tension in the rope? P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

10 Example What is the tension in the rope? T F G P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

11 Example What is the tension in the rope? T F G The force due to gravity F G = ma F G = mg P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

12 Example What is the tension in the rope? T F G The force due to gravity F G = ma F G = mg F i = T m 6 g = 0 T = m 6 g = 6.0 kg 9.8 m/s 2 = 58.8 N i P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

13 Example The net traction force needs to pull straight out on the leg. What is the proper angle θ for the upper rope? P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

14 Example The net traction force needs to pull straight out on the leg. What is the proper angle θ for the upper rope? y F m 4 g T 1 T 2 x P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

15 Example The net traction force needs to pull straight out on the leg. What is the proper angle θ for the upper rope? y F m 4 g T 1 T 2 x T = T 1 = T 2 = 58.8 N Fy = T sinθ m 4 g T sin(15 ) = 0 sinθ = (m 4 g + T sin(15 ))/T θ = 67.5 Fx = T cos(15 ) + T cos θ F = 0 F = 79.0 N P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

16 Example The net traction force needs to pull straight out on the leg. What is the proper angle θ for the upper rope? y F m 4 g T 1 T 2 x T = T 1 = T 2 = 58.8 N Fy = T sinθ m 4 g T sin(15 ) = 0 sinθ = (m 4 g + T sin(15 ))/T θ = 67.5 Fx = T cos(15 ) + T cos θ F = 0 F = 79.0 N P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

17 Example The net traction force needs to pull straight out on the leg. What is the proper angle θ for the upper rope? y F m 4 g T 1 T 2 x T = T 1 = T 2 = 58.8 N Fy = T sinθ m 4 g T sin(15 ) = 0 sinθ = (m 4 g + T sin(15 ))/T θ = 67.5 Fx = T cos(15 ) + T cos θ F = 0 F = 79.0 N P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

18 Friction Next to gravity, friction is the most common force that we interact with. It allows us to walk, slows us down, and prevents us from moving. There are 3 types of friction (all act to oppose motion) Static fraction f s µ s N when no motion occurs; Kinetic friction f k = µ k N, when object is moving; Rolling friction f r = µ r N, when objects rolls. P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

19 Clicker Joe and Bill are playing tug-o-war. Joe is pulling with a force of 200 N. Bill is simply hanging on, but skidding towards Joe at a constant velocity. What is the magnitude of the force of friction between Bill s feet and the ground. A) 200 N B) 400 N C) 0 N D) 300 N D) None of the above P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

20 Example A 50 kg steel box is in the back of a dump truck. The truck s bed, also made of steel, is slowly tilted. At what angle will the file cabinet begin to slide? Brief description: A 50 kg steel box is on a steel incline plane. What is the maximum angle the incline can have for the box to remain in static equilibrium? P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

21 Solution Known µ s = 0.80, m = 50 kg Unknown angle θ of incline Normal force n Equations of motion: } mg sin θ µ s n = 0 mg cos θ + n = 0 µ s = tanθ θ = tan 1 µ s = 38.7 P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

22 Announcements Read chapter 6. Reading quiz on chapter 5 and 6; due by 11:59 PM today. New homework available. P. Gutierrez (University of Oklahoma) Physics 2514 February 21, / 13

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