Physics Lecture 13. P. Gutierrez. Department of Physics & Astronomy University of Oklahoma

Transcription

1 Physics 2514 Lecture 13 P. Gutierrez Department of Physics & Astronomy University of Oklahoma P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

2 Goal Goals for today s lecture: Application of Newton s second law continue Equilibrium Static and Dynamic. Gravity and weight. Continue with the application of friction Static and Kinetic P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

3 Clicker An elevator suspended by a cable is moving downwards and slowing to a stop. Which free-body diagram is correct? P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

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 23, / 14

5 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 23, / 14

6 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 23, / 14

7 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 23, / 14

8 Solution Known µ s = 0.80, m = 50 kg Unknown angle θ of incline Normal force n Newton s second law: } mg sin θ µ s n = 0 n mg cos θ = 0 µ s = tanθ θ = tan 1 µ s = 38.7 P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

9 Solution Known µ s = 0.80, m = 50 kg Unknown angle θ of incline Normal force n Newton s second law: } mg sin θ µ s n = 0 n mg cos θ = 0 µ s = tanθ θ = tan 1 µ s = 38.7 P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

10 Solution Known µ s = 0.80, m = 50 kg Unknown angle θ of incline Normal force n Newton s second law: } mg sin θ µ s n = 0 n mg cos θ = 0 µ s = tanθ θ = tan 1 µ s = 38.7 P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

11 Example Gravity and Weight Mass is an intrinsic property of an object (objects inertia). Gravity is a long range force acting between any two masses. (Newton s law of gravity.) F G = Gm 1m 2 r 2 Gravity near Earth s surface (Newton s second law.) ˆr m a = F G = GmM e R 2 e ˆr g a = GM e R 2 e = 9.8 m/s 2 G = N m 2 /kg 2 M e = kg R e = m P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

12 Example Gravity and Earth m a = GmM e (R e + y) 2 ˆr g a = GM e (R e + y) 2 y distance above the earth s surface y (km) g (m/s 2 ) Earth s surface Cruising altitude of a commercial aircraft miles up Height of space shuttle 400, Height of the moon P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

13 Example Weight Weight is a measurement An objects weight results from the force exerted on a spring scale could be a pulling or pushing contact force. If the system is in static equilibrium (rest frame) w = mg. P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

14 Example Weight Weight is a measurement An objects weight results from the force exerted on a spring scale could be a pulling or pushing contact force. If the system is in static equilibrium (rest frame) w = mg. P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

15 Example Example You are standing on a scale inside an elevator. When the elevator is stationary, you find your weight is 680 N. What is your weight if the elevator is moving downward with a velocity of 10 m/s, but the accleration is upward at 3 m/s 2? P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

16 Example Example You are standing on a scale inside an elevator. When the elevator is stationary, you find your weight is 680 N. What is your weight if the elevator is moving downward with a velocity of 10 m/s, but the accleration is upward at 3 m/s 2? P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

17 Example Solution P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

18 Example Solution F yi = F sp mg = ma i w = ma+mg = m(a+g) = 888 N w = N = F sp P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

19 Example Solution F yi = F sp mg = ma i w = ma+mg = m(a+g) = 888 N w = N = F sp P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

20 Example Clicker In the example the elevator is moving downwards at 10 m/s, accelerating upwards at 3 m/s 2 and the weight is found to be 888 N. Now assume that the elevator is moving upwards at 10 m/s and accelerating upwards at 3 m/s 2, what is the weight? (Recall that for the stationary elevator the weight was 680 N.) A) 888 N B) 680 N C) 471 N D) 0 N C) -888 N P. Gutierrez (University of Oklahoma) Physics 2514 February 23, / 14

21 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 23, / 14