February 20, Week 6. Homework #4, Due tonight. Mastering Physics: 9 problems from chapters 1 and 3 Written Question: 3.56
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1 February 20, Week 6 Today: Chapter 5, Applying Newton s Laws Homework #4, Due tonight. Mastering Physics: 9 problems from chapters 1 and 3 Written Question: 3.56 Exam #2, Next Friday, February 24 Review Session, Thursday, February 23, 7:30PM Chapter 3 review questions on Mastering Physics. Newton s Laws p. 1/7
2 Applying Newton s Laws There are two main tasks for which we will apply Newton s Laws Newton s Laws p. 2/7
3 Applying Newton s Laws There are two main tasks for which we will apply Newton s Laws To find the magnitude and sometimes direction of unknown forces. Newton s Laws p. 2/7
4 Applying Newton s Laws There are two main tasks for which we will apply Newton s Laws To find the magnitude and sometimes direction of unknown forces. To find the acceleration of masses. Newton s Laws p. 2/7
5 Applying Newton s Laws There are two main tasks for which we will apply Newton s Laws To find the magnitude and sometimes direction of unknown forces. To find the acceleration of masses. It is imperative that we always identify and use the forces acting ON objects (and not the forces exerted by objects). Newton s Laws p. 2/7
6 Applying Newton s Laws There are two main tasks for which we will apply Newton s Laws To find the magnitude and sometimes direction of unknown forces. To find the acceleration of masses. It is imperative that we always identify and use the forces acting ON objects (and not the forces exerted by objects). a = 0 are called equilibrium or statics problems Newton s Laws p. 2/7
7 Applying Newton s Laws There are two main tasks for which we will apply Newton s Laws To find the magnitude and sometimes direction of unknown forces. To find the acceleration of masses. It is imperative that we always identify and use the forces acting ON objects (and not the forces exerted by objects). a = 0 are called equilibrium or statics problems a 0 are called dynamic or kinetics problems Newton s Laws p. 2/7
8 Tension Tension - T, pulling force exerted by a thin rope, chain, or spring. Always in the same direction as the rope itself. Newton s Laws p. 3/7
9 Tension Tension - T, pulling force exerted by a thin rope, chain, or spring. Always in the same direction as the rope itself. M = Ropes Newton s Laws p. 3/7
10 Tension Tension - T, pulling force exerted by a thin rope, chain, or spring. Always in the same direction as the rope itself. M T1 = Ropes T1 = Tension exerted by 1st rope Newton s Laws p. 3/7
11 Tension Tension - T, pulling force exerted by a thin rope, chain, or spring. Always in the same direction as the rope itself. T2 M T1 = Ropes T1 = Tension exerted by 1st rope T2 = Tension exerted by 2nd rope Newton s Laws p. 3/7
12 Steps Steps for applying Newton s Laws in problems: Newton s Laws p. 4/7
13 Steps Steps for applying Newton s Laws in problems: Draw a picture. Newton s Laws p. 4/7
14 Steps Steps for applying Newton s Laws in problems: Draw a picture. For any object with mass, identify the forces acting on that object. Newton s Laws p. 4/7
15 Steps Steps for applying Newton s Laws in problems: Draw a picture. For any object with mass, identify the forces acting on that object. For each object with mass, draw a free body diagram. Newton s Laws p. 4/7
16 Steps Steps for applying Newton s Laws in problems: Draw a picture. For any object with mass, identify the forces acting on that object. For each object with mass, draw a free body diagram. Find the net force components from vector addition and set them equal to M a. Newton s Laws p. 4/7
17 Steps Steps for applying Newton s Laws in problems: Draw a picture. For any object with mass, identify the forces acting on that object. For each object with mass, draw a free body diagram. Find the net force components from vector addition and set them equal to M a. Solve for unknowns. Newton s Laws p. 4/7
18 Clicker Quiz A 1kg mass is accelerated upwards at 1m/s 2 by pulling on a massless rope. What is the tension in the rope? 1m/s 2 1kg Newton s Laws p. 5/7
19 Clicker Quiz A 1kg mass is accelerated upwards at 1m/s 2 by pulling on a massless rope. What is the tension in the rope? 1m/s 2 1kg (a) 1N Newton s Laws p. 5/7
20 Clicker Quiz A 1kg mass is accelerated upwards at 1m/s 2 by pulling on a massless rope. What is the tension in the rope? 1m/s 2 1kg (a) 1N (b) 9.8N Newton s Laws p. 5/7
21 Clicker Quiz A 1kg mass is accelerated upwards at 1m/s 2 by pulling on a massless rope. What is the tension in the rope? 1m/s 2 1kg (a) 1N (b) 9.8N (c) 10.8N Newton s Laws p. 5/7
22 Clicker Quiz A 1kg mass is accelerated upwards at 1m/s 2 by pulling on a massless rope. What is the tension in the rope? 1m/s 2 1kg (a) 1N (b) 9.8N (c) 10.8N (d) 8.8N Newton s Laws p. 5/7
23 Clicker Quiz A 1kg mass is accelerated upwards at 1m/s 2 by pulling on a massless rope. What is the tension in the rope? 1m/s 2 1kg (a) 1N (b) 9.8N (c) 10.8N (d) 8.8N ΣF y = Ma y T W = Ma y T 9.8N = 1N Newton s Laws p. 5/7
24 Clicker Quiz A 1kg mass is accelerated upwards at 1m/s 2 by pulling on a massless rope. What is the tension in the rope? 1m/s 2 1kg (a) 1N (b) 9.8N (c) 10.8N (d) 8.8N ΣF y = Ma y T W = Ma y T 9.8N = 1N Newton s Laws p. 5/7
25 Massless Ropes Massless ropes have the very useful property that the tension on each side must always be equal. Newton s Laws p. 6/7
26 Massless Ropes Massless ropes have the very useful property that the tension on each side must always be equal. First think of the forces exerted by the rope Newton s Laws p. 6/7
27 Massless Ropes Massless ropes have the very useful property that the tension on each side must always be equal. TC TM TM = force on mass due to bottom of rope TC = force on ceiling due to top of rope Newton s Laws p. 6/7
28 Massless Ropes Massless ropes have the very useful property that the tension on each side must always be equal. TC TM This one time only! Look at forces on the rope Newton s Laws p. 6/7
29 Massless Ropes Massless ropes have the very useful property that the tension on each side must always be equal. TT 3 rd Law TT = force on rope TB due to the ceiling = tension at top TB = force on rope due to the mass = tension at bottom Newton s Laws p. 6/7
30 Massless Ropes Massless ropes have the very useful property that the tension on each side must always be equal. TT 3 rd Law TT = force on rope TB due to the ceiling = tension at top TB = force on rope due to the mass = tension at bottom Σ F = M a Newton s Laws p. 6/7
31 Massless Ropes Massless ropes have the very useful property that the tension on each side must always be equal. TT 3 rd Law TT = force on rope TB due to the ceiling = tension at top TB = force on rope due to the mass = tension at bottom Σ F = M a T B + T T = M rope arope Newton s Laws p. 6/7
32 Massless Ropes TB + T T = M rope arope Newton s Laws p. 7/7
33 Massless Ropes TB + T T = M rope arope M rope = 0 Newton s Laws p. 7/7
34 Massless Ropes TB + T T = M rope arope M rope = 0 T B + T T = 0 Newton s Laws p. 7/7
35 Massless Ropes TB + T T = M rope arope M rope = 0 T B + T T = 0 T B = T T Newton s Laws p. 7/7
36 Massless Ropes TB + T T = M rope arope M rope = 0 T B + T T = 0 T B = T T The magnitude of the tension at the top and bottom of a massless rope is always the same. Newton s Laws p. 7/7
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