Mechanics Newton s Laws

Transcription

1 Mechanics Newton s Laws Lana heridan De Anza College Oct 15, 2018

2 Last time circular motion force net force

3 Overview net force example Newton s first law Newton s second law mass vs weight force diagrams

4 the eave Figure Rank the four cases, A, B, C, and D, in order of the magnitude of the puck s acceleration, starting with the smallest. Indicate ties with an equal sign. A hockey puck is acted on by one or more forces, as shown. What is the net force on each puck? Net Force Question 3 N 5 N 7 N 3 N A B t 3 N 3 N 3 N t C In case C, assume that the forces make an angle of 60 to each other. FIGURE 5 19 Conceptual Exercise 10 1 Figure from Walker, Physics, page. D

5 els Net Using Force Newton s and econd Equilibrium Law 121 What is the net force on this lamp? exerted by des no help- T they act on exerted by rium model. a b F g ith the paris Newton s Figure 5.7 (a) A lamp suspended from a ceiling by a chain of negligible mass. (b) The forces acting on the lamp are the gravi-

6 els Net Using Force Newton s and econd Equilibrium Law 121 What is the net force on this lamp? T exerted by des no helpthey act on exerted by rium model. When the net force on aan object is zero: b F g ith the paris Newton s Figure 5.7 (a) A lamp F i = 0sus- F net = pended from a ceiling i by a chain we say that the of object negligible is in equilibrium. mass. (b) The forces acting on the lamp are the gravi-

7 examples of a class of between two objects. molecules on the wall Isaac Newton was able to articulate simple rules that govern the way in which forces act and effect motion. Newton Isaac Newton English physicist and mathematician Bridgeman-Giraudon/Art Resource, NY Another class of f between two objects. of attraction between of this class of force. the planets in orbit ar that one electric char force between an elec of a field force is the f The distinction be have been led to beli level, all the forces w (field) forces of the ty els for macroscopic ph The only known fund forces between object forces between subato tive decay processes. and electromagnetic

8 Newton s First Law Newton I (as commonly stated) An object in motion will stay in motion with constant velocity and an object at rest will stay at rest, unless acted upon by a (non-zero) net force. An object for these purposes is something with mass.

9 Velocity and Newton s First Law If an object is in motion and there is zero net force on the object, does the speed or velocity have to be constant?

10 Velocity and Newton s First Law If an object is in motion and there is zero net force on the object, does the speed or velocity have to be constant? Both are constant! Neither the speed or the direction of motion can change.

11 Galileo and Inertia As we said earlier, Galileo had already proposed the idea of inertia when he considered balls rolling on inclined surfaces.

12 Galileo and Inertia As we said earlier, Galileo had already proposed the idea of inertia when he considered balls rolling on inclined surfaces. Inertia (from the Latin word for lazy) is the tendency of objects to stay doing whatever they are already doing, unless they are interfered with. Galileo s idea of inertia: A body moving on a level surface will continue in the same direction at a constant speed unless disturbed. Newton specifically understood the disturbance to be a net force.

13 Newton s First Law This was a really radical idea in the 1600s. In our everyday environment, everything seems to naturally slow to a stop. 1 Figure from JPL.

14 Newton s First Law This was a really radical idea in the 1600s. In our everyday environment, everything seems to naturally slow to a stop. But we now know of other environments where there are very few resistive forces and we see this behavior. 1 Figure from JPL.

15 Newton s First Law Newton I (another way to state it) If an object does not interact with other objects, it is possible to identify a reference frame in which the object has zero acceleration. A zero-acceleration reference frame is called an inertial reference frame. 1 The situation is different in the theory of general relativity.

16 Newton s First Law Newton I (another way to state it) If an object does not interact with other objects, it is possible to identify a reference frame in which the object has zero acceleration. A zero-acceleration reference frame is called an inertial reference frame. All frames that move with constant velocity relative to an inertial frame, are also inertial frames. 1 1 The situation is different in the theory of general relativity.

17 BA Different Observers Observer A is at rest and observer B is moving with velocity v BA. uppose observer A sees the particle P at rest. Observer B sees it (4.23) W W Galilean velocity moving, with velocity v BA. ver A and transformation up B is its city rather than v, nce frames.) Equaations. They relate A B P in relative motion. lative velocities are rpa rpb es (P, A) match the ies for the particle, erify that by taking A vbat B vba Figure 4.20 A particle located Both agree that Newton s first law holds for P! at P is described by two observers, one in the fixed frame of refer- in inertial A and the frames. other in the Newton s laws holdence frame, which moves to the right x

18 Newton s First Law Implications Question 2 Which of the following statements is correct? I. It is possible for an object to have motion in the absence of forces on the object. II. It is possible to have forces on an object in the absence of motion of the object. A I. only B II. only C Neither I. or II. D Both I. and II. 2 erway & Jewett, Physics for cientists and Engineers, p114.

19 Newton s First Law Implications Question 2 Which of the following statements is correct? I. It is possible for an object to have motion in the absence of forces on the object. II. It is possible to have forces on an object in the absence of motion of the object. A I. only B II. only C Neither I. or II. D Both I. and II. 2 erway & Jewett, Physics for cientists and Engineers, p114.

20 Newton s econd Law Galileo also proposed the concept of acceleration, but Newton realized: acceleration net Force (Remember net force is the sum of all the forces on an object) If the net force on an object is doubled, the acceleration is twice as big also.

21 Newton s econd Law The really important one. Newton II In an inertial reference frame, the sum of the forces (net force) on an object is equal to the mass of the object times its acceleration: F net = m a F net = i F i where F i are individual separate forces that we sum to get the net force. (We are assuming the mass of the object is constant.)

22 Newton s econd Law F net = m a Acceleration is directly proportional to the net force and in the same direction. The constant of proportionality is the mass, m. Alternatively, given a net force, the acceleration is inversely proportional to the mass of the object.

23 Units of Force Newton s second law gives us units for force. F net = ma Newtons, N = (kg) (ms 2 ) 1N = 1 kg m s 2 : on Earth s surface there are roughly 10 N per kg. Why?

24 Mass vs. Weight mass, m A measure of the amount of matter in an object. Also, a measure of the inertia of an object, that is, its resistance to changes in its motion. weight The force due to gravity on an object. Weight is a force. It is measured in Newtons (N) as are all forces. weight = mg Weight depends on mass, m. The mass that appears in the equation above is sometimes called the gravitational mass. Mass is an amount of stuff, measured in kilograms (kg).

25 Mass and Inertia Mass is also a measure of resistance to acceleration. For a constant net applied force: acceleration 1 mass The mass, m, in the equation F net = ma is sometimes called inertial mass.

26 Weight and acceleration Let the weight of an object be written F g. F g = mg Mass in this equation is sometimes called gravitional mass.

27 Weight and acceleration Let the weight of an object be written F g. F g = mg Mass in this equation is sometimes called gravitional mass. We can find the acceleration of an object when the only force on it is due to gravity: a = F g m = mg m = g

28 Weight and acceleration Let the weight of an object be written F g. F g = mg Mass in this equation is sometimes called gravitional mass. We can find the acceleration of an object when the only force on it is due to gravity: a = F g m = mg m = g As we would expect! This is because the inertial mass is the same as the gravitational mass. That is why all objects, no matter their mass, fall at the same rate (with the same acceleration).

29 brief period of free fall. To decelerate your fall, must the force exerted you by the parachute be greater than, less than, or Question equal to your weight? A hockey puck is acted on by one or more forces, as shown in Figure Rank the four cases, A, B, C, and D, in order of the magnitude of the puck s acceleration, starting with the smallest. Indicate ties with an equal sign. A hockey puck is acted on by one or more forces, as shown. Rank the four cases, A, B, C, and D, in order of the magnitude of the puck s acceleration, starting with the smallest. Ties are shown in brackets. 3 N 5 N A 3 N 3 N 7 N B 3 N 3 N A A, B, C, D B D, C, B, A C A, D, B, C D D, (B and C), A C D FIGURE 5 19 Conceptual Exercise 10 1 Walker, Physics, page.

30 brief period of free fall. To decelerate your fall, must the force exerted you by the parachute be greater than, less than, or Question equal to your weight? A hockey puck is acted on by one or more forces, as shown in Figure Rank the four cases, A, B, C, and D, in order of the magnitude of the puck s acceleration, starting with the smallest. Indicate ties with an equal sign. A hockey puck is acted on by one or more forces, as shown. Rank the four cases, A, B, C, and D, in order of the magnitude of the puck s acceleration, starting with the smallest. Ties are shown in brackets. 3 N 5 N A 3 N 3 N 7 N B 3 N 3 N A A, B, C, D B D, C, B, A C A, D, B, C D D, (B and C), A C D FIGURE 5 19 Conceptual Exercise 10 1 Walker, Physics, page.

31 Diagrams of Forces We can draw pictures to aid our reasoning. This is always a good idea. The process will be to identify a system of interest. omething we want to study. We will make a mathematical model of it. Everything that is not part of the system, but interacts with it, is part of the environment. We do not describe the environment mathematically.

32 Diagrams of Forces This is a physical picture. (a) ketch the forces Physical picture We need to identify the system we want to study. Here: the chair. 1 (b) Isolate the object of interest (c) Choose a convenient coordinate sy Diagrams from Walker, Physics.

33 (c) Choose a convenient coordinate system (d) Resolve forces into their components Diagrams of Forces t indicates each and every external force acting on a h is referred to as a free-body diagram. If we are nal motion, as is the case in this and the next chapt as a point particle and apply each of the forces acts Figure 5 5 shows. Once the forces are drawn, we resolve each force into components. At this point, plied to each coordinate direction separately. PROBLEM-OLVING NOTE External Forces External forces acting on an object fall into two main classes: (i) Forces at the This is a physical picture, but point nowof contact we consider with another object, the and forces that act (ii) forces exerted by an external agent, on the system (chair) from thesuch environment as gravity. (everything else). (a) ketch the forces F W Physical picture N

34 Diagrams of Forces: Free-Body Diagram N Physical picture This is a free-body diagram. We represent the chair as a point-particle with force vectors pointing outward. interest (c) Choose a convenient coordinate system (d) Resolve fo y N N N x = 0 N y = N W F W W x = 0 W y = O x Free-body diagram We also picked a coordinate system (x, y axes).

35 N Diagrams of Forces: Free-Body Diagram To analyze the forces, we must break them into components along ate system our chosen axes. (d) Resolve forces into their components N N x = 0 N y = N y x W W x = 0 W y = W F x = F cos θ F y = θ F sin θ F x

36 object, which we will model as a particle. T us isolate only those forces on the object and We can choose our system analysis. to be more than one object. This is three interacting objects, a monitor sitting on a table, on the Earth: Diagrams of Forces n F tm n F tm F mt F g F me F Em F g F Em 1 Figure from erway & Jewett. a b

37 ly those forces on the object and eliminate the Force Diagrams We could later refine our system into pieces. Here is a depiction of the forces that act on a single object, the monitor. tm n F tm n F tm F g F Em F g F Em F g F Em

38 ummary Newton s 1st and 2nd laws Midterm on Thursday, Oct 18. Homework Ch 5 Ques: 1, 5; Probs: 5, 7, 25, 27 will be set this week: Ch 5 Ques: 9; Probs: 17, 29, 31, 33, 39, 45, 49, 53, 55, 87