Introduction to Mechanics Dynamics Forces Newton s Laws

Transcription

1 Introduction to Mechanics Dynamics Forces Newton s Laws Lana heridan De Anza College Nov 1, 2017

2 Last time Newton s second law mass and weight examples free-body diagrams

3 Overview Newton s second law examples Newton s third law action-reaction pairs of forces

4 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.

5 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.

6 (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

7 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).

8 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

9 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

10 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

11 Clearly, we would like to use Newton s second law gas that can be released through varying combinati around the unit, producing a force of about 10 pou enough propellant for a six-hour EVA (extra-vehicular We show the physical situation in Figure 5 7 (a), w An astronaut useson a jet a 655-kg pack tosatellite. push on The a 655-kg corresponding satellite. If free-body the d satellite starts at rest shown and in moves Figure m(b). after Note 5.00that seconds we have of chosen pushing, what is the direction force, F, of exerted the push. on itnow, by theif astronaut? the satellite starts at after 5.00 seconds of pushing, what is the force, F, exer Force Diagrams, Newton s econd Law, and Kinematics astronaut using a jet llite ation. (b) The freehe satellite. Only one ellite, and it is in the. y F x (a) Physical picture (b) Free-body

12 be released through varying combinations of 24 nozzles spaced nit, Force producing Diagrams, a force of Newton s about 10 pounds. econd The Law, MMUs and contain llant Kinematics for a six-hour EVA (extra-vehicular activity). he physical An astronaut situation uses in Figure 5 7 a jet pack to (a), push where on a an 655-kg astronaut satellite. pushes If the atellite. The corresponding free-body diagram for the satellite is satellite starts at rest and moves m after 5.00 seconds of re 5 7 (b). Note that we have chosen the x axis to point in the pushing, what is the force, F, exerted on it by the astronaut? he push. Now, if the satellite starts at rest and moves m nds of ketch: pushing, what is the force, F, exerted on it by the astronaut? y F x picture (b) Free-body diagram!!

13 Force Diagrams, Newton s econd Law, and Kinematics An astronaut uses a jet pack to push on a 655-kg satellite. If the satellite starts at rest and moves m after 5.00 seconds of pushing, what is the force, F, exerted on it by the astronaut?

14 Force Diagrams, Newton s econd Law, and Kinematics

15 Newton s econd Law Implications Quick Quiz You push an object, initially at rest, across a frictionless floor with a constant force for a time interval t, resulting in a final speed of v for the object. You then repeat the experiment, but with a force that is twice as large. What time interval is now required to reach the same final speed v? A 4 t B 2 t C t 2 D t 4 4 &J page 116.

16 Example Three forces on a mass. Find the acceleration of the object. Write it as a vector and write out the x- and y-components.

17 Newton s Third Law Newton s Third Law is commonly stated as For every action, there is an equal and opposite reaction. However it is more precisely stated: Newton III If two objects (1 and 2) interact the force that object 1 exerts on object 2 is equal in magnitude and opposite in direction to the force that object 2 exerts on object 1. F 1 2 = F 2 1

18 Newton s Third Law Main idea: you cannot push on something, without having it push back on you. If object 1 pushes on (or interacts with) object 2, then the force that object 1 exerts on object 2, and the force that object 2 exerts on object 1 form an action reaction pair.

19 us isolate only those forces Newton s Third Law: Action Reaction analysis. Pairs ewton s Third Law 119 n F tm s 2 F 12 F 21 r - t s - F 12 F 21 Figure 5.5 Newton s third law. The force F 12 exerted by object 1 on object 2 is equal in magnitude and opposite in direction to the force F 21 exerted by object 2 1 a F mt F g F me F Em

20 5.6a. The gravita- Pitfall Prevention 5.6 Defining a ystem Consider5.6 these Newton s particles Third which Law exert a force119 on each other: n two objects, we ted by a on b. The erts on object 2 is ect 1 is called the rthermore, either e terms for convet objects and must, the force acting by the Earth on 2 Figure 5.5 Newton s third law. agnitude They are of attracted. this The Each force will F12 accelerate exerted by object toward 1 the other. xerted by the procelerate the Earth on object 2 is equal in magnitude and opposite in direction to the force F21 exerted by object 2 projectile toward on object 1. s acceleration due F 12 F 12 F 21 F 21 1

21 Defining a ystem Consider5.6 these Newton s particles Third which Law exert a force119 on each other: n two objects, we ted by a on b. The erts on object 2 is ect 1 is called the rthermore, either e terms for convet objects and must, the force acting by the Earth on agnitude of this xerted by the procelerate the Earth projectile toward s acceleration due 2 F 12 F 12 F 21 F 21 Figure 5.5 Newton s third law. They are attracted. The Each force will F12 accelerate exerted by object toward 1 the other. on object 2 is equal in magnitude But wait: do the forces and opposite cancel? in direction to the force F21 exerted by object 2 F on object = F 2 1 F F 2 1 = 0 Is the net force zero? How can they each accelerate? 5.6a. The gravita- Pitfall Prevention 5.6 1

22 Defining a ystem Consider these 5.6 particles Newton s Third which Law exert a force 119 on each other: between two objects, we e exerted by a on b. The t 1 exerts on object 2 is on object 1 is called the ms; furthermore, either se these terms for conveifferent objects and must ample, the force acting xerted by the Earth on Is the net force zero? the magnitude of this orce exerted by the proust accelerate the Earth tes the projectile toward ver, its acceleration due 2 F 12 F 12 igure The 5.6a. only The force gravitao this accelerates. force is the force n Does Not Always Equal mg In on particle Pitfall Prevention 1 is F , so the net force is not zero: it onitor does not acceler- the situation shown in Figure 5.6 F 21 Figure 5.5 Newton s third law. The force F12 exerted by object 1 on object 2 is equal in magnitude No! The forces act on and different opposite in objects. direction to To find if particle 1 accelerates, we find the force net Fforce 21 exerted onby particle object 2 1. We do not on object 1. consider forces on particle 2. F 21 1

23 Action and Reaction Why when we fire a cannon does the cannon ball move much faster forward than the cannon does backwards? Why when we drop an object does it race downwards much faster than the Earth comes up to meet it?

24 Action and Reaction Why when we fire a cannon does the cannon ball move much faster forward than the cannon does backwards? Why when we drop an object does it race downwards much faster than the Earth comes up to meet it? The masses of each object are very different! From Newton s second law a = F m If m is smaller, a is bigger. If m is very, very big (like the Earth), the acceleration is incredibly small.

25 ject, which we will model as a particle. Therefore, a free-body dia isolate Forceonly Diagrams those forces on the object and eliminate the other forc alysis. Question. Do the two forces shown in the diagram that act on the monitor form an action-reaction pair under Newton s third law? n F tm n F tm n F tm F mt F g F me (A) Yes. (B) No. F Em Figure 5 F g F Em F g F Em b c the force the gravi exerted b force F m diagram s shows th

26 ummary Newton s second law and kinematics problem solving with vectors Newton s third law Homework Walker Physics: Ch 5, onward from page 138. Questions: 8, 11, 13, 23; Problems: 11, 16 & 17, 19, 33