Introduction to Mechanics Dynamics Forces Newton s Laws

Transcription

1 Introduction to Mechanics Dynamics Forces Newton s Laws Lana heridan De Anza College Feb 20, 2018

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 Newton s econd Law Implications Question. If an object with mass 16 kg is acted upon by two forces, F 1 = (10N)i and F 2 = (2N)i, what is the object s acceleration?

5 Newton s econd Law Implications Question. If an object with mass 16 kg is acted upon by two forces, F 1 = (10N)i and F 2 = (2N)i, what is the object s acceleration? A 1 2 ms 2 i. B ms 2 i. C 3 4 ms 2 i. D 2 ms 4 i.

6 Newton s econd Law Implications Question. If an object with mass 16 kg is acted upon by two forces, F 1 = (10N)i and F 2 = (2N)i, what is the object s acceleration? A 1 2 ms 2 i. B ms 2 i. C 3 4 ms 2 i. D 2 ms 4 i.

7 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, C, A C A, D, B, C D D, (B and C), A C D FIGURE 5 19 Conceptual Exercise 10 1 Walker, Physics, page.

8 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, C, A C A, D, B, C D D, (B and C), A C D FIGURE 5 19 Conceptual Exercise 10 1 Walker, Physics, page.

9 Newton s econd Law Implications Question. If an object is not accelerating, can there be forces acting on it? A Yes. B No. C I choose randomly because I ve no idea what s going on.

10 Newton s econd Law Implications Question. If an object is not accelerating, can there be forces acting on it? A Yes. B No. C I choose randomly because I ve no idea what s going on. X

11 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.

12 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.

13 (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

14 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).

15 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

16 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

17 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

18 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

19 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!!

20 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? Hypothesis: The satellite is very massive. Its not moving very far very fast, but it is accelerating. Guess: maybe F = 30 N, directed in the positive x-direction.

21 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? Hypothesis: The satellite is very massive. Its not moving very far very fast, but it is accelerating. Guess: maybe F = 30 N, directed in the positive x-direction. Given: x, t, m Want: F

22 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? Hypothesis: The satellite is very massive. Its not moving very far very fast, but it is accelerating. Guess: maybe F = 30 N, directed in the positive x-direction. Given: x, t, m Want: F trategy: to find the force we must find the acceleration. x = v 0x t a xt 2

23 Force Diagrams, Newton s econd Law, and Kinematics x = 0 v 0x t a xt 2 a x = 2( x) t 2 a x = m/s 2

24 Force Diagrams, Newton s econd Law, and Kinematics x = 0 v 0x t a xt 2 a x = 2( x) t 2 a x = m/s 2 Newton s second law (x-component): F x = ma x F x = 35.4 N F = 35.4 N i

25 Reasonable: Hypothesis was a ballpark guess, but this is very close! eems reasonable. Force Diagrams, Newton s econd Law, and Kinematics x = 0 v 0x t a xt 2 a x = 2( x) t 2 a x = m/s 2 Newton s second law (x-component): F x = ma x F x = 35.4 N F = 35.4 N i

26 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.

27 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.

28 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