Dynamics: Laws of Motion Newton s 1st & 2nd Laws Forces Fundametally

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1 Dynamics: Laws of Motion Newton s 1st & 2nd Laws Forces Fundametally Lana heridan De Anza College Oct 9, 2017

2 Last Time nonuniform circular motion Introduced forces

3 Overview Newton s Laws! (1st & 2nd)

4 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.

5 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).

6 Forces are Vectors +y N + W = (N W ) j = 0 or sometimes written F n + F g = (F n F g ) j = 0 1 Figure from

7 Forces are Vectors A downward force F 1 elongates the spring 1.00 cm. A downward force F 2 elongates the spring 2.00 cm. When F 1 and F 2 are applied together in the same direction, the spring elongates by 3.00 cm. When F 1 is downward and F 2 is horizontal, the combination of the two forces elongates the spring by 2.24 cm F 1 u F 2 F a F 1 b F 2 c F 1 F 2 d Figure 5.2 of a force is t scale. and its direction is u 5 tan 21 (20.500) Because forces have been experimentally verified to behave as vectors, you must use the rules of vector addition to obtain the net force on an object.

8 examples of a class of between two objects. molecules on the wall The simple rules that govern the way in which forces act Another and effect class of f motion. Newton s Laws Isaac Newton English physicist and mathematician Bridgeman-Giraudon/Art Resource, NY 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

9 Newton s First Law Newton I (as commonly stated) In an inertia reference frame, an object in motion tends to stay in motion (with constant velocity) and an object at rest tends to stay at rest, unless acted upon by a nonzero net force. Newton I (textbook version) 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-acceration reference frame is called an inertial reference frame. An object for these purposes is something with mass.

10 Newton s First Law This does not really correspond with our expectation from daily life. In our everyday environment, everything seems to naturally slow to a stop. 0 Figure from JPL.

11 Newton s First Law This does not really correspond with our expectation from daily life. In our everyday environment, everything seems to naturally slow to a stop. But we now know of other environments where we see this behavior. 0 Figure from JPL.

12 BA Different Observers Observer A is at rest and observer B is moving with constant relative velocity v BA. uppose observer A sees the particle P at (4.23) W W Galilean velocity rest. Observer B sees it 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 reference A and the other in the frame, which moves to the right x

13 BA Different Observers Observer A is at rest and observer B is moving with constant relative velocity v BA. uppose observer A sees the particle P at (4.23) W W Galilean velocity rest. Observer B sees it 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 reference A and the frame, other what in the does he see?) (But if B is in an accelerated frame, which moves to the right x

14 Newton s First Law Implications Quick Quiz 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 &J page 114

15 Newton s First Law Implications Quick Quiz 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 &J page 114

16 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.

17 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. F net a Alternatively, given a net force, the magnitude of the acceleration is inversely proportional to the mass of the object. a 1 m This expression assumes the mass of the object is constant!

18 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 of weight per kg of mass. Why?

19 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?

20 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.

21 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.

22 ummary Newton s laws! (1st & 2nd) (Uncollected) Homework erway & Jewett, Ch 5, onward from page 136. Questions: Objective Q 1, Problems 3, 5, 9, 11, 15, 19