Dynamics Laws of Motion More About Forces

Transcription

1 Dynamics Laws of Motion More About Forces Lana heridan De Anza College Oct 10, 2017

2 Overview Newton s first and second laws

3 Warm Up: Newton s econd Law Implications Question. If an object is not accelerating, can there be forces acting on it? A Yes. B No.

4 Warm Up: Newton s econd Law Implications Question. If an object is not accelerating, can there be forces acting on it? A Yes. B No.

5 Warm Up: 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.

6 Warm Up: 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.

7 Overview mass and weight fundamental forces fields Newton s 3rd Law action-reaction pairs of forces some types of mechanical forces

8 Mass What is mass?

9 Mass What is mass? Very loosely speaking, it is a measure of the amount of stuff in an object.

10 Mass What is mass? Very loosely speaking, it is a measure of the amount of stuff in an object. As Newton s second law implies, an object with greater mass is more resistant to forces changing its velocity.

11 Mass What is mass? Very loosely speaking, it is a measure of the amount of stuff in an object. As Newton s second law implies, an object with greater mass is more resistant to forces changing its velocity. We call this resistance to changes in velocity inertia.

12 Mass What is mass? Very loosely speaking, it is a measure of the amount of stuff in an object. As Newton s second law implies, an object with greater mass is more resistant to forces changing its velocity. We call this resistance to changes in velocity inertia. The mass that appears in Newton s second law is sometimes called inertial mass.

13 Mass What is mass? Very loosely speaking, it is a measure of the amount of stuff in an object. As Newton s second law implies, an object with greater mass is more resistant to forces changing its velocity. We call this resistance to changes in velocity inertia. The mass that appears in Newton s second law is sometimes called inertial mass. It happens to be equal to gravitational mass, because the strength of gravitational interactions depends on mass. (More on this in a minute...)

14 The Difference between Mass and Weight What is the difference between mass and weight?

15 The Difference between Mass and Weight What is the difference between mass and weight? Mass is a measure of inertia. Weight is a force an object experience due to a gravitational interaction.

16 The Difference between Mass and Weight mass 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. Objects in free-fall can be said to be weightless, but they still have mass.

17 The Difference between Mass and Weight mass 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. Objects in free-fall can be said to be weightless, but they still have mass. Weight F g, Units: Newtons. F g = mg

18 Forces at a Fundamental Level Previously, we talked about two kinds of forces: contact forces and field forces (ie. forces that act at a distance). In mechanics problems, usually gravity is the only field force that we need to consider. The rest are all contact forces.

19 Forces at a Fundamental Level Previously, we talked about two kinds of forces: contact forces and field forces (ie. forces that act at a distance). In mechanics problems, usually gravity is the only field force that we need to consider. The rest are all contact forces. However, at a fundamental level, all forces that we know of are field forces.

20 Forces at a Fundamental Level Contact forces are a result of electrostatic repulsion at very small scales.

21 Forces at a Fundamental Level Contact forces are a result of electrostatic repulsion at very small scales. The fundamental forces (interactions): Force Rel. strength Range (m) Attract/Repel Carrier Gravitational attractive graviton Electromagnetic 10 2 attr. & rep. photon Weak Nuclear < attr. & rep. W +, W, Z 0 trong Nuclear 1 < attr. & rep. gluons

22 Forces at a Fundamental Level Contact forces are a result of electrostatic repulsion at very small scales. The fundamental forces (interactions): Force Rel. strength Range (m) Attract/Repel Carrier Gravitational attractive graviton Electromagnetic 10 2 attr. & rep. photon Weak Nuclear < attr. & rep. W +, W, Z 0 trong Nuclear 1 < attr. & rep. gluons

23 Forces at a Fundamental Level Contact forces are a result of electrostatic repulsion at very small scales. The fundamental forces (interactions): Force Rel. strength Range (m) Attract/Repel Carrier Gravitational attractive graviton Electromagnetic 10 2 attr. & rep. photon Weak Nuclear < attr. & rep. W +, W, Z 0 trong Nuclear 1 < attr. & rep. gluons Gravity is actually quite a weak force, but it is the only one that (typically) matters on large scales.

24 Fields field A field is any kind of physical quantity that has values specified at every point in space and time.

25 Fields field A field is any kind of physical quantity that has values specified at every point in space and time. Fields were first introduced as a calculation tool. A force-field can be used to identify the force a particular particle will feel at a certain point in space and time based on the other objects in its environment that it will interact with. We do not need a description of the sources of the field to describe what their effect is on our particle.

26 Fields To be clear: When we adopt a field model of force interactions we separate two interacting objects, placing one in the system and the other in the environment. Environment Field ystem F g The Earth

27 Examples of Fields Gravity and the electrostatic force have associated fields. g = 9.8 j N/kg, the gravitational field strength. F G = mg F E = qe

28 Examples of Fields Gravity and the electrostatic force have associated fields. g = 9.8 j N/kg, the gravitational field strength. F G = mg F E = qe We can also think of g as an acceleration. (m/s 2 = N/kg) Can we think of E as an acceleration (due to the electrostatic force)?

29 Examples of Fields Gravity and the electrostatic force have associated fields. g = 9.8 j N/kg, the gravitational field strength. F G = mg F E = qe We can also think of g as an acceleration. (m/s 2 = N/kg) Can we think of E as an acceleration (due to the electrostatic force)? No. q m

30 e end of ection 25.2, the equipotential surfaces associated ric Representing field consist of a family Fields of planes perpendicular to the 1a shows some representative equipotential surfaces for this roduced rge Fields are drawn with lines showing the direction of force that a test particle will feel at that point. The density of the lines at that point in the diagram indicates the approximate magnitude of the force ata that spherically point. symmetric electric Gravitation: field produced by a point charge An electric field produced by an electric dipole Electrostatic: q E b c

31 Examples of Fields The gravitational field caused by the un-earth system can be represented as: 1 Figure from

32 Examples of Fields re intersections 1 Figure from of these erway surfaces & Jewett with the page) and elecetric electric An electric field produced by an point The charge electrostatic electric field caused dipoleby an electric dipole system can be represented as: c

33 Newton s Third Law 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 Or, as commonly stated: every action has an equal and opposite reaction.

34 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

35 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

36 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

37 ome types of forces Gravitation The force that massive objects exert on one another. Newton s Law of Universal Gravitation F G = Gm 1m 2 r 2 for two objects, masses m 1 and m 2 at a distance r. G = Nm 2 kg 2. (Challenge: check the units of G.)

38 ome types of forces Gravitation cont d For the moment, we will care about this force in that it gives objects weight, w. F g = w = mg and g = GM Earth R 2 Earth The force F g or w, acts downwards towards the center of the Earth.

39 ome types of forces The Normal Force The reactive force of a surface, as implied by Newton s Third Law. It acts in a direction perpendicular to the surface. For an object of weight F g sitting on a level surface, the normal force, F N (or n in the textbook) is F N = F g Be careful! There are many cases in which the above equation is not true! 1 Figure from

40 ome types of forces Friction (will not be on 1st test) The force a surface exerts on an object to resist its motion.

41 ome types of forces Friction (will not be on 1st test) The force a surface exerts on an object to resist its motion. There are two kinds of friction, static friction, F sf, and kinetic friction, F kf.

42 ome types of forces Friction (will not be on 1st test) The force a surface exerts on an object to resist its motion. There are two kinds of friction, static friction, F sf, and kinetic friction, F kf. The amount of friction depends on properties of the object and the surface. More about this to follow!

43 ome types of forces Friction (will not be on 1st test) The force a surface exerts on an object to resist its motion. There are two kinds of friction, static friction, F sf, and kinetic friction, F kf. The amount of friction depends on properties of the object and the surface. More about this to follow! The friction force always acts to oppose motion. That means the kinetic friction F kf always points opposite to the velocity vector.

44 ome types of forces Tension The force exerted by a rope or chain to suspend or pull an object with mass. Problems involving tensions often require solving systems of vector equations. 1 Figure from

45 ome types of forces Elastic Forces prings exert forces as they are being compressed or extended. They have a natural length, at which they remain if there are no external forces acting. Hooke s Law gives F spring = kx where k is a constant. x is the amount of displacement of one end of a spring from it s natural length. (The amount of compression or extension. 1 Figure from CCRMA tanford Univ.

46 prings Question. A mass is attached to the end of a spring which obeys Hooke s Law. The spring is compressed and then released. Is the acceleration of the mass constant? (A) Yes. (B) No.

47 prings Question. A mass is attached to the end of a spring which obeys Hooke s Law. The spring is compressed and then released. Is the acceleration of the mass constant? (A) Yes. (B) No.

48 ummary mass and weight forces and fields Newton s 3rd law types of forces First Test Friday (Oct 13). (Uncollected) Homework erway & Jewett, Ch 5, onward from page 136. Problems: 17, 23