UNIVERSITY PHYSICS I CHAPTER 5 Newton's law 85.1 Newton's first law of motion and the concept of force 1. Newton's first law of motion Any system in mechanical equilibrium remains in mechanical equilibrium unless compelled to change that state by a nonzero total force acting on the system Osystem-a particle or particles whose motion is to be studied Mechanical equilibrium-a system with a constant velocity is in equilibrium
1 1. Newton’s first law of motion Any system in mechanical equilibrium remains in mechanical equilibrium unless compelled to change that state by a nonzero total force acting on the system. 1system—a particle or particles whose motion is to be studied. §5.1 Newton’s first law of motion and the concept of force 2 Mechanical equilibrium—a system with a constant velocity is in equilibrium
85.1 Newtons first law of motion and the concept of force 3 The causes of acceleration of a system--The first law of motion states that zero total force exists when the system has a constant velocity; a nonzero total force on the system causes its acceleration d≠0分Fom≠0 @Inertial reference frames- -the reference frames in which Newton's first law is valid 85.1 Newton's first law of motion and the concept of force 2. The concept of force Force is a vector quantity-the vector sum of all the forces on a system is the force Ftotal on the system. 2 The measurement of force and the unit of force--N(Newton)($ 5.4) 3. The fundamental forces of nature Gravitational force Electromagnetic force Strong force Weak force
2 4Inertial reference frames—the reference frames in which Newton’s first law is valid 3 The causes of acceleration of a system--The first law of motion states that zero total force exists when the system has a constant velocity; a nonzero total force on the system causes its acceleration. 0 0 a ≠ ⇔ Ftotal ≠ r r §5.1 Newton’s first law of motion and the concept of force 2. The concept of force 1force is a vector quantity—the vector sum of all the forces on a system is the force on the system. Ftotal r 2 The measurement of force and the unit of force-- N (Newton) (§5.4) §5.1 Newton’s first law of motion and the concept of force 3. The fundamental forces of nature Gravitational force Electromagnetic force Strong force Weak force
85.1 Newtons first law of motion and the concept of force 4. Some common forces ① Normal force of a surface.(§5.10 Tensions in ropes, strings, and cables; (8 5.11) 3 Static friction and kinetic friction;($5.12-5.13 85.2 Newton's second law and third law of motion 52 Newton's second law of motion and Newton's third law of motion 1. Newton's second law of motion and its aspects Protal=ma E-ma=.=ma, or F_=mam F= mat P176-177 F,total=ma A force of magnitude 1n on the standard kilogram produces an acceleration of magnitude Im/s2 1N=1 kg m/s2
3 4. Some common forces 1 Normal force of a surface. (§5.10) 2 Tensions in ropes, strings, and cables;(§5.11) 3 Static friction and kinetic friction; (§5.12~5.13) §5.1 Newton’s first law of motion and the concept of force §5.2 Newton’s second law and third law of motion §5.2 Newton’s second law of motion and Newton’s third law of motion 1. Newton’s second law of motion and its aspects A force of magnitude 1 N on the standard kilogram produces an acceleration of magnitude 1m/s2. 1 N=1 kg·m/s2 P176-177 ⎪ ⎩ ⎪ ⎨ ⎧ = = = = ⇒ z z y y x x F ma F ma F ma F ma ,total ,total ,total total r r ⎩ ⎨ ⎧ = = = t t n n F ma F ma F ,total ,total r or
85.2 Newton's second law and third law of motion 2. Newton's third law of motion If a system A exerts a force on another system B, then B exerts a force of the same magnitude on a but in the opposite direction. Bon a a third law force pair are equal magnitude and opposite direction, but act on different systems 85.3 the limitation to applying Newtons law of motion 85.3 The limitation to applying Newton's law of motion 1. Reference frames Newtons law can only be used in inertial reference frames(that are not being accelerated 2. Speed limits Newtonian mechanics is a good approximation as long as the speed of the system is much less than the speed of light
4 2. Newton’s third law of motion If a system A exerts a force on another system B, then B exerts a force of the same magnitude on A but in the opposite direction. FA on B FB on A r r = − A third law force pair are equal magnitude and opposite direction , but act on different systems. §5.2 Newton’s second law and third law of motion §5.3 the limitation to applying Newton’s law of motion §5.3 The limitation to applying Newton’s law of motion 1. Reference frames Newton’s law can only be used in inertial reference frames (that are not being accelerated). 2. Speed limits Newtonian mechanics is a good approximation as long as the speed of the system is much less than the speed of light
85.3 the limitation to applying Newtons law of m otion 3. Quantum mechanics Newtonian mechanics can not describe or account for many phenomena on the atomic and nuclear scale 4. Force propagation Force somehow take time to propagate from one place to another Newtons third law does not account for such propagation delays 85.3 the limitation to applying Newtons law of motion 5. Chaotic--nonlinear system One of the hallmarks of newton's laws is their ability to predict the future behavior of a system, if we know the forces that act and the initial motion One of the particular theme of chaotic dynamics is that tiny changes in the initial conditions of a problem can be greatly amplified and can cause substantial differences in the predicted outcomes
5 3. Quantum mechanics Newtonian mechanics can not describe or account for many phenomena on the atomic and nuclear scale. 4. Force propagation Force somehow take time to propagate from one place to another. Newton’s third law does not account for such propagation delays. §5.3 the limitation to applying Newton’s law of motion 5. Chaotic—nonlinear system One of the hallmarks of Newton’s laws is their ability to predict the future behavior of a system,if we know the forces that act and the initial motion. One of the particular theme of chaotic dynamics is that tiny changes in the initial conditions of a problem can be greatly amplified and can cause substantial differences in the predicted outcomes. §5.3 the limitation to applying Newton’s law of motion
85.3 the limitation to applying Newtons law of m otion The trajectory of the Cassini mission to Saturn Saturn arrival us flyby 10Ju|2004 Venus flyby 29Jun1999 米 Launch 8 Jan 2000 15oct1997 Earth flyby 25Auq1999 85.4 Some topics of discussion 1. Do inertial frames really exist? Inertial reference frame is an ideal model The earth spins on its axis. The centripetal acceleration is less than 3. 4x10-2m/s2 The surface of the earth is a approximate inertial reference frame The earth moves around the sun. The centripetal acceleration is 6x10-m/s2
6 §5.3 the limitation to applying Newton’s law of motion The trajectory of the Cassini mission to Saturn 1. Do inertial frames really exist? Inertial reference frame is an ideal model. The earth spins on its axis. The centripetal acceleration is less than 3.4×10-2m/s2. The surface of the earth is a approximate inertial reference frame. The earth moves around the sun. The centripetal acceleration is 6×10-3m/s2. §5.4 Some topics of discussion
85.4 Some topics of discussion 2. Noninertial reference frames Alice Bob Newton's law is not valid in the car 85.4 Some topics of discussion B O4
7 §5.4 Some topics of discussion 2. Noninertial reference frames Alice Bob a0 r N mg A ? Newton’s law is not valid in the car. A 0 a r A B m mg N 0 a r B mg m N §5.4 Some topics of discussion
85.4 Some topics of discussion B Noninertial reference frames are accelerated reference frames 85.4 Some topics of discussion 3. Applying Newtons second law of motion in noninertial reference frames r=+r P dr dr dr Vpo =Vpo+ve 00 apo=apo +aoo a=a+a 0 8
8 ω r m A τ r F r n s B O r F r F0 r ω G r Noninertial reference frames are accelerated reference frames. §5.4 Some topics of discussion §5.4 Some topics of discussion r = R+ r′ r r PO PO O O PO PO O O a a a v v v ′ ′ ′ ′ = + = + r r r r r r t r t R t r d d d d d d ′ = + r r r O O’ r r r′ r R r P 3. Applying Newton’s second law of motion in noninertial reference frames a a a0 r r r = ′ +
85.4 Some topics of discussion total =ma= ma+ mao Fota +(-mao)=ma' dictate F pseudo=-mao called pseudo force. The pseudo force arise only because of the acceleration of the noninertial reference frame Without the pseudo force term, the accelerated frame cannot properly describe the motion of the particle using Newtons law. 85.5 applications of Newtons law How to apply Newtons laws of motion Identifies the system; 2 draw the free-body diagrams and illustrates all forces acting on the system with their direction indicated explicitly in the diagram; choose a coordinate system; Omake appropriate vector sum of all the forces and describe the motion by using Newton's second law of motion
9 F ma ma F ma ma ma + − = ′ = = ′ + r r r r r r r ( ) total 0 total 0 The pseudo force arise only because of the acceleration of the noninertial reference frame. Without the pseudo force term, the accelerated frame cannot properly describe the motion of the particle using Newton’s law. Fpseudo ma0 r r dictate called pseudo force. = − §5.4 Some topics of discussion How to apply Newton’s laws of motion 1identifies the system; 2 draw the free-body diagrams and illustrates all forces acting on the system with their direction indicated explicitly in the diagram; 3choose a coordinate system; 4make appropriate vector sum of all the forces and describe the motion by using Newton’s second law of motion. §5.5 applications of Newton’s law
85.5 applications of Newton's law Example 1: A submarine is sinking in the sea. If the buoyancy is F, the kinetic friction isf=-kAv, where A is the area of the cross section of the submarine Find the function of the speed of the submarine with respect to the time 85.5 applications of Newtons law Solution: y, total=-F-kAv+ mg mas d y mg v〓n d t mdv d t 0 mg -F-kAv 0在mgFk4p) d t mg-F-k4ν ln(mg-F-k4ν 4
10 Example 1: A submarine is sinking in the sea. If the buoyancy is , the kinetic friction is , where A is the area of the cross section of the submarine. Find the function of the speed of the submarine with respect to the time. F r f kAv r r = − §5.5 applications of Newton’s law c F r f r W r o y ∫ ∫ = − − − − = v t t mg F kAv m v t v mg F kAv m 0 0 d d d d ∫ ∫ = − − v − t t mg F kAv mg-F-kAv kA m 0 0 d d( ) t v mg-F-kAv kA m − = 0 ln( ) Solution: Fy,total = −F − kAv + mg = ma y §5.5 applications of Newton’s law