Chapter 5. Force and Motion I Newton s Laws Concepts of Mass and Force Newton s Three Laws But first, let s review the last lecture.. Physics, Page 1
Summary of the last lecture 1. Projectile Motion x = x 0 + v 0 t v = v 0x y = y 0 + v 0y t - 1/ gt v y = v 0y - gt v y = v 0y -g Δy. Circular motion ω=πf [S -1 ] v= rω v ω = r Period T 1 T = f π = ω π r = v dv dθ a = = v = vω dt dt v a = a = vω = rω = r 3. Relative Motion r = r r v = v v PB PA BA PB PA BA Physics, Page
Isaac Newton (164 ~ 177) Physics, Page 3
Question You are driving a car up a hill with constant velocity. On a piece of paper, How many forces are acting on the car? 1 3 4 5 correct F N V f W Physics, Page 4
Question The net force on the car is, F N V 1. Zero correct. Pointing up the hill 3. Pointing down the hill 4. Pointing vertically downward 5. Pointing vertically upward f f W F N W ΣF = ma = 0 Physics, Page 5
Question You are driving a car up a hill with constant acceleration. How many forces are acting on the car? 1 3 4 5 correct F N a f W Physics, Page 6
Question Suppose you are an astronaut in outer space giving a brief push to a spacecraft whose mass is bigger than your own. 1) Compare the magnitude of the force you exert on the spacecraft, F S, to the magnitude of the force exerted by the spacecraft on you, F A, while you are pushing: 1. F A = F S. F A > F S 3. F A < F S correct Third Law! ) Compare the magnitudes of the acceleration you experience, a A, to the magnitude of the acceleration of the spacecraft, a S, while you are pushing: 1. a A = a S. a A > a S 3. a A < a S correct Second Law! a = F/m F same lower mass give larger a Physics, Page 7
Newton s First Law The motion of an object does not change unless it is acted upon by a net force. If v=0, it remains 0. If v is some value, it stays at that value. Another way to say the same thing: No net force (F net = 0) velocity is constant. acceleration is zero. Physics, Page 8
Mass or Inertia Mass (m) is the property of an object that measures how hard it is to change its motion. Units: [M] = kg Examples of 1st Law braking car vs. train car vs. bus going around curve push on light or heavy object Physics, Page 9
Newton s Second Law a = F net m = = Fnet F ma Cause ( 원인 ) Result ( 결과 ) Physics, Page 10
Question An airplane is flying from Seoul airport to Jegu. Many forces act on the plane, including weight (gravity), drag (air resistance), the trust of the engine, and the lift of the wings. At some point during its trip the velocity of the plane is measured to be constant (which means its altitude is also constant). At this time, the total force on the plane: 1. is pointing upward. is pointing downward 3. is pointing forward 4. is pointing backward 5. is zero correct drag lift weight thrust Physics, Page 11
Questions (common misconceptions) gravity would be working against the airplane flying at a level altitude, so the total force would need to be upward. Gravity never goes away, so the force on the plane will be pointing downwards. The force has to be pointing forward since the velocity is moving forward. the up and down forces are zero because the plane is not going up or down, and the plane is pushing back against the air propelling it forward. something to think about the plane is constantly pointing down because the earth is round and constant altitude would mean it has to decrease its altitude constantly to keep a constant distance from the ground True, but the effect is small.. On a cross-country trip (300 miles), a flat trip would have distance to center of earth varying by 0.5% Physics, Page 1
Example 1 F 1 M M=10 kg, F 1 =00 N Find a. a = F net /M = 00N/10kg = 0 m/s F 1 M F M=10 kg F 1 =00 N F = 100 N Find a. a = F net /M = (00N-100N)/10kg = 10 m/s Physics, Page 13
Example A force F acting on a mass m 1 results in an acceleration a 1. The same force acting on a different mass m results in an acceleration a = a 1. What is the mass m? m 1 m F a 1 F a = a 1 (a) m 1 (b) m 1 (c) 1/ m 1 F=ma F= m 1 a 1 = m a = m (a 1 ) Therefore, m = m 1 / Or, in words twice the acceleration means half the mass. Physics, Page 14
Examples of Force 1. Gravity ( 중력, 혹은무게 ) Physics, Page 15
Gravitational Force F m m 1 1 F 1 F = Gm F 1 F m = : Gravitational force between massive objects 1 1 rˆ 1 r1 rˆ 1 = rˆ 1 Gm 1 m 1 rˆ 1 r 1 F = 1 G = universal gravitation constant = 6.67 x 10-11 N-m /kg On the Earth m M E = 6 10 4 kg R E = 6.4 10 6 m R Earth F GM m = E R E mg g = GM R 6. 67 10 11 4 E = = 9. 8 E 6 6 ( 6. 4 10 ) 10 m / sec Physics, Page 16
Examples of Force. Normal force ( 수직힘, 수직항력, 법선력 ) F N W book at rest on table: What are forces on book? Weight is downward System is in equilibrium (acceleration = 0 net force = 0) Therefore, weight balanced by another force F N = normal force = force exerted by surface on object F N is always perpendicular to surface and outward For this example F N = W Physics, Page 17
Another Example: F hand F N Book at rest on table: Push down with F hand What is F N? W Equilibrium: F N + W + F hand = 0 F N = W+F hand What is direction of F N? Physics, Page 18
Examples of Force 3. Friction ( 쓸림, 쓸림힘, 마찰력 ) ( 접촉마찰력 ) Physics, Page 19
Examples of Force 4. Tension ( 장력 ) M H F M M : T = Ma H : T = F F M M : T = Ma m m : T mg = -ma Physics, Page 0
Newton s Third Law For every action, there is an equal and opposite reaction. ( 두물체가상호작용할때서로에게작용하는힘 ( 짝힘 ) 은항상크기가같고방향이반대이다.) F finger box Finger pushes on box F finger box = force exerted on box by finger F box finger Box pushes on finger F box finger = force exerted on finger by box Third Law: F box finger = - F finger box Physics, Page 1
Newton's Third Law... F A,B = - F B,A. is true for all types of forces F w,m F m,w F m,f F f,m Physics, Page
Example of Bad Thinking Since F m,b = - F b,m why isn t F net = 0, and a = 0? a?? F b,m F m,b ice Physics, Page 3
Example of Good Thinking Consider only the box! F on box = ma box = F m,b Free Body Diagram (which means a diagram including all forces existing) What about forces on man? a box F b,m F m,b ice Physics, Page 4
Newton's Third Law... (a) 참외에작용하는힘은? F CE ( 중력 ), F CT ( 식탁이주는수직힘 ) 이두힘은짝힘인가? 아니다! (b) 참외와지구사이에작용하는제 3 법칙의짝힘은? F CE ( 지구인력 ) = - F EC ( 참외인력 ) (c) 참외와식탁사이에작용하는제 3 법칙의짝힘은? F TC ( 참외가식탁에가한수직힘 ) = - F CT ( 식탁이참외에가한수직힘 ) Physics, Page 5
Summary Newton s First Law: The motion of an object does not change unless it is acted on by a net force Newton s Second Law: F net = ma Newton s Third Law: F a,b = - F b,a Types of Forces Gravity Normal Force Friction Tension Physics, Page 6
Application of Newton's Laws T 1 F = 4 N M = 4 kg M 1 = kg Find acceleration of blocks and tension T 1 Answers: a = 4 m/s and T 1 = 16 N Physics, Page 7
Example T 1 T=4 N M = kg M 1 = 4 kg Turn blocks around. Find acceleration of blocks and tension T 1 Answers: a= 4 m/s (the same) and T 1 = 8 N (smaller) Physics, Page 8
Example m a mg θ Find acceleration and normal force Answers: a= g sin(θ) F N = mg cos (θ) Physics, Page 9
Example : Pulley Problem I What is the tension in the string? A) T<W B) T=W C) W<T<W D) T=W T E) T>W W W W Pull with force = W Same answer Physics, Page 30
Example : Pulley Problem II What is the tension in the string? A) T<W B) T=W C) W<T<W T D) T=W W E) T>W a W T a Physics, Page 31
Example : Pulley Problem III Procedure for Solving Problems Identify forces Set up axes Write F net = ma for each axis Solve! and, Verify Gravity Tension Normal force Friction Physics, Page 3
M m 예 ) 차원비교? T < mg? Physics, Page 33
Atwood s Machine T T m 1 m m 1 g F1 = T m 1 g = m 1a F = m g T = m a m g = m m +) ( ) ( )a a m 1 1 + = m m 1 g m + m, m 1m T = m + m g 1 1 m g F m 1 m P P a F = P = m a F1 = F P = m 1a F = ( m 1 + m )a = F m 1 + m m P = m 1 + m F +) Physics, Page 34
Example : Weighting in an Elevator (1) a () a T T (1) F = T - mg = ma T = m(g + a) mg m mg () F = mg - T = ma T = m(g - a) Physics, Page 35