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Physics 101: Lecture 8, Pg 1 Physics 101: Lecture 8 Newton's Laws l Today’s lecture will be a review of Newton’s Laws and the four types of forces discussed in Chapter 4. è Concepts of Mass and Force è Newton’s Three Laws è Gravitational, Normal, Frictional, Tension Forces

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Physics 101: Lecture 8, Pg 2 Sir Isaac Newton, English Physicist,

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Physics 101: Lecture 8, Pg 3 Newton’s First Law è 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 è Another way to say the same thing: No net force velocity is constant acceleration is zero no change of direction of motion

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Physics 101: Lecture 8, Pg 4 Mass or Inertia è Inertia is the tendency of an object to remain at rest or in motion with constant speed along a straight line. è Mass (m) is the quantitative measure of inertia. Mass is the property of an object that measures how hard it is to change its motion. è Units: [M] = kg

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Physics 101: Lecture 8, Pg 5 Newton’s Second Law èThis law tells us how motion changes when a net force is applied. è acceleration = (net force)/mass

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Physics 101: Lecture 8, Pg 6 Newton’s Second Law è Units: è [F] = [M] [a] è [F] = kg m/s 2 è 1 Newton (N) 1 kg m/s 2 è A vector equation: è F net,x = Ma x è F net,y = Ma y

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Physics 101: Lecture 8, Pg 7 Newton’s 1. Law total An airplane is flying from Buffalo airport to O'Hare. 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 (or net) force on the plane: 1. is pointing upward 2. is pointing downward 3. is pointing forward 4. is pointing backward 5. is zero lift weight drag thrust correct

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Physics 101: Lecture 8, Pg 8 Newton’s 1. Law Newton's first law states that if no net force acts on an object, then the velocity of the object remains unchanged. Since at some point during the trip, the velocity is constant, then the total force on the plane must be zero, according to Newton's first law. lift weight drag thrust F= ma = m0 = 0

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Physics 101: Lecture 8, Pg 9 Example: Newton’s 2. Law M F1F1 M=10 kg F 1 =200 N Find a a = F net /M = 200N/10kg = 20 m/s 2 M F1F1 M=10 kg F 1 =200 N F 2 = 100 N Find a F2F2 a = F net /M = (200N-100N)/10kg = 10 m/s 2

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Physics 101: Lecture 8, Pg 10 Newton’s Third Law è For every action, there is an equal and opposite reaction. Finger pushes on box F finger box = force exerted on box by finger F finger box F box finger Box pushes on finger F box finger = force exerted on finger by box Third Law: F box finger = - F finger box

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Physics 101: Lecture 8, Pg 11 Newton's Third Law... FF l F A,B = - F B,A. is true for all types of forces F F w,m F F m,w F F f,m F F m,f

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Physics 101: Lecture 8, Pg 12 Conceptual Question: Newton’s 3.Law FFFa l Since F m,b = -F b,m why isn’t F net = 0, and a = 0 ? a ?? F F b,m F F m,b ice

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Physics 101: Lecture 8, Pg 13 Conceptual Question: Answer only the box l Consider only the box ! è F net, aF è F net, box = m box a box = F m,b a box F F b,m F F m,b ice What about forces on man? è FaF è F net,man = m man a man = F b,m

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Physics 101: Lecture 8, Pg 14 2) 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 2. a A > a S 3. a A < a S Newton’s 2. and 3. Law Suppose you are an astronaut in outer space giving a brief push to a spacecraft whose mass is bigger than your own (see Figure 4.7 in textbook). 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 2. F A > F S 3. F A < F S correct a=F/m F same lower mass gives larger a Third Law!

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Physics 101: Lecture 8, Pg 15 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

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Physics 101: Lecture 8, Pg 16 Forces: 1. Gravity r 12 m1m1 m2m2 F 2,1 F 1,2 F 1,2 = force on m 1 due to m 2 = = F 2,1 = force on m 2 due to m 1 Direction: along line connecting the masses; attractive G = universal gravitation constant = x N m 2 /kg 2 Example: two 1 kg masses separated by 1 m Force = 6.67 x N (very weak, but this holds the universe together!)

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Physics 101: Lecture 8, Pg 17 Gravity and Weight Force on mass: MeMe ReRe mass on surface of Earth m g F g W = mg

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Physics 101: Lecture 8, Pg 18 Forces: 2. Normal Force book at rest on table: What are forces on book? W Weight is downward System is “in equilibrium” (acceleration = 0 net force = 0) Therefore, weight balanced by another force FNFN 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

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Physics 101: Lecture 8, Pg 19 Forces: 3. Kinetic Friction Kinetic Friction (aka Sliding Friction): A force, f k, between two surfaces that opposes relative motion. Magnitude: f k = k F N k = coefficient of kinetic friction a property of the two surfaces W FNFN Ffkfk direction of motion

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Physics 101: Lecture 8, Pg 20 Forces: 3. Static Friction W FNFN F fsfs Static Friction: A force, f s, between two surfaces that prevents relative motion. f s ≤ f s max = s F N force just before breakaway s = coefficient of static friction a property of the two surfaces

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Physics 101: Lecture 8, Pg 21 Forces: 4. Tension Tension: force exerted by a rope (or string) Magnitude: same everywhere in rope Not changed by pulleys Direction: same as direction of rope. T

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Physics 101: Lecture 8, Pg 22 Forces: 4. Tension example: box hangs from a rope attached to ceiling T W y F y = ma y T - W = ma y T = W + ma y In this case a y = 0 So T = W

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Physics 101: Lecture 8, Pg 23 Examples: Inertia l Seat-belt mechanism (see textbook) l A man dangles his watch from a thin chain as his plane takes off. He observes that the chain makes an angle of 30 degrees with respect to the vertical while the plane accelerates on the runway for takeoff, which takes 16 s. What is the speed of the aircraft at takeoff ?

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Physics 101: Lecture 8, Pg 24 Examples: Tension l A lamp of mass 4 kg is stylishly hung from the ceiling by two wires making angles of 30 and 40 degrees. Find the tension in the wires.

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Physics 101: Lecture 8, Pg 25 Examples: l Consider two blocks of mass m1 and m2 respectively tied by a string (massless). Mass m1 sits on a horizontal frictionless table, and mass m2 hangs over a pilley. If the system is let go, compute the aceleration and the tension in the string.

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