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

Sir Isaac Newton, English Physicist, 1643-1727

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  velocity is constant acceleration is zero no change of direction of motion

Mass or Inertia Inertia is the tendency of an object to remain at rest or in motion with constant speed along a straight line. 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. Units: [M] = kg

Newton’s Second Law This law tells us how motion changes when a net force is applied. acceleration = (net force)/mass Stimulus is Force (cause) Resistance is mass (control rod) Response is acceleration (effect)

Newton’s Second Law Units: [F] = [M] [a] A vector equation: [F] = kg m/s2 1 Newton (N)  1 kg m/s2 A vector equation: Fnet,x = Max Fnet,y = May

Newton’s 1. Law 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

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 SF= ma = m0 = 0

Example: Newton’s 2. Law M=10 kg F1=200 N Find a F1 M a = Fnet/M = 200N/10kg = 20 m/s2 M F1 M=10 kg F1=200 N F2 = 100 N Find a F2 a = Fnet/M = (200N-100N)/10kg = 10 m/s2

Newton’s Third Law For every action, there is an equal and opposite reaction. Finger pushes on box Ffingerbox = force exerted on box by finger Ffingerbox Box pushes on finger Fboxfinger = force exerted on finger by box Fboxfinger Third Law: Fboxfinger = - Ffingerbox

Newton's Third Law... FA ,B = - FB ,A. is true for all types of forces Fw,m Fm,w Ff,m Fm,f

Conceptual Question: Newton’s 3.Law Since Fm,b = -Fb,m why isn’t Fnet = 0, and a = 0 ? Fb,m Fm,b a ?? ice

Conceptual Question: Answer Consider only the box ! Fnet, box = mbox abox = Fm,b What about forces on man? Fnet,man = mman aman = Fb,m Fb,m Fm,b abox Skateboard demo: get two students with obviously different masses. Show that acceleration is different although force is same. ice

Newton’s 2. and 3. Law Third Law! a=F/m 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, FS, to the magnitude of the force exerted by the spacecraft on you, FA, while you are pushing: 1. FA = FS 2. FA > FS 3. FA < FS Third Law! correct 2) Compare the magnitudes of the acceleration you experience, aA, to the magnitude of the acceleration of the spacecraft, aS, while you are pushing: 1. aA = aS 2. aA > aS 3. aA < aS correct a=F/m F same  lower mass gives larger a

Summary: Newton’s First Law: Newton’s Second Law: Fnet = ma The motion of an object does not change unless it is acted on by a net force Newton’s Second Law: Fnet = ma Newton’s Third Law: Fa,b = -Fb,a

Forces: 1. Gravity r12 m1 m2 F2,1 F1,2 F1,2 = force on m1 due to m2 = Direction: along line connecting the masses; attractive G = universal gravitation constant = 6.673 x 10-11 N m2/kg2 Example: two 1 kg masses separated by 1 m Force = 6.67 x 10-11 N (very weak, but this holds the universe together!)

 Fg  W = mg Gravity and Weight m Re mass on surface Force on mass: Me Re mass on surface of Earth m Force on mass:  g Fg  W = mg

Forces: 2. Normal Force FN 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 FN = “normal force” = force exerted by surface on object FN is always perpendicular to surface and outward For this example FN = W

Forces: 3. Kinetic Friction FN direction of motion fk F W Kinetic Friction (aka Sliding Friction): A force, fk, between two surfaces that opposes relative motion. Magnitude: fk = kFN k = coefficient of kinetic friction a property of the two surfaces

Forces: 3. Static Friction FN fs F W Static Friction: A force, fs, between two surfaces that prevents relative motion. fs ≤ fsmax= sFN force just before breakaway s = coefficient of static friction a property of the two surfaces

Forces: 4. Tension T Tension: force exerted by a rope (or string) Magnitude: same everywhere in rope Not changed by pulleys Direction: same as direction of rope.

Forces: 4. Tension example: box hangs from a rope attached to ceiling y SFy = may T - W = may T = W + may T W In this case ay = 0 So T = W

Examples: Inertia Seat-belt mechanism (see textbook) 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 ?

Examples: Tension 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.

Examples: 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.