Phys 1501Q 1st Edition Lecture 7Outline of Last Lecture: Relative Motion & Uniform Circular MotionI. Relative MotionII. Reference FrameIII. Reference Frame ExampleIV. 2-D Relative Motion ExampleV. Moving Sidewalk ExampleVI. Crossing a River ExampleVII. Uniform Circular Motion/Centripetal Accelerationa. Velocity Vector b. Finding accelerationVIII. Example of Circular MotionIX. Getting Accelerationa. Using Derivativeb. Finding magnitudec. Finding directionX. Circular Motion Important Notesa. Angles/Angular Frequencyb. PeriodThese notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.c. CircumferenceXI. Calculating Centripetal Acceleration ExampleOutline of Current Lecture: Newton’s LawsI. Newton’s First LawII. Inertial Reference FrameIII. Force IV. MassV. InertiaVI. Newton’s Second LawVII. Newton’s Third LawVIII. Example of Third LawIX. Units of ForceX. Examples of Forcesa. Weightb. Normal Forcec. Frictiond. Tensione. Spring ForceXI. Steps of Applications of Newton’s LawsXII. Piano Hanging ExampleCurrent Lecture: Newton’s Laws I. Newton’s First Law- An object maintains its velocity if no net force acts on it- This applies to objects at rest (v=0) and objects moving at constant velocity- A force does NOT have to be applied to KEEP an object in motionII. Inertial Reference Frame- A reference frame that is not accelerating- All observers in inertial reference frames agree with forces occurring thereIII. Force - Something that acts on an object and causes it to accelerate- Force is a vector and must be treated as such- Net force: Sum of all forces acting on an objectIV. Mass- Intrinsic property of a body, the amount of matter in an object- Mass is NOT weight. Mass is measured in kg.o Weight is a force measured in Newtons.- Mass determines how hard it is to accelerateo Large mass=hard to accelerate (more inertia)o Smaller mass=easier to accelerate (less inertia)V. Inertia- An object’s reluctance to change in motion- Property of an object to maintain velocityVI. Newton’s Second Law- Fnet = ma (force and acceleration are vectors)- Fnet is the sum of all external forces acting on a body- If F=0  a=0 V= constant or 0- When a force acts on an object it makes it accelerate in the same direction as the force- MASS – determines the magnitude of the acceleration- FORCE – determines the direction and the cause of accelerationVII. Newton’s Third Law- For every action, there is an equal and opposite reaction-FAB= FBA- Forces are never isolated and always come in pairs- Note FAB means the force exerted on A by BVIII. Third Law ExampleEarth exerts gravitational force on you, you exert the SAME force (opposite direction) back on earth.- Because Mass of Earth > Mass of You, the acceleration of Earth is SMALLER compared to the acceleration you experience- Forces are the same, accelerations are not- Forces do not cancel, they act on different objectsIX. Units of ForceName/Symbol Units Mass Acceleration SystemNewton(N) Kg*m/s^2 Kg m/s2 SI System Pound (lb) Slug*ft/s^2 Slug Ft/s^2 Imperial SystemX. Examples of Forcesa. Weighto W= - mass *gravity j (vertical direction)o Due to gravitational attractionb. Normal Forceo Force perpendicular to surfacec. Frictiono Opposes acceleration/sliding motiono Due to surface contactd. Tensiono Force exerted by a taut cord/wire/rope/string/chaino Tension is always directed along the direction of the corde. Spring Forceo A restoring force that acts to bring the spring back to its original positionXI. Steps of Applications of Newton’s Laws1. Draw a picture of the system2. Focus on one object at a time3. Draw a free body diagram showing all forces acting on each object4. Choose a coordinate systema. Put one force parallel along an axis5. Apply Newton’s second law to each component in the system. The sum of all forces must equal mass* acceleration6. Include constraints7. Solve component equations for unknowns8. Check limiting casesXII. Piano Hanging Example2 people are holding a piano between 2 buildings by ropes- Ropes are not necessarily the same length- Find tension (T) in each rope1. Free body diagramWe know net force = 0 because it’s not accelerating2. Find x and y componentsX component: -T1sinθ+T2sinθ2 = max = 0  T2 = T1sinθ/sinθ2*Y component: T1cosθ + T2cosθ2 – w = 0  w=mg*substitute this T2 value equation into the Y component equationT1cosθ + (T1sinθ/sinθ2)*cosθ2 = mgSolve for T1T1 = mg/(cosθ + (sinθ/tanθ2))Solve for T2T2 = mg/((sinθ2/tanθ)+cosθ2)Note:If θ=θ2  T1=T2  = mg/2cosθIf θ=0  T1=mg T2=0  piano hangs straight down from one