Phys 1501Q 1st Edition Lecture 8Outline of Last 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 ExampleOutline of Current Lecture: Forces and Free Body DiagramsThese 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.I. Spring ForceII. Hooks LawIII. GravityIV. Newton’s Law of Universal GravitationV. Calculate Mass Using Newton’s Law of GravityVI. Tension CheckpointVII. Spring CheckpointVIII. Elevator AccelerationIX. Block on an Inclined Plane ExampleCurrent Lecture: Forces and Free Body DiagramsI. Spring ForceIf a spring is stretched (made longer) or compressed (made shorter) from its equilibrium (normal position), it pulls or pushes back with a Force (Fs).- Restoring Force:Fs is a restoring force meaning it acts to restore the spring to its original position  this leads to oscillations back and forth*x position has opposite sign as FsII. Hooks Law- Spring force  Fs= -kx- K is a spring constant value units of Newtons per meter (N/m)- This law applies for small values of x, not so big that the spring bends and distortsIII. Gravity (Fg)- For us gravity on the surface of the earth is Fg* -mg- Fg decreases as we move away from Earth - Gravity on Earth is the same gravity throughout the solar systemIV. Newton’s Law of Universal Gravitation- Any two masses in the universe attract each other with a force (gravity) that is directly proportional to the product of their masses and inversely proportional to thedistance(r) squared between the two masses- If you have a sphere (aka a uniform circular mass) it attracts as if all mass were concentrated in the center (point mass)- We can use this to calculate the mass of spherical objects like planets- G = Newton’s Gravitational ConstantG= 6.67 * 10^-11 Nm^2/kg^2Note: The force acts along the line “connecting”the two masses, forming an action/reaction pair.V. Calculate Mass Using Newton’s Law of GravityCalculate the mass of Earth. Earth’s surface radius (Re = 6.38*10^6)m.F=mg=Gm∗MeR2m cancelsF=Me=g∗R2GMe=9.8∗(6.38∗106)26.67∗10−11=radius of earth∗gravitygravitational constantMe=5.98 ∗1024kgVI. Tension CheckpointA box of mass is hung from an elevator accelerating upward. Whatis the T in the rope? T > mgThis is because the upward acceleration is making the box pulldown on the rope.T-mg = maT=a(m+g)VII. Spring CheckpointA box of mass is hung from a spring as an elevator acceleratesupward.  Spring gets longer, force increases This is because the box is pulling down on the spring Fs = m(a+g) Note: negative acceleration would make less tension and thespring would get shorted (ex if the elevator was acceleratingdownward)VIII. Elevator AccelerationYou are in an elevator and standing on a scale. You near the top as you slow down, the scale reads--? Less than your actual weight Why?N-mg = maN = m(g+a)N<NoIf a is negative g+a<gIX. Block on an Inclined Plane ExampleA block is on an inclined frictionless plane. Draw a free body diagram. Choose a convenientcoordinate system (align acceleration with axis)Force in X Direction: ax=- gsinθForce in Y Direction: y = -mgcosθ +N = m*ay = 0(Force in vertical direction is zero because blockdoesn’t jump off track)Limiting cases:Θ = 0° (flat plane)  sin0° = 0Θ = 90° (vertical plane)  then the box is in freefall at gaccelerationFree body diagram