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Mass and Weight An Introduction to Forces PHYS& 121: Eyres Mass and Weight Gm1m2 F= r2 • Mass ( in kg) is a fundamental quantity • Weight is the attractive force between 2 objects that have mass. ( in N) F= Gm1m2 r2 Four Types • weight: – Pulling – Between 2 objects with mass • Tension: – Pulling – Must have a rope or string or spring attached Gmearth (mobject ) F= r2 • normal: – Pushing – Due to contact with a surface • friction: N F = 9.8 (mobject ) kg – Opposite direction to motion or the direction of potential motion – Rubbing (kinetic friction) or “Stickyness” associated with “trying to move it” (static friciton) Force Notation Newton’s Laws • I am pushing down on a book that is lying on the table. Force Type By On Symbol Direction Weight Earth Book W E on B Down Normal Me Book NM on B Down Normal Table Book NT on B Up • Newton’s 1st Law If there is no net Force, there is a constant velocity. What might the x vs t graph look like? What might the v vs t graph look like? What might the a vs t graph look like? 1 Newton’s Laws • Newton’s 1st Newton’s Laws • Newton’s 2nd Law Law ΣF = ma If there is no net Force, there is a constant velocity. What might the x vs t graph look like? What might the x vs t graph look like? What might the v vs t graph look like? What might the v vs t graph look like? What might the a vs t graph look like? What might the a vs t graph look like? Newton’s Laws • Newton’s 2nd 1st Law or 2nd Law? Graph Sketches? Law F = ma What might the x vs t graph look like? X=0 What might the v vs t graph look like? What might the a vs t graph look like? 1st Law or 2nd Law? Graph Sketches? X=0 x vs. t 1st Law or 2nd Law? Graph Sketches? X=0 Constant Speed therefore ∆v=0 and a=0 v vs. t therefore 1st Law a vs. t 2 1st Law or 2nd Law? Graph Sketches? 1st Law or 2nd Law? Graph Sketches? X=0 X=0 x vs. t Speeding up therefore v vs. t ∆v not 0 and a not 0 therefore 2nd Law a vs. t 1st Law or 2nd Law? Graph Sketches? X=0 x vs. t Slowing down Newton’s Laws • Newton’s 3rd Law If Object 1 pushes on Object 2 then Object 2 pushes on Object 1 v vs. t Law On 1 By 2 • This can help to identify forces therefore 2nd N21 N12 therefore ∆v not 0 and a not 0 On 2 By 1 a vs. t Free-Body Diagrams • Circle the object of interest • Choose a coordinate system Is the object moving horizontal or vertical? Pick a standard system Is the object moving up or down a slope? Pick a slanted system or Free-Body Diagrams • Identify your vectors On and By and Direction of Forces Table By Weight Earth On B Normal Ground B Normal Dad B 3 Free-Body Diagrams • Draw coordinate system • Add vectors (don’t worry about length) By Use FBD to Solve On Weight Earth • Add component information to the vector table. • Put in values if you know them. B Normal Ground B Normal Dad B NBG + WBE Use FBD to Solve • Write Newton’s 2nd Law Equations in Component Form Weight 0 y -wy + ny Normal + nx 0 + nBD = max Normal 0 -wy + ny Normal + nx 0 NBG NBD Other Force Information x Normal 0 ΣFx = max Weight 0 y + NBD WBE x ΣFy = may − wBE + nBG = may • • • • Weight: w=mg Friction: f=µn T is the same all along a taught rope/string Springs: nbyspring=-ksp∆x or Tbyspring=-ksp∆x – Springs push (n) when they are constricted – Springs pull (T) when they are extended Note: Why the minus sign? Because ∆x is in the opposite direction to Fsp 4
