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Transcript
Physics 1710 Chapter 5: Laws of Motion—II 1′ Lecture • Newton’s Laws of Motion are: Acceleration (or deceleration) occurs if and only if there is a net external force. a = F/m [Note this is a vector eqn.] The force exerted by a first object on a second is always equal and opposite the the force exerted by the second on the first. F12 = - F21 Physics 1710 Chapter 5: Laws of Motion—II 1′ Lecture –continued (30″ more) • Weight is the force of gravity equal to the mass of the object. g times • g =9.80 N/kg • The force of friction is opposed to the motion of a body and proportional to the normal force. • Free body diagrams are sketches of all the forces acting on a body. Physics 1710 Chapter 5: Laws of Motion—II Laws of Motion 1st Law: An acceleration is caused by a net external force. Physics 1710 Chapter 5: Laws of Motion—II 2nd Law of Motion: a= F /m Note the vector nature of the equation: ax= Fx /m ay= Fy /m Physics 1710 Chapter 5: Laws of Motion—II 2nd Law of Motion: Implications The Newton [N] is the unit of force in SI units. [F] = [m] [ a ] [N] = [kg] [m/s/s] Physics 1710 Chapter 5: Laws of Motion—II 2nd Law of Motion: Implications • Consider free fall (in the absence of air resistance): Weight = F = m g fact #1 F=ma fact #2 ∴ m ag = m g ∴ ag = g Physics 1710 Chapter 5: Laws of Motion—II 2nd Law of Motion: Implications Feather and Penny Demonstration Physics 1710 Chapter 5: Laws of Motion—II 2nd Law of Motion: Implications When a sheet of paper and a book are dropped at the same time, what will happen? Will (1) the book accelerate faster that the sheet; (2) vice versa or (3) will they each accelerate at the same rate? Why do you think so? Physics 1710 Chapter 5: Laws of Motion—II 2nd Law of Motion: Implications Book and Paper Book wins! CDrag v2 Book - gM CDrag v2 Paper - gm aPaper = (- gm+ CDrag v2 Paper) /m aBook = (- gM + CDrag v2 Book)/M Physics 1710 Chapter 5: Laws of Motion—II 2nd Law of Motion: Implications Book and Paper Tie! CDrag v2 - gm - gM aBook+Paper = (- gM - gm+ CDrag v2)/(M+m) Physics 1710 Chapter 5: Laws of Motion—II 2nd Law of Motion: Implications Atwood Machine Physics 1710 Chapter 5: Laws of Motion—II 2nd Law of Motion: Implications Atwood Machine F = g (m2 – m1) a = F/(m2 +m1) a = g(m2 – m1)/(m2 +m1) a a g m1 g m2 Physics 1710 Chapter 5: Laws of Motion—II 2nd Law of Motion: Implications • How much force is one Newton? • How much mass weighs 1 N? F=mg 1.00 N = mN (9.80 N/kg) mN = 1.00/ 9.80 kg mN = 0.102 kg Experience “Newton’s apple” Physics 1710 Chapter 5: Laws of Motion—II 2nd Law of Motion: Implications • What acceleration will one Newton produce on a mass of one kilogram? a = F /m a = 1.00 N /1.00 kg a = 1.00 m/s2 [ m/s2] = [N ]/[kg] Physics 1710 Chapter 5: Laws of Motion—II 2nd Law of Motion: Implications Mysterious Spool Puzzle Spool F⃗ Pull Away from F Toward F No acceleration ????????? Physics 1710 Chapter 5: Laws of Motion—II 2nd Law of Motion: Implications Mysterious Spool Puzzle Spool F⃗ Pull Toward F a = F/m; a, always in the direction of F Physics 1710 Chapter 5: Laws of Motion—II Summary: • Newton’s Laws of Motion are: (1) Acceleration (or deceleration) occurs if and only if there is a net external force. (2) a = F/m [Note this is a vector eqn.] (3) The force exerted by a first object on a second is always equal and opposite the the force exerted by the second on the first. F12 = - F21 Physics 1710 Chapter 5: Laws of Motion—II Summary (cont’d.) : • Weight is the force of gravity equal to g times the mass of the object. • g =9.80 N/kg • The force of friction is opposed to the motion of a body and proportional to the normal force. • Free body diagrams are sketches of all the forces acting on a body.