1′ Lecture Newton’s Laws of Motion are: Newton’s Laws of Motion are: Acceleration (or deceleration) occurs if and only if there is a net external force. Acceleration (or deceleration) occurs if and only if there is a net external force. a = F/m [Note this is a vector eqn.] 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. F 12 = - F 21 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. F 12 = - F 21 Physics 1710 Chapter 5: Laws of Motion—II

1′ Lecture –continued (30″ more) Weight is the force of gravity equal to g times the mass of the object. Weight is the force of gravity equal to g times the mass of the object. g =9.80 N/kg g =9.80 N/kg The force of friction is opposed to the motion of a body and proportional to the normal force. 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. Free body diagrams are sketches of all the forces acting on a body. Physics 1710 Chapter 5: Laws of Motion—II

Laws of Motion 1 st Law: An acceleration is caused by a net external force. Physics 1710 Chapter 5: Laws of Motion—II

2 nd Law of Motion: a= F /m Note the vector nature of the equation: a x = F x /m a y = F y /m Physics 1710 Chapter 5: Laws of Motion—II

2 nd 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

2 nd Law of Motion: Implications Consider free fall (in the absence of air resistance): Consider free fall (in the absence of air resistance): Weight = F = m g fact #1 F = m a fact #2 ∴ m a g = m g ∴ a g = g Physics 1710 Chapter 5: Laws of Motion—II

2 nd Law of Motion: Implications Feather and Penny Demonstration Physics 1710 Chapter 5: Laws of Motion—II

2 nd 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

2 nd Law of Motion: Implications Book and Paper Physics 1710 Chapter 5: Laws of Motion—II a Book = (- gM + C Drag v 2 Book )/M a Paper = (- gm+ C Drag v 2 Paper ) /m - gM - gm C Drag v 2 Book C Drag v 2 Paper Book wins!

2 nd Law of Motion: Implications Book and Paper Physics 1710 Chapter 5: Laws of Motion—II a Book+Paper = (- gM - gm+ C Drag v 2 )/(M+m) - gM - gm C Drag v 2 Tie!

2 nd Law of Motion: Implications Atwood Machine Physics 1710 Chapter 5: Laws of Motion—II

2 nd Law of Motion: Implications Atwood Machine F = g (m 2 – m 1 ) a = F/(m 2 +m 1 ) a a g m 1 g m 2 a = g(m 2 – m 1 )/(m 2 +m 1 )

2 nd Law of Motion: Implications How much force is one Newton? How much force is one Newton? How much mass weighs 1 N? How much mass weighs 1 N? F = m g 1.00 N = m N (9.80 N/kg) m N = 1.00/ 9.80 kg m N = kg Experience “Newton’s apple” Physics 1710 Chapter 5: Laws of Motion—II

2 nd Law of Motion: Implications What acceleration will one Newton produce on a mass of one kilogram? What acceleration will one Newton produce on a mass of one kilogram? Physics 1710 Chapter 5: Laws of Motion—II a = F /m a = 1.00 N /1.00 kg a = 1.00 m/s 2 [ m/s 2 ] = [N ]/[kg]

2 nd Law of Motion: Implications Mysterious Spool Puzzle Physics 1710 Chapter 5: Laws of Motion—II Spool F ⃗ Toward F Away from F No acceleration Pull ?????????

2 nd Law of Motion: Implications Mysterious Spool Puzzle Physics 1710 Chapter 5: Laws of Motion—II Spool F ⃗ Toward F Pull a = F/m; a, always in the direction of F

Summary: Newton’s Laws of Motion are: Newton’s Laws of Motion are: (1) Acceleration (or deceleration) occurs if and only if there is a net external force. (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.] (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. F 12 = - F 21 (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. F 12 = - F 21 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. Weight is the force of gravity equal to g times the mass of the object. g =9.80 N/kg g =9.80 N/kg The force of friction is opposed to the motion of a body and proportional to the normal force. 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. Free body diagrams are sketches of all the forces acting on a body. Physics 1710 Chapter 5: Laws of Motion—II