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—III

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—III

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

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—III REVIEW

Third Law of Motion: If two objects interact, the force of the 1 st on the 2 nd is equal and opposite to the force of the 2 nd acting on the 1st body. F 12 = - F 21 F 12 = - F 21 Physics 1710 Chapter 5: Laws of Motion—III F 12 F 12 F 21 F 21 #1#2

3 rd Law in Action—Tug of War Physics 1710 Chapter 5: Laws of Motion—III ? It’s the Law! F 12 = - F 21 #1#2 F 12 F 21

Third Law of Motion, Implications : Baron von Munchenhausen Draw “free body diagram” Physics 1710 Chapter 5: Laws of Motion—III Lou Geels As Baron von Munchenhausen Arm force = - Reaction force Net force = 0 F 12 = - F 21

1. 1.The tree is not pushing on the elephant The tree is pushing back, but the elephant is pushing harder The tree is pushing harder on the elephant that she is pushing on the tree The tree and elephant push equally against each other. Physics 1710 Chapter 5: Laws of Motion—III 1. 1.The tree is not pushing on the elephant The tree is pushing back, but the elephant is pushing harder The tree is pushing harder on the elephant that she is pushing on the tree The tree and elephant push equally against each other. But how can you have acceleration in this case? The acceleration of object #2 is a 2 = F 12 /m 2 Not 0 = ( F 12 +F 21 )/(m 1 + m 2 )

Third Law of Motion, Implications : Tug of war Draw “free body diagram” Physics 1710 Chapter 5: Laws of Motion—III

Third Law of Motion, Implications : Tug of war :“free body diagram” m M Rope tension F 12 F 21 -mg-Mg Floor reaction: mg Mg Friction: -μ (mg) Friction: μ (Mg) Weight Resultant: F m = F 12 – μ(mg) F M = 0 Physics 1710 Chapter 5: Laws of Motion—III

Third Law of Motion, Implications : Why does mud fly backward from the tire when an automobile accelerates in mud? Why does mud fly backward from the tire when an automobile accelerates in mud? For each “action” and equal but “opposite action” must happen. For each “action” and equal but “opposite action” must happen. Physics 1710 Chapter 5: Laws of Motion—III

2 nd and 3 rd Laws of Motion: Implications Why does air have “resistance?” Physics 1710 Chapter 5: Laws of Motion—III - gm F drag F drag - gm F drag F drag

No Talking! Think! Confer! Peer Instruction Time Physics 1710 Chapter 5: Laws of Motion—III

2 nd and 3 rd Laws of Motion: Implications Why does air have “resistance?” Physics 1710 Chapter 5: Laws of Motion—III - gm F drag F drag Δm air = ρAv Δt a air = v/ Δt F air, max = Δm air a air = (ρAv Δt)(v/ Δt) = ρAv 2 F air = ½ D ρAv 2 = - F drag - gm F drag F drag Inertia of the air in the way

Why do objects stop moving? Why do objects stop moving? Friction is a force that resists motion. Friction is a force that resists motion. Friction is proportional to the “normal” forceFriction is proportional to the “normal” force (ie perpendicular force) and opposed to the direction of the applied force. Physics 1710 Chapter 5: Laws of Motion—III

F f = - μN, in opposite direction of applied force. μ is the coefficient of friction, which μ is the coefficient of friction, which depends upon the nature of the two surfaces in contact and the state of motion. Physics 1710 Chapter 5: Laws of Motion—III Empirical Observation:

Friction is caused by “welding” of the two surfaces. Lubrication changes the nature of the contact and/or the surface, atomically. Physics 1710 Chapter 5: Laws of Motion—III

Friction is caused by “welding” of the two surfaces. Physics 1710 Chapter 5: Laws of Motion—III Welds

Effect of Normal Force—more contact. Physics 1710 Chapter 5: Laws of Motion—III N N More contact points F f,max = μN

Friction is caused by “welding” of the two surfaces. Physics 1710 Chapter 5: Laws of Motion—III Lubrication changes the nature of the contact and/or the surface, atomically.

Rolling Friction: Physics 1710 Chapter 5: Laws of Motion—III F f = μN N Normal Force Adhesion

Rolling Friction: Lubrication Physics 1710 Chapter 5: Laws of Motion—III F f = μN N Normal Force No Adhesion

No Talking! Think! Confer! Peer Instruction Time Physics 1710 Chapter 5: Laws of Motion—III

Friction, Application: For constant velocity F = -F f = -(- μ N) For constant velocity F = -F f = -(- μ N) N = m g = (5.2 kg)(9.8 N/kg) = 51. N N = m g = (5.2 kg)(9.8 N/kg) = 51. N F = (0.30) (51. N) = 15. N F = (0.30) (51. N) = 15. N Physics 1710 Chapter 5: Laws of Motion—III

Third Law of Motion, Implications : A father (100 kg) and his daughter A father (100 kg) and his daughter (50 kg) are ice skating. The push off from each other. Who pushes harder? What is there relative acceleration? What is there relative acceleration? Physics 1710 Chapter 5: Laws of Motion—III

Mm Mm F Dad F kid Third Law of Motion, Implications : A father (100 kg) and his daughter A father (100 kg) and his daughter (50 kg) are ice skating. The push off from each other. Who pushes harder? Physics 1710 Chapter 5: Laws of Motion—III

Mm Mm -FF Third Law of Motion, Implications : A father (100 kg) and his daughter A father (100 kg) and his daughter (50 kg) are ice skating. The push off from each other. Who pushes harder? Physics 1710 Chapter 5: Laws of Motion—III a M =-F/M a m =F/m 3 rd Law of Motion says they push the same and opposite.

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—III

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—III