Physics 1501: Lecture 7, Pg 1 Physics 1501: Lecture 7 Today’s Agenda l Announcements: çPhysics Learning Center P201: »Schedule posted on the door çHomeworks »Lowest HW will be dropped »HW 02: due next Monday çToday’s topics: »Newton’s laws »Applications of Newton’s laws

Physics 1501: Lecture 7, Pg 2 Dynamics

Physics 1501: Lecture 7, Pg 3 Review Newton’s Laws 1 and 2 l Isaac Newton ( ) published Principia Mathematica in In this work, he proposed three “laws” of motion: Law 1: An object subject to no external forces is at rest or moves with a constant velocity if viewed from an inertial reference frame. FFa Law 2: For any object, F NET =  F = ma Force and mass

Physics 1501: Lecture 7, Pg 4 Lecture 7, ACT 1 Newton’s Second Law A constant force is exerted on a cart that is initially at rest on an air table. The force acts for a short period of time and gives the cart a certain final speed. Air Track Cart Force For a second shot, I can apply a force only half as large (I’m getting tired). To reach the same final speed, for how long must I apply the force ? A) 4 x as longB) 2 x as longC) Same time D) 1/2 as longE) 1/4 x as long

Physics 1501: Lecture 7, Pg 5 Lecture 7, ACT 2 Newton’s Second Law I push with a force of 2 Newtons on a cart that is initially at rest on an air table with no air. I push for a second. Because there is no air, the cart stops after I finish pushing. It has traveled a certain distance. Air Track Cart Force For a second shot, I push just as hard but keep pushing for 2 seconds. The distance the cart moves the second time versus the first is, A) 4 x as longB) 2 x as longC) Same D) 1/2 as longE) 1/4 x as long

Physics 1501: Lecture 7, Pg 6 Lecture 7, ACT 3 Newton’s Second Law A constant force is exerted on a cart that is initially at rest on an air table. This force is applied for a short period of time and the cart acquires a certain final speed, which I call v f1. Air Track Cart Force I repeat the experiment, but this time the cart is already moving with constant speed when I start applying the force. After exerting the same constant force for the same time interval, the cart’s final speed is, A) v f1 B) 2v f1 C) v f1 2 D) cannot be determined from the information given.

Physics 1501: Lecture 7, Pg 7 Newton’s Third Law: If object 1 exerts a force on object 2 (F 2,1 ) then object 2 exerts an equal and opposite force on object 1 (F 1,2 ) F 1,2 = -F 2,1 For every “action” there is an equal and opposite “reaction” This is among the most abused concepts in physics. REMEMBER: Newton ’ s 3rd law concerns force pairs which act on two different objects (not on the same object) !

Physics 1501: Lecture 7, Pg 8 An Example F B,E = - m B g EARTH F E,B = m B g Consider the forces on an object undergoing projectile motion F B,E = - m B g F E,B = m B g

Physics 1501: Lecture 7, Pg 9 Lecture 7, ACT 4 Newton’s Third Law A fly gets smushed onto the windshield of a speeding bus.  The force exerted by the bus on the fly is, A) greater than B) the same as C) less than that exerted by the fly on the bus.

Physics 1501: Lecture 7, Pg 10 Lecture 7, ACT 5 Newton’s Third Law A fly gets smushed onto the windshield of a speeding bus.  The acceleration due to this collision of the bus is, A) greater than B) the same as C) less than that of the fly.

Physics 1501: Lecture 7, Pg 11 Newton's Third Law... FF l F A,B = - F B,A an example, F F m,w F F w,m F F m,f F F f,m

Physics 1501: Lecture 7, Pg 12 Example of Bad Thinking FFFa l Since F m,b = -F b,m why isn’t F net = 0, and a = 0 ? a ?? F F m,b F F b,m ice

Physics 1501: Lecture 7, Pg 13 Example of Good Thinking only the box l Consider only the box as the system! çFree Body Diagram F F m,b F F b,m ice

Physics 1501: Lecture 7, Pg 14 Example of Good Thinking only the box l Consider only the box as the system! çFree Body Diagram a box F F b,m FgFg FNFN a box = F b,m /m box

Physics 1501: Lecture 7, Pg 15 Free Body Diagram A heavy sign is hung between two poles by a rope at each corner extending to the poles. Eat at Bob ’ s What are the forces on the sign ?

Physics 1501: Lecture 7, Pg 16 Free Body Diagram Eat at Bob ’ s   T1T1 T2T2 Add vectors  mgmg  T1T1 T2T2 mgmg

Physics 1501: Lecture 7, Pg 17 Free Body Diagram Eat at Bob ’ s   T1T1 T2T2 mgmg Vertical : mg = T 1 sin  1 + T 2 sin  2 Horizontal : T 1 cos  1 = T 2 cos  2

Physics 1501: Lecture 7, Pg 18 Normal Forces and String Tension Certain forces act to keep an object in place. These have what ever force needed to balance all others (until a breaking point). F T,B F B,T

Physics 1501: Lecture 7, Pg 19 Force Pairs Newton’s 3rd law concerns force pairs. Two members of a force pair cannot act on the same object. Don’t confuse gravity (the force of the earth on an object) and normal forces. It’s an extra part of the problem. F T,B F B,T F B,E = -mg F E,B = mg

Physics 1501: Lecture 7, Pg 20 Lecture 7, Act 6 Newton’s 3rd Law l Two blocks are being pushed by a finger on a horizontal frictionless floor. How many action-reaction pairs of forces are present in this system? (a) 2 (b) 4(c) 6 a b

Physics 1501: Lecture 7, Pg 21 An Example Consider the following two cases

Physics 1501: Lecture 7, Pg 22 An Example The Free Body Diagrams mgmgmgmg F B,T = N Ball Falls For Static Situation N = mg

Physics 1501: Lecture 7, Pg 23 An Example The action/reaction pair forces F B,E = -mg F B,T = N F E,B = mg F B,E = -mg F E,B = mg F T,B = -N

Physics 1501: Lecture 7, Pg 24 Lecture 7, ACT 7 Gravity and Normal Forces A woman in an elevator is accelerating upwards The normal force exerted by the elevator on the woman is, A) greater than B) the same as C) less than the force due to gravity acting on the woman

Physics 1501: Lecture 7, Pg 25 Lecture 7, ACT 7b Gravity and Normal Forces A woman in an elevator is accelerating upwards The normal force exerted by the elevator on the woman is, A) greater than B) the same as C) less than the force the woman exerts on the elevator.

Physics 1501: Lecture 7, Pg 26 Exercise: Inclined plane A block of mass m slides down a frictionless ramp that makes angle  with respect to horizontal. What is its acceleration a ?  m a

Physics 1501: Lecture 7, Pg 27 Inclined plane... l Define convenient axes parallel and perpendicular to plane: ç Acceleration a is in x direction only.  m a i j

Physics 1501: Lecture 7, Pg 28 Inclined plane... l Consider x and y components separately: i i: mg sin  = ma a = g sin  j j: N - mg cos . N = mg cos  gmggmg N mg sin  mg cos   amaama i j

Physics 1501: Lecture 7, Pg 29 Angles of an Inclined plane    ma = mg sin    mg N