Exam 1: Chapters % Problems – one problem from WebAssign with different numbers Understand homework problems Review notes and text Try new problems 25% Concept Questions Review Power Points (on web page) Review Before Class Assignments Try Questions Graphs, Pictures and Drawings (Sketches)

Chapter 5 The Laws of Motion 5.1 Force – a push or pull. CT1: The force of the elevator on Norbert and Zot is A. up. B. down.

CT2: The force of the non-sticky elevator surface on Norbert and Zot is A. up. B. down. Assume the elevator is near the Earth’s surface and that it is right-side up in the cartoon.

CT3: The acceleration of Norbert and Zot is A. up. B. down. C. zero Assume the elevator is near the Earth’s surface and that it is right-side up in the cartoon.

Fig. 5.1, p.113

A. B. C. D. E. CT4

5.2 Newton’s First Law: A body remains in uniform motion (or at rest) unless acted upon by a net external force.  acceleration due to Earth’s rotation  0.03 m/s 2  acceleration due to Earth’s orbit  m/s 2  acceleration due to Sun’s orbit  2 x m/s 2 We will assume that the Earth’s surface is an inertial frame and not make errors greater than 0.03/10 = 0.3%. An inertia frame of reference is a coordinate system (or frame) in which Newton’s Law’s hold.

Newton’s First Law involves force which is a vector so we can look at it separately in both the x and y directions. Remember Galileo! A mass which has inertia won’t move unless a force is applied. Demonstration What will happen to the egg, which is currently in a state of rest?

5.3 Mass: Mach’s definition uses the fact that for two isolated masses acting on each other m u a u = m s a s (where a 1 and a 2 are magnitudes) This fact is consistent with Newton’s formulation – in particular the 2 nd Law. Then m u = m s a s /a u

5.4 Newton’s Second Law: The net external force is equal to the mass times the acceleration. F = ma F x = ma x F y = ma y remember Galileo! F z = ma z Normally we will do problems in a plane with only x and y components.

A. B. C. D. E. CT5

A. B. C. D. E. CT6

5.5 Gravitational Force F g = mg (weight) g = -9.8 j (m/s 2 ) x y

5.6 Newton’s Third Law: If body A acts on body B, then body B acts back on body A with a force equal in magnitude but opposite in direction. A B F BA F AB

A. C. B. D. E. CT7

5.7 Applications of Newton’s Laws  Equilibrium is defined as F = 0. Remember Galileo!  Ropes, strings, cords, etc. are assumed massless unless otherwise stated. Thus tensions are the same throughout the rope, string, cord, etc.  Pulleys are assumed massless and mounted on frictionless bearings unless otherwise stated. Thus pulleys only change the direction of the force.

Applications of Newton’s Laws - Method  Draw picture of the problem.  Choose body (bodies) to isolate.  Draw Free Body Diagrams (FBDs) for isolated bodies.  Choose and label coordinate axes.  Apply Newton’s 2 nd Law: F x = ma x and F y = ma y  Solve for F, m or a.  Work out kinematics.  Check solution is reasonable. P5.2 (p.128)

F 1 = 20 N; F 2 = 15 N; m = 5.00 kgP5.9 (p.128)

CT8: What is a x in 6.9a in m/s 2 ? A. 1 B. 2 C. 3 D. 4 E. 5 CT9: What is a y in 6.9a in m/s 2 ? A. 1 B. 2 C. 3 D. 4 E. 5

Applications of Newton’s Laws - Method  Draw picture of the problem.  Choose body (bodies) to isolate.  Draw Free Body Diagrams (FBDs) for isolated bodies.  Choose and label coordinate axes.  Apply Newton’s 2 nd Law: F x = ma x and F y = ma y  Solve for F, m or a.  Work out kinematics.  Check solution is reasonable. P5.17 (p.129)

F = 18.0 N m 1 = 2.00 kg m 2 = 3.00 kg m 3 = 4.00 kg P5.54 (p.133)

P5.31 (p.131)

Fx (N)a (m/s2) a = F x /8 a = (F x -2g)/10 a = -g

D. C. B. A. CT10

X The engine or battery exerts a force on the object. X If an object is moving there is a “force of motion.”. X An object can’t exert a force on itself. X X X

D. C. B. A. CT11

X If an object moves, the third law pair forces must be unbalanced. X The moving object or a faster moving object exerts a greater force. X The student believes that inanimate/passive objects cannot exert a force. X X X X Newton’s Third Law! X

D. C. B. A. CT12

X The more active or energetic object exerts more force. X The bigger or heavier object exerts more force. X The student uses the effects of a force as an indication of the relative magnitudes of the forces in an interaction. X X X Newton’s Third Law!

D. C. B. A. CT13

X If an object moves, the third law pair forces must be unbalanced. X The student identifies equal force pairs, but indicates that both forces act on the same object. (For the example of a book at rest on a table, the gravitational force down on the book and the normal force up by the table on the book are identified as an action-reaction pair.) X The bigger or heavier object exerts more force. Newton’s Third Law! X X X

A. B. CT14

P5.27 (p.130)

5.8 Force of Friction

Force of Friction - Model  Static Friction f s   s n (as needed to maintain equilibrium)  Kinetic Friction f k =  k n (opposing motion)

A. B. C. D. E. CT15

 s = 0.25 m = 3.00 kg P5.39 (p.131) P5.44 (p.132)

Fig. P5.45, p.145 F = 68.0 N m 1 = kg m 2 = kg  k = P5.43 (p.132)

Applications of Newton’s Laws - Method  Draw picture of the problem.  Choose body (bodies) to isolate.  Draw Free Body Diagrams (FBDs) for isolated bodies.  Choose and label coordinate axes.  Apply Newton’s 2 nd Law: F x = ma x and F y = ma y  Solve for F, m or a.  Work out kinematics.  Check solution is reasonable.