Chapter 4 Outline Newton’s Laws of Motion

1. Chapter 4 OutlineNewton’s Laws of Motion • Forces • Contact and long range • Superposition • Free-body diagrams • Newton’s first law • Inertial frames of reference • Newton’s second law • Mass vs. weight • Newton’s third law

2. Forces • Forces are interactions between two bodies or between a body and the environment. • Contact force • Push, pull, friction… • Long-range • Gravitational, electric, magnetic… • Vectors!

3. Superposition of Forces • When more than one force is acting on a body, the net force is the vector sum of the forces. • Sometimes the net force is called the resultant force, .

4. Free-Body Diagram • A free-body diagram helps us to understand what forces are relevant and how to apply them to analyze a situation. • Choose the body • Only include forces acting on that body

5. Newton’s First Law • Natural state of an object • Aristotle, Galileo, Descartes… • From Pricipia, the Latin followed by an English translation. “Lex I: Corpus omneperseverare in statusuoquiescendivelmovendiuniformiter in directum, nisi quatenus a viribusimpressiscogiturstatumillummutare.” “Law I: Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.” • From our text: A body acted on by no net force moves with constant velocity (which may be zero) and zero acceleration.

6. Inertial Frame of Reference • Is Newton’s first law always obeyed? • An inertial frame of reference is a frame in which Newton’s first law holds. • The frame moves with constant velocity. • Any inertial frame is equally valid, so we choose the one that is easiest to work with.

7. Newton’s Second Law • What happens when the net force is not zero? • From Pricipia, the Latin followed by an English translation. “Lex II: Mutationemmotusproportionalemesse vi motriciimpressae, et fierisecundumlineamrectam qua vis illaimprimitur.” “Law II: The alteration of motion is ever proportional to the motive force impress'd; and is made in the direction of the right line in which that force is impress'd.” • From our text: If a net external force acts on a body, the body accelerates. The direction is the same as the direction of the net force. The mass of the body times the acceleration of the body equals the net force vector.

8. Newton’s Second Law • More succinctly, • Units: • We measure mass in and acceleration in , so force must have the unit of . • This is a newton, . • A pound (or pound-force) is about .

9. Newton’s Second Law Example

10. Mass vs. Weight • Weight is the force due to gravity acting on a body. • Force, so measured in newtons, . • On the earth’s surface, , but the local gravity, and therefore weight is different elsewhere. • Mass is intrinsic to the body and describes its inertial properties (as well as gravitational attraction to other masses). • Measured in kilograms, .

11. Mass vs. Weight Example

12. Newton’s Third Law • Forces arise from interactions between bodies. Can one body exert a force on another without being affected itself? • From Pricipia, the Latin followed by an English translation. “Lex III: Actionicontrariam semper et æqualemessereactionem: sivecorporumduorumactiones in se mutuo semper esseæquales et in partescontrariasdirigi.” “Law III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.” • From our text: If body exerts a force on body (an “action”), then body exerts a force on body (a “reaction”). These two forces have the same magnitude but are opposite in direction. These two forces act on different bodies.

13. Newton’s Third Law Example

14. Chapter 4 SummaryNewton’s Laws of Motion • Forces • Superposition: • Free-body diagrams • Draw all forces acting on a body • Newton’s first law: • Inertial frames of reference • Newton’s second law: • Mass vs.weight: • Newton’s third law:

15. Newton’s Second Law Example #2

16. Newton’s Third Law Example #2