The laws of motion (chapter four)

1. The laws of motion (chapter four) • Kinematics – answers the question “how?” • Statics and dynamics answer the question “why?” • Force • Newton’s 1st law (object at rest/motion stays that way) • Inertial mass • Newton’s 2nd law (F=ma) • Gravity • Newton’s 3rd law (Action-reaction)

2. Force • Intuitive concept of force • Contact and field forces • Most of the forces we experience are due to gravitational or electromagnetic • Vector nature of forces – acceleration will be in same direction as net force • Notation: F12 is the force exerted by object 1 on object 2

3. Newton’s 1st law • “In the absence of external forces, an object at rest remains at rest and an object in motion continues in motion with a constant velocity (that is, with a constant speed in a straight line).” • In other words, objects accelerate only if there is a net force on them • ConcepTest

4. Inertial frames & inertial mass • Inertial frame of reference = frame in which 1st law is valid • at rest or at constant velocity • Inertial mass is the resistance of an object to a change in motion in response to an external force (basically it’s defined by F=ma) • SI unit: kg • not the same as weight (=force due to gravitational attraction of earth)

5. Newton’s 2nd law • “The acceleration of an object is proportional to the net force acting on it and inversely proportional to its mass.” • i.e. the net (vector) force on an object is proportional to the (vector) acceleration of the object Units: “Newton” (N) = kgm/s2

6. m Example An object of mass m slides down a frictionless inclined plane (angle  with respect to the horizontal). What is its acceleration? 

7. Example An object of mass m slides down a frictionless inclined plane (angle  with respect to the horizontal). What is its acceleration? Step one - draw the force vectors acting on the object N Fg 

8. N Fg  Example An object of mass m slides down a frictionless inclined plane (angle  with respect to the horizontal). What is its acceleration? Component along direction of motion = Fgsin Along this axis Fgsin=ma, or a= Fgsin/m what happens along the direction perpendicular to the direction of motion?

9. 2nd law - ConcepTests

10. Gravitational force and weight What we call weight is the force of gravity on an object at sea level, it is proportional to the mass of the object Note: this equation is valid even for no acceleration – so the gravitational mass and the inertial mass don’t have to be the same, but they are.

11. A neutron walks into a bar; he asks the bartender, 'How much for a beer?' The bartender looks at him, and says 'For you, no charge.‘ • "We cannot learn without pain."-Aristotle • "The only thing that interferes with my learning is my education."-Albert Einstein • "Do not worry about your problems with mathematics, I assure you mine are far greater."-Albert Einstein

12. Newton’s 3rd law (action-reaction) • If two objects interact, the force F12 exerted by object 1 on object 2 is equal in magnitude but opposite in direction to the force F21 exerted by object 2 on object 1, i.e., • Conceptually, a little hard to grasp. Even for an accelerating object, there are always equal and opposite forces. Even when it seems like there is only a single object, i.e., an object in space, there must be a corresponding object which “receives” the reaction force.

13. Applications of Newton’s laws • Statics • Block on the incline from earlier, now being held up by a force F • If the block doesn’t move, the acceleration must be zero y x   Free body diagram

14. Applications of Newton’s laws • After making the free body diagram write out components of force vectors, then apply Newton’s second law along each axis

15. +y m1 m1 m2 m2 Applications of Newton’s laws • Atwood machine • assume m2>m1

16. Applications of Newton’s laws • One block pushing others F m2 m1 m3

17. Applications of Newton’s laws • Pulley’s m2 m1

18. m2 Applications of Newton’s laws • Combination with circular motion m1