1. Physics 106 Lesson #4 Newton’s Laws of Motion Dr. Andrew Tomasch 2405 Randall Lab atomasch@umich.edu

2. Last Time: A Puzzle All objects near the earth are attracted with the same acceleration g = 9.8 m/s 2 toward the Earth’s center (“downward”) irrespective of their masses Forces cause motion More massive objects have a larger downward force acting on them due to gravity How can these facts be consistent? Enter Sir Isaac Newton!

3. The Three Laws First laid down by Isaac Newton in his Principia Mathematica in 1687 –Newton’s 1st Law: The Law of Inertia –Newton’s 2nd Law: Force and Momentum (Acceleration) –Newton’s 3rd Law: Action and Reaction Built on the work of Galileo Considered the model of a scientific treatise Newton

4. “Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by outside forces impressed upon it.” Inertia (a scalar) is also called mass ( m ), which is measured in kilograms (SI) Newton’s First Law: The Law of Inertia

5. It is the natural tendency of objects to keep on doing what they're doing. Objects do not change their state of motion unless a FORCE is applied. No net force →momentum is constant (or zero)→ velocity is constant (or zero) → acceleration is zero. Newton’s First Law: More Ways to Say It Demo: Pulling the tablecloth from under the dishes

6. Why Seat Belts? If a car abruptly stops and seat belts are not being worn, the passengers continue to move in a straight line with the same speed. Newton’s First Law → Inertia http://www.physicsclassroom.com/mmedia/newtlaws/cci.html Caution Quiz Ahead There is no “force” that ejects the passenger. Rather, the passenger continues to move with a constant velocity after the car has stopped, until something applies a force to stop him (ouch!)

7. Concept Test #1 Harry and Sally are arguing in a bakery. Harry says that if he throws his jelly donut at her with a greater speed it will have a greater inertia. Sally argues that inertia does not depend upon speed, but rather upon mass. With whom do you agree? A)Harry B)Sally Inertia is simply another word for mass. The more mass, the more inertia.

8. “To every action there is always imposed an equal reaction; or, the mutual action of two bodies upon each other are always equal and directed to contrary parts.” Two rules: –Third law pairs never act on the same object. –When one member of the action - reaction pair is removed, the other member also vanishes. Newton’s Third Law: Action and Reaction F N → H = - F H → N F H → N Caution Quiz Ahead

9. Concept Test #2 You use your car to push a friend’s pickup truck that has broken down. To bring both of you to a stop, your friend applies the brakes in the truck. In magnitude, the force of the car on the truck is _______ the force of the truck on the car. A)greater than B)equal to C)less than The car exerts a force on the truck (action). The truck exerts an equal and opposite force on the car (reaction).

10. Newton’s Second Law “The change in the quantity of motion is proportional to the motive force impressed and is made in the direction of the line in which that force is impressed.” Newton

11. In modern language, Newton’s “quantity of motion” is called momentum. Momentum is a vector and is defined as the product of an object’s mass and velocity: Newton’s Second Law and Momentum

12. Newton’s Second Law: Momentum and Force In it’s most general form, Newton’s Second Law states that the net external force acting on an object equals the rate at which its momentum changes with time: This is a vector equation

13. Newton’s Second Law: Impulse and Momentum If we multiply both sides of Newton’s Second Law by time, we get another way to say it: “The impulse (force x time) delivered by the net force equals the change in an object’s momentum” This is also called the Impulse -- Momentum Theorem This is a vector equation Force X Time = Change in Momentum This is our jet car experiment

14. Newton’s Second Law: Force and Acceleration do not change their mass Many objects do not change their mass during motion. For these situations the mass factors out of the momentum and we can write Newton’s Second Law to relate force, mass and acceleration: This is a vector equation The direction of the force is the same as the direction of the acceleration

15. Galileo’s Puzzle Solved! All objects fall with the same downward acceleration ! Same m on both sides → Einstein’s Equivalence Principle → General Relativity A Falling Object… m Our Hero!

16. Rocket Science: Thrust Demo: Water Rocket + y Cannot be described with F = ma ! Thrust = Exhaust Speed x (Ejected Mass/Time)

17. Account for most motions Newton’s laws don’t work: –on atomic distance scales (Quantum Mechanics) –at speeds near the speed of light (Einstein’s Special Theory of Relativity) –in very strong gravitational fields (near black holes → Einstein’s General Theory of Relativity) Newton’s laws apply to almost all everyday situations Newton’s Powerful Laws Newton

18. First Law: Objects continue their state of motion (rest or constant velocity) unless acted upon by a net external force. Second Law: The action of a net external force on an object is to cause its momentum to change with time. For objects with a constant mass this can be written as F = ma. Third Law: Any object which exerts a force on another object experiences an equal and opposite force from the object it acts upon. Newton’s Laws: Summary