Physics of Technology PHYS 1800

1. Physics of TechnologyPHYS 1800 Lecture 7 Newton’s Laws

2. PHYSICS OF TECHNOLOGYSpring 2009 Assignment Sheet *Homework Handout

3. Physics of TechnologyPHYS 1800 Lecture 6 Newton’s Laws Introduction and Significance

4. Describing Motion Position—where you are in space (L-meter) Speed—how fast position is changing with time (LT-1 or m/s) Acceleration—how fast speed is changing with time (LT-2 or m/s2) Question: How do we get things to accelerate?

5. - V V Change in velocity 1 2 = Average acceleration = t Time interval r r D V = 2 a m s t Acceleration Acceleration is the rate at which velocity changes. • Our bodies don’t feel velocity, if the velocity is constant. • Our bodies feel acceleration. • A car changing speed or direction. • An elevator speeding up or slowing down. Acceleration can be either a change in the object’s speed or direction of motion. In this Chapter acceleration is a variable, caused by FORCE.

6. Acceleration Due to Gravity • Earth exerts a gravitational force on objects that is attractive (towards Earth’s surface). • Near Earth’s surface, this force produces a constant acceleration downward. • To measure this acceleration, we need to slow down the action. • Galileo was the first to accurately measure this acceleration due to gravity. • By rolling objects down an inclined plane, he slowed the motion enough to establish that the gravitational acceleration is uniform, or constant with time.

7. How does this trajectory happen? Key: - resolve motion into its HORIZONTAL and VERTICAL components. VH = constant VG (due to gravity) VTOTAL But we know VG increases with time due to gravity acceleration! VH (constant) At any instant the total velocity is vector sum of VH and VG Uniform increase in VG with time Resultant TRAJECTORYSTEEPENS with increasing time. As NO horizontal acceleration the ball moves equal distances horizontally in equal time (assuming NO air resistance).

8. One Heck of a Ball Team!!! Hart’s list of most influential people in the history of the world: Newton (2)* Einstein (10) Galileo Galilei (12)* Aristole (13)*** Copernicus (19) * Kepler (75) * *(even though they got the wrong answer on the test) Simmon’s list of most influential scientists in the history of the world Newton (1)* (and 2 and 6 and 40) Einstein (2) Galileo Galilei (7)* Copernicus (9) Kepler (10) Tyco Brahe (22) Aristole (an honorable mentioned)***

9. Newton’s Contribution • Newton built on Galileo’s work, expanding it. • He developed a comprehensive theory of motion that replaced Aristotle’s ideas. • Newton’s theory is still widely used to explain ordinary motions.

10. Aristotle’s View • A force is needed to keep an object moving. • Air rushing around a thrown object continues to push the object forward.

11. Galileo’s Contribution • Galileo challenged Aristotle’s ideas that had been widely accepted for many centuries. • He argued that the natural tendency of a moving object is to continue moving. • No force is needed to keep an object moving. • This goes against what we seem to experience.

12. Newton’s First and Second Laws • Put Galileo's notions of motion on a mathematical footing with calculus • Set up the framework to explain motion. • How do forces affect the motion of an object? • What exactly do we mean by force? Is there a difference between, say, force, energy, momentum, impulse? • What do Newton’s first and second laws of motion tell us, and how are they related to one another? • Developed the first hints of a concervation law— Newton’s 3rd Law of Motion. • Developed the first formulation of a force—the gravitational force. • Made seminal contributions in thermodynamics and optics.

13. Inconsistencies in Physics cira 1900 • Statistical Mechanics • Boltzmann Distribution • Entropy and counting states • Blackbody radiation • Wein’s Law • Photoelectric effect • Diffraction of x rays • Discrete atomic spectra • Radioactive decay • Brownian motion • Existence of Atoms!

14. Newton’s Law of Universal Gravitation • Newton recognized the similarity between the motion of a projectile on Earth and the orbit of the moon. • If a projectile is fired with enough velocity, it could fall towards Earth but never reach the surface. • The projectile would be in orbit. • Newton’s law of universal gravitation says the gravitational force between two objects is proportional to the mass of each object, and inversely proportional to the square of the distance between the two objects. • G is the Universal gravitational constantG.

15. Dennison’s Laws of Motion • Stuff happens (or not). • The bigger they are the harder they fall. • You get what you give.

16. Newton’s First Law of Motion An object remains at rest, or in uniform motion in a straight line, unless it is compelled to change by an externally imposed force.

17. Newton’s Second Law of Motion The acceleration of an object is directly proportional to the magnitude of the imposed force and inversely proportional to the mass of the object. The acceleration is the same direction as that of the imposed force.

18. Newton’s Second Law of Motion • Note that a force is proportional to an object’s acceleration, not its velocity. • Precise definitions of some commonly used terms: • The mass of an object is a quantity that tells us how much resistance the object has to a change in its motion. • This resistance to a change in motion is called inertia. Force has dimensions of (MLT-2)

19. Net Forces • It is the total force or net force that determines an object’s acceleration. • If there is more than one vector acting on an object, the forces are added together as vectors, taking into account their directions.

20. Two equal-magnitude horizontal forces act on a box. Is the object accelerated horizontally? • Yes. • No. • You can’t tell from this diagram. Since the two forces are equal in size, and are in opposite directions, they cancel each other out and there is no acceleration.

21. Is it possible that the box is moving, since the forces are equal in size but opposite in direction? • Yes, it is possible for the object to be moving. • No, it is impossible for the object to be moving. Even though there is no acceleration, it is possible the object is moving at constant speed.

22. Two equal forces act on an object in the directions shown. If these are the only forces involved, will the object be accelerated? • Yes. • No. • It is impossible to determine from this figure. The vector sum of the two forces results in a force directed toward the upper right corner. The object will be accelerated toward the upper right corner.

23. Two forces act in opposite directions on a box. What is the mass of the box if its acceleration is 4.0 m/s2? • 5 kg • 7.5 kg • 12.5 kg • 80 kg • 120 kg The net force is50 N - 30 N = 20 N, directed to the right. From F=ma, the mass is given by: m = F/a = (20 N) / (4 m/s2) = 5 kg.

24. A 4-kg block is acted on by three horizontal forces. What is the net horizontal force acting on the block? • 10 N • 20 N • 25 N • 30 N • 40 N The net horizontal force is: 5 N + 25 N - 10 N = 20 N directed to the right.

25. A 4-kg block is acted on by three horizontal forces. What is the horizontal acceleration of the block? • 10 N • 20 N • 25 N • 30 N • 40 N From F=ma, the acceleration is given by: a = F/m = (20 N) / (4 kg) = 5 m/s2 directed to the right.

26. A ball hangs from a string attached to the ceiling. What is the net force acting on the ball? • The net force is downward. • The net force is upward. • The net force is zero. Since the ball is hanging from the ceiling at rest, it is not accelerating so the net force is zero. There are two forces acting on the ball: tension from the string and force due to gravitation. They cancel each other.

27. Two masses connected by a string are placed on a fixed frictionless pulley. If m2 is larger than m1, will the two masses accelerate? • Yes. • No. • You can’t tell from this diagram. The acceleration of the two masses will be equal and will cause m2 to fall and m1 to rise.

28. Newton’s Third Law • Where do forces come from? • If we push on an object like a chair, does the chair also push back on us? • If objects do push back, who experiences the greater push, us or the chair? • Does our answer change if we are pushing against a wall? • How does Newton’s third law of motion help us to define force, and how is it applied?

29. Newton’s Third Law (“action/reaction”) For every action (force), there is an equal but opposite reaction (force).

30. Identifying the forces acting on an object. • The forces acting on the book are W (gravitational force from Earth) and N (normal force from table). • Normal force refers to the perpendicular force a surface exerts on an object.

31. Third-Law Action/Reaction Pair An uncompressed spring and the same spring supporting a book. The compressed spring exerts an upward force on the book.

32. Third-Law Action/Reaction Pair If the cart pulls back on the mule equal and opposite to the mule’s pull on the cart, how does the cart over move?

33. Third-Law Action/Reaction Pair The car pushes against the road, and the road, in turn, pushes against the car.

34. Newton’s Laws in Review • 2nd Law (and 1st Law)—How motion of a object is aeffected by a force. • 3rd Law—Forces come from interactions with other objects. • Two branches of Mechanics: • Statics using the 1st Law with a=0 or Fnet=0 • Dynamics using the 2nd Law with a≠0 or Fnet ≠0 • Note: At the most fundamental level, there are only 4 forces in nature, gravity, electricity and magnetism, tweak nuclear force and strong nuclear force.

35. Dennison’s Laws of Motion • Stuff happens (or not). • The bigger they are the harder they fall. • You get what you give.

36. Free Body Diagrams • Fancy Science: Vector analysis of complex force problems is facilitated by use of a free body diagram. • Common Sense: A picture is worth a 100 words. (A scale picture is worth an A!) • Key is to: • Isolate a single body and draw all the forces acting on it. • Add up all the arrows (vectors). • What’s left is the net force. • Net force (and masses)  a. • A plus initial conditions motion!

37. Physics of Technology Next Lab/Demo: Forces Thursday 1:30-2:45 ESLC 53 Ch 3 Next Class: Wednesday 10:30-11:20 BUS 318 room Read Ch 4