Newton’s Laws

1. Newton’s Laws The Study of Dynamics

3. What is Force? • A vector quantity measured in Newtons (N). • A force is a push or pull on an object. • Forces cause an object to accelerate… • To speed up • To slow down • To change direction

4. Normal force • The normal force is a force that keeps one object from penetrating into another object. • The normal force is always perpendicular a surface. • The normal exactly cancels out the components of all applied forces that are perpendicular to a surface.

5. Force Diagram Free Body Diagram N N Physics W W Diagrams • Draw a force diagram and a free body diagram for a book sitting on a table.

6. FT FG Sample Problem • A monkey hangs by its tail from a tree branch. Draw a free body diagram representing all forces on the monkey

7. Fa1 Fa2 FG Sample Problem • Now the monkey hangs by both hands from two vines. Each of the monkey’s arms are at a 45o from the vertical. Draw a force diagram representing all forces on the monkey.

8. N mg Normal force on flat surface • The normal force is equal to the weight of an object for objects resting on horizontal surfaces. • N = W = mg

9. friction applied force weight normal Normal force not associated with weight. • A normal force can exist that is totally unrelated to the weight of an object. N = applied force

10. Video

11. Newton’s First Law • A body in motion stays in motion at constant velocity in the same direction and a body at rest stays at rest unless acted upon by a net external force. • This law is commonly referred to as the Law of Inertia.

12. The First Law is Counterintuitive Aristotle firmly believed this. But Physics B students know better!

13. Implications of Newton’s 1st Law • If there is zero net force on a body, it cannot accelerate, and therefore must move at constant velocity (or remain at rest) which means • it cannot turn, • it cannot speed up, • it cannot slow down.

14. The table pushes up on the book. FT Gravity pulls down on the book. FG What is Zero Net Force? A book rests on a table. Physics Even though there are forces on the book, they are balanced. Therefore, there is no net force on the book. SF = 0

16. Mass and Inertia • Chemists like to define mass as the amount of “stuff” or “matter” a substance has. • Physicists define mass as inertia, which is the ability of a body to resist acceleration by a net force.

17. Mass and Weight • Many people think mass and weight are the same thing. They are not. • Mass is inertia, or resistance to acceleration. • Weight can be defined as the force due to gravitation attraction. • W = mg

19. Newton’s Second Law • A body accelerates when acted upon by a net external force. • The acceleration is proportional to the net force and is in the direction which the net force acts.

20. Newton’s Second Law

21. Working 2nd Law Problems • Draw a force or free body diagram. • Set up 2nd Law equations in each dimension. SFx = max and/or SFy = may • Identify numerical data. Knowns and unknowns x-problem and/or y-problem • Substitute numbers into equations. “plug-n-chug” • Solve the equations.

22. Sample Problem In a grocery store, you push a 14.5-kg cart with a force of 12.0 N. If the cart starts at rest, how far does it move in 3.00 seconds?

23. Sample Problem A 747 jetliner lands and begins to slow to a stop as it moves along the runway. If its mass is 3.50 x 105 kg, its speed is 27.0 m/s, and the net braking force is 4.30 x 105 N a) what is its speed 7.50 s later? b) How far has it traveled in this time?

24. Apparent weight • If an object subject to gravity is not in free fall, then there must be a reaction force to act in opposition to gravity. • We sometimes refer to this reaction force as apparent weight.

25. Elevator rides • When you are in an elevator, your actual weight (mg) never changes. • You feel lighter or heavier during the ride because your apparent weight increases when you are accelerating up, decreases when you are accelerating down, and is equal to your weight when you are not accelerating at all.

26. v > 0 a > 0 v = 0 a = 0 v > 0 a = 0 v > 0 a < 0 Heavy feeling Normal feeling Normal feeling Light feeling Wapp Wapp Wapp Wapp W W W W Between floors Ground floor Just starting up Arriving at top floor Going Up?

27. v < 0 a > 0 v = 0 a = 0 v < 0 a = 0 v < 0 a < 0 Heavy feeling Normal feeling Normal feeling Light feeling Wapp Wapp Wapp Wapp W W W W Between floors Top floor Arriving at Ground floor Beginning descent Going Down?

28. Sample Problem An 85-kg person is standing on a bathroom scale in an elevator. What is the person’s apparent weight a) when the elevator accelerates upward at 2.0 m/s2? b) when the elevator is moving at constant velocity between floors? c) when the elevator begins to slow at the top floor at 2.0 m/s2?

29. Sample Problem A 5-kg salmon is hanging from a fish scale in an elevator. What is the salmon’s apparent weight when the elevator is a) at rest? b) moving upward and slowing at 3.2 m/s2? c) moving downward and speeding up at 3.2 m/s2? d) moving upward and speeding up at 3.2 m/s2?

30. Newton’s Third Law • For every action there exists an equal and opposite reaction. • If A exerts a force F on B, then B exerts a force of -F on A.

32. Examples of Newton’s 3rd Law

33. Sample Problem You rest an empty glass on a table. a) How many forces act upon the glass? b) Identify these forces with a free body diagram. c) Are these forces equal and opposite? d) Are these forces an action-reaction pair?

35. Newton’s 2nd Law in 2-D • The situation is more complicated when forces act in more than one dimension. • You must still identify all forces and draw your force diagram. • You then resolve your problem into an x-problem and a y-problem (remember projectile motion????).

36. Forces in 2-D

37. Forces in 2-D

38. Forces in 2-D

39. Forces in 2-D

40. Forces in 2-D

41. N mg Normal force on flat surface • The normal force is equal to the weight of an object for objects resting on horizontal surfaces. • N = W = mg

42. …but this is by no means always the case!

43. N mgsin mgcos  mg  Normal force on ramp • The normal force is perpendicular to angled ramps as well. It’s always equal to the component of weight perpendicular to the surface. N = mgcos

44. Sample problem • Find the normal force exerted on a 2.5-kg book resting on a surface inclined at 28o above the horizontal. • If the angle of the incline is reduced, do you expect the normal force to increase, decrease, or stay the same?

45. Sample problem A gardener mows a lawn with an old-fashioned push mower. The handle of the mower makes an angle of 320 with the surface of the lawn. If a 249 N force is applied along the handle of the 21-kg mower, what is the normal force exerted by the lawn on the mower?

46. Sample problem Larry pushes a 200 kg block on a frictionless floor at a 45o angle below the horizontal with a force of 150 N while Moe pulls the same block horizontally with a force of 120 N. a) Draw a free body diagram. b) What is the acceleration of the block? c) What is the normal force exerted on the block?

48. Newton’s Laws Applications

49. Friction • Friction is the force that opposes a sliding motion. • Friction is due to microscopic irregularities in even the smoothest of surfaces. • Friction is highly useful. It enables us to walk and drive a car, among other things. • Friction is also dissipative. That means it causes mechanical energy to be converted to heat. We’ll learn more about that later.

50. N (friction) Fpush f W Microscopic View Big view: Surfaces look perfectly smooth. Small view: Microscopic irregularities resist movement. Friction may or may not exist between two surfaces. The direction of friction, if it exists, is opposite to the direction object will slide when subjected to a horizontal force. It is always parallel to the surface.