Chapter 2

1. Chapter 2 Newton’s Laws

2. Force • Force is a push or pull on a body. • It usually causes: • a distortion in the body, • a change in the body’s velocity, or • both. • Force is the agent for a change in motion.

3. Force, cont’d • The units of force include: • SI: newton (N), dyne or metric ton (2000 N) • English: pound (lb), ounce (oz) or ton (2000 lb). • To convert between SI and English:

4. Weight • Weight is the force of gravity acting on a body. • We typically use the symbol W. • Your weight depends on which planet you are on. • A 200 lb person on Earth weighs about 33 lb on the Moon.

5. Weight, cont’d • Although weight always acts toward the Earth’s center, it might not always appear that way. • Consider a box on a ramp.

6. Weight, cont’d • The weight is always straight down. • We can break the weight into “components” parallel and perpendicular to the ramp.

7. Weight, cont’d • The perpendicular component only acts to hold the box on the ramp. • The parallel component acts to accelerate the box down the ramp.

8. Weight, cont’d • As the ramp becomes more steep, the parallel component increases: • The box tends to accelerate more quickly.

9. Friction • Friction is a resistive force to relative motion between two bodies or substances in contact. • Between your tire and the road; • Between your car and the air.

10. Friction, cont’d • Static friction is the resistance you experience when you try to start sliding an object. • It is static because there is no relative motion between the surfaces. • Kinetic friction is the resistance you experience while sliding an object. • It is kinetic since there is relative motion.

11. Newton’s first law of motion • Newton’s First Law of Motion states: An object will remain at rest or in motion with constant velocity unless acted on by a net external force. • An external force is a force applied to the object from some other object. • force from an impact, gravity, air resistance, etc.

12. Newton’s first law of motion, cont’d • The net force is the vector sum of all external forces. • If you and a friend push on opposite ends of a truck with the same force, the net force is zero — the forces cancel. • If you push in the same direction, there is a non-zero net force.

13. Newton’s first law of motion, cont’d • If the two forces are in different directions, the net force is an “in-between” direction.

14. Newton’s first law of motion, cont’d • Remember centripetal acceleration? • The acceleration experienced by an object moving in a circular path. • There must be a force pulling the object toward the center. • Otherwise the object would fly off.

15. Newton’s first law of motion, cont’d • You can create an “artificial gravity” in a space station by rotating it.

16. Mass • Mass is a measure of an object’s resistance to acceleration, i.e., changes in the object’s motion. • It also indicates the amount of matter in an object. • SI units: kilogram (kg) or gram (g); • English unit: slug.

17. Mass, cont’d • An object of little mass requires little force to accelerate it. • A massive object requires a much larger force to give it the same acceleration.

18. Mass, cont’d • The weight of an object depends on which planet you measure the weight. • The mass of the object is independent of the planet.

19. Newton’s 2nd law of motion • Newton’s 2nd Law of Motion states that an object is accelerated when a net external force acts on it. • The net force equals the object’s mass times its acceleration:

20. Newton’s 2nd law of motion, cont’d • Think about why you might add more dogs to a sled…

21. Newton’s 2nd law of motion, cont’d • The object will accelerate according to • If the object experiences a centripetal acceleration, the centripetal force is

22. Newton’s 2nd law of motion, cont’d • The SI unit of force, the newton, is defined according to Newton’s 2nd law:

23. Newton’s 2nd law of motion, cont’d • A falling object accelerates due to the Earth’s gravity at • So the force the object feels from Earth, i.e., its weight, is:

24. ExampleExample 2.2 An automobile manufacturer decides to build a car that can accelerate uniformly from 0 to 60 mph (27 m/s) in 10 s. The car’s mass is to be about 1,000 kilograms. What is the force required?

25. ExampleExample 2.2 ANSWER: The problem gives us: The force is:

26. ExampleExample 2.2 DISCUSSION: What produces this force? • The friction between the car’s tires and the road. • If the road is too slick, the tires cannot get enough “grip” and you “peel-out.”

27. ExampleExample 2.3 In Example 1.5, we computed the centripetal acceleration of a car going 10 m/s around a curve with a radius of 20 meters. If the car’s mass is 1,000 kilograms, what is the centripetal force that acts on it?

28. ExampleExample 2.3 ANSWER: The problem gives us: The force is:

29. ExampleExample 2.3 DISCUSSION: What causes this force? • It is the friction between the tire’s and the road. • If the road is too slick, the road could not generate this force and you slide into the ditch.

30. Types of motionfree-fall • Free-fall is a type of motion in which the only force acting on the object is the object’s weight. • There is no friction, no air resistance, etc. • Gravity always acts toward the Earth’s center.

31. Types of motionfree-fall, cont’d • A ball thrown upward will slow-down because gravity is “pulling” down on the ball.

32. Types of motionfree-fall, cont’d • Eventually it will stop. • It will then fall back to the Earth due to gravity. • The time it takes to go up is the same amount of time for it to fall.

33. Types of motionfree-fall, cont’d • Why does a football follow a curved trajectory?

34. Types of motionfree-fall, cont’d • Why does a football follow a curved trajectory? ANSWER: • Gravity acts in the vertical. • So the vertical speed changes. • Ideally, there is no force in the horizontal direction. • The horizontal speed does not change.

35. Types of motionfree-fall, cont’d • Why does a football follow a curved trajectory? ANSWER: • So the ball goes up and down just like if you had thrown it straight-up. • But the horizontal speed carries it downfield.

36. Types of motionsimple harmonic motion • Imagine a block attached to a spring. • If we stretch the spring and release it, the block moves in a regular, periodic fashion.

37. Types of motionsimple harmonic motion • This type of motion is called simple harmonic motion. • Notice that the speed is a maximum when the block is farthest from its rest position.

38. Types of motionfalling with air resistance • What happens when you “really” drop an ball? • Think about the forces acting on the ball. • Gravity is accelerating it downward. • The air offers resistance, trying to prevent the ball’s descent.

39. Types of motionfalling with air resistance, cont’d • The ball’s weight pulls it down. • The air has to be forced out of the ball’s way — it exerts an upward trying to slow the ball down.

40. Types of motionfalling with air resistance, cont’d • As the ball’s speed increases, the air resistance force increases. • Eventually the ball no longer accelerates. • At this point, you’ve reached the terminal speed.

41. Newton’s third law of motion • Newton’s 3rd Law of Motion states that forces always occur in pairs: • When one object exerts a force on a second object, the second exerts an equal and opposite force on the first.

42. Newton’s third law of motion, cont’d • If object A exerts a force on object B, then object B exerts an equal force in the opposite direction on A: • When you fall down, you feel the Earth exerting a force on you but you also exert that same force on the Earth.

43. Newton’s third law of motion, cont’d • Think about pushing off against a wall. • You push against the wall. • The wall pushes back. • If the wall is weak, it might fall down. • If not, you moveaway.

44. Newton’s third law of motion, cont’d • Consider an airplane’s wing. • Due to the angle of attack, the air impacts the bottom of the wing. • The wing pushes the air out of the way. • The air pushes back and provides somelift.

45. The law of universal gravitation • Newton’s Law of Universal Gravitation states that every object exerts a gravitational force on every other object. • The force increases as either object’s mass increases. • The force decreases as the objects move farther apart.

46. The law of universal gravitation, cont’d • Mathematically, we can write • m1 is the mass of one object • m2 is the mass of the other object • d is the center-to-center distance separating the objects.

47. The law of universal gravitation, cont’d • Note that Newton’s 3rd law means: • the Earth pulls down on you with a force equal to your weight, and • you pull “up” on the Earth with you’re a force equal to your weight. • You move more than the Earth because the Earth is much more massive than you.

48. The law of universal gravitation, cont’d • If you could stand on a tower 4,000 miles high, you would weigh one-fourth your usual weight. • You are 2×’s farther from the Earth’s center.

49. The law of universal gravitation, cont’d • Using the gravitational constant, we can write the law of gravity as

50. ExampleProblem 2.25 A space probe is launched from the Earth, headed for deep space. At a distance of 10,000 miles from the Earth’s center, the gravitational force on it is 600 lb. What is the size of the force when it is 20,000 miles from the Earth’s center?