Chapter 12 Forces and Motion

1. Chapter 12 Forces and Motion Section 12.2 Newton’s First and Second Laws of Motion Section 12.3 Newton’s Third Law of Motion and Momentum

2. Section 12.2 Newton’s First and Second Laws of Motion • Aristotle, Galileo, and Newton • **It took about 2000 years to develop the understanding of the relationships between force and motion. • Aristotle • Incorrectly proposed that force is required to keep an object moving at constant speed • Error held back progress in the study of motion for almost 2000 years

3. Section 12.2 Newton’s First and Second Laws of Motion • Galileo • Studied how gravity produces constant acceleration • Concluded that moving objects not subjected to friction or any other force would continue to move indefinitely

4. Section 12.2 Newton’s First and Second Laws of Motion • Newton • Built on the work of other scientists (like Galileo) • Published his results many years later in a book entitled Principia (first had to define mass and force) • Then introduced his laws of motion

5. Isaac Newton (1642 – 1727) During the years of 1665 and 1666, Newton developed three laws which describe all sates of motion – rest, constant motion and accelerated motion • FACTS: • Born Jan. 4th, 1642 in Woolsthorpe, Lincolnshire, England. • 1687 – proposed the idea of gravity. • 1705 –f first scientist to be be knighted in England. • Early 1700’s – invented the form of math that became today’s calculus. • Died in March 31st, 1727 in London, England. • Buried in the famous Westminster Abbey Newton’s 1st Law – Inertia Newton’s 2nd Law – Acceleration cannot occur without force Newton’s 3rd Law – Action/Reaction Newton also proved the existence of gravity. Newton is considered the founder of modern physics!

6. Section 12.2 Newton’s First and Second Laws of Motion • Newton’s First Law of Motion • **Newton summarized his study of force and motion in several laws of motion. • Key Concept: According to Newton’s first law of motion, the state of motion of an object does not change as long as the net force acting on the object is zero.

7. Section 12.2 Newton’s First and Second Laws of Motion • Newton’s First Law of Motion • Unless an unbalanced force acts, an object at rest remains at rest, and an object in motion remains in motion with the same speed and direction. • Ex. Ball (at rest is kicked; slows down from friction between the ball and the ground) • First law aka the law of inertia. • Def.-the tendency of an object to resist a change in its motion

8. Section 12.2 Newton’s First and Second Laws of Motion • Inertia property of matter that resists a change in motion • An object with great mass has high inertia

9. Section 12.2 Newton’s First and Second Laws of Motion • http://www.teachertube.com/view_video.php?viewkey=5be397a06a7dddd0679d

10. Section 12.2 Newton’s First and Second Laws of Motion • Newton’s Second Law of Motion • **How do unbalanced forces affect the motion of an object? • An unbalanced force causes an object’s velocity to change (the object accelerates). • The more force used, the more acceleration there is. • Newton: the acceleration of an object depends on its mass

11. Section 12.2 Newton’s First and Second Laws of Motion • Newton’s Second Law of Motion • Mass-a measure of the inertia of an object and depends on the amount of matter the object contains • Key Concept: According to Newton’s second law of motion, the acceleration of an object is equal to the net force acting on it divided by the object’s mass. • Ie. Doubling an object’s mass will cut its acceleration by half. F = ma

12. F a m Section 12.2 Newton’s First and Second Laws of Motion F m F = ma F: force (N) m: mass (kg) a: accel (m/s2) 1 N = 1 kg ·m/s2

13. Section 12.2 Newton’s First and Second Laws of Motion The greater the mass of an object, the greater the force required to change its motion.

14. Section 12.2 Newton’s First and Second Laws of Motion • The greater the acceleration of an object, the greater the force required to change its motion.

15. Section 12.2 Newton’s First and Second Laws of Motion • Newton’s Second Law of Motion • The acceleration of an object is in the same direction as the net force. • Newton’s 2nd law also applies when a net force acts in the direction opposite to the object’s motion. (The force causes a deceleration that reduces the speed) • Ex. Seat belt, volleyball

16. Figure 13 Effects of a Force on Acceleration

17. Figure 13 Effects of a Force on Acceleration

18. Figure 13 Effects of a Force on Acceleration

19. Section 12.2 Newton’s First and Second Laws • Weight and Mass • **Mass and weight are not the same, but are related. • Weight-the force of gravity acting on an object • An object’s weight is the product of the objects mass and acceleration due to gravity acting on it. • Weight=Mass x Acceleration due to gravity, or W=mg; g=9.8 m/s2 • (F)orce or (W)eight is expressed in Newtons; Acceleration due to grativty (a or g) is expressed in m/s2 • Mass is expressed in kilograms.

20. Section 12.2 Newton’s First and Second Laws of Motion • Weight and Mass • Mass and weight are proportional; doubling mass, doubles the object’s weight • Key Concept: Mass is a measure of the inertia of an object; weight is a measure of the force of gravity acting on an object.

21. Section 12.2 Newton’s First and Second Laws of Motion f = m x a A F = 1000 kg x 0.05 m/s/s F = 50N B F = 2000 kg x 0.05 m/s/s F = 100N

22. http://www.teachertube.com/view_video.php?viewkey=3c50653dfeca80d85ea6http://www.teachertube.com/view_video.php?viewkey=3c50653dfeca80d85ea6

23. F a m Calculations • What force would be required to accelerate a 40 kg mass by 4 m/s2? GIVEN: F = ? m = 40 kg a = 4 m/s2 WORK: F = ma F = (40 kg)(4 m/s2) F = 160 N

24. F a m Calculations • A 4.0 kg shotput is thrown with 30 N of force. What is its acceleration? GIVEN: m = 4.0 kg F = 30 N a = ? WORK: a = F ÷ m a = (30 N) ÷ (4.0 kg) a = 7.5 m/s2

25. F a m Calculations • Mrs. J. weighs 557 N. What is her mass? GIVEN: F(W) = 557 N m = ? a(g) = 9.8 m/s2 WORK: m = F ÷ a m = (557 N) ÷ (9.8 m/s2) m = 56.8 kg

26. The frog leaps from its resting position at the lake’s bank onto a lily pad. If the frog has a mass of 0.5 kg and the acceleration of the leap is 3 m/s2, what is the force the frog exerts on the lake’s bank when leaping? • A 0.2 N • B 0.8 N • C 1.5 N • D 6.0 N Formula chart says F=ma, m is mass in kg, a is acceleration in m/s2. So, .5 kg x 3 m/s2= 1.5 N

27. Section 12.3 Newton’s Third Law of Motion and Momentum • Newton’s Third Law • **A force can’t exist alone. Forces always exist in pairs. • Key Concept: According to Newton’s third law of motion, whenever one object exerts a force on a second object, the second object exerts an equal and opposite force on the first object. • The two forces are called: action and reaction.

28. Section 12.3 Newton’s Third Law of Motion and Momentum • Action and Reaction Forces • Action force-the force exerted by the first object • Reaction force- the force exerted by the second object • Both forces are equal in size and opposite in direction • Ex. Pushing on a wall

29. Section 12.3 Newton’s Third Law of Motion and Momentum • Action-Reaction Forces and Motion • Not all action and reaction forces produce motion (pushing a wall). • Action-Reaction Forces Do Not Cancel • **Net force is not zero with action reaction forces. • b/c action and reaction forces do not act on the same object (swimmer in water) • Only when equal and opposite forces act on the same object do they result in a net force of 0.

30. NO!!! Section 12.3 Newton’s Third Law of Motion and Momentum • Problem: • How can a horse pull a cart if the cart is pulling back on the horse with an equal but opposite force? • Aren’t these “balanced forces” resulting in no acceleration?

31. Section 12.3 Newton’s Third Law of Motion and Momentum • Explanation: • forces are equal and opposite but act on different objects • they are not “balanced forces” • the movement of the horse depends on the forces acting on the horse

32. Section 12.3 Newton’s Third Law of Motion and Momentum • Action-Reaction Pairs • The hammer exerts a force on the nail to the right. • The nail exerts an equal but opposite force on the hammer to the left.

33. FG FR Section 12.3 Newton’s Third Law of Motion and Momentum • Action-Reaction Pairs • The rocket exerts a downward force on the exhaust gases. • The gases exert an equal but opposite upward force on the rocket.

34. F m F a m Section 12.3 Newton’s Third Law of Motion and Momentum • Action-Reaction Pairs • Both objects accelerate. • The amount of acceleration depends on the mass of the object. F = ma • Small mass  more acceleration • Large mass  less acceleration

35. Section 12.3 Newton’s Third Law of Motion and Momentum

36. Section 12.3 Newton’s Third Law of Motion and Momentum • http://www.teachertube.com/view_video.php?viewkey=5f46aa97a9b69cbad002

37. Section 12.3 Newton’s Third Law of Motion and Momentum • Momentum • Def.-the product of an objects mass and its velocity • **An object with more momentum is hard to stop. • Key Concept: An object has a large momentum if the product of its mass and velocity is large. • Momentum for any object at rest is 0. • Momentum= Mass x Velocity (kg * m/s)

38. p v m Section 12.3 Newton’s Third Law of Motion and Momentum • Momentum • quantity of motion p = mv p: momentum (kg ·m/s) m: mass (kg) v: velocity (m/s)

39. Section 12.3 Newton’s Third Law of Motion and Momentum • Conservation of Momentum • What happens when objects collide? • Under certain conditions, collisions obey the law of conservation of momentum. • ***Conservation of momentum means that momentum does not increase or decrease. • If a system is closed the momentum is conserved • Closed system-other objects and forces cannot enter or leave a system

40. Section 12.3 Newton’s Third Law of Motion and Momentum • Conservation of Momentum • Objects within the system can exert forces on one another. • Law of conservation of momentum-law stating that the total momentum of a system does not change if no net force acts on the system • Key Concept: In a closed system, the loss of momentum of one object equals the gain in momentum of another object—momentum is conserved.

41. Section 12.3 Newton’s Third Law of Motion and Momentum • Law of Conservation of Momentum • The total momentum in a group of objects doesn’t change unless outside forces act on the objects. pbefore = pafter

42. p v m Momentum • Find the momentum of a bumper car if it has a total mass of 280 kg and a velocity of 3.2 m/s. GIVEN: p = ? m = 280 kg v = 3.2 m/s WORK: p = mv p = (280 kg)(3.2 m/s) p = 896 kg·m/s

43. p v m Momentum • The momentum of a second bumper car is 675 kg·m/s. What is its velocity if its total mass is 300 kg? GIVEN: p = 675 kg·m/s m = 300 kg v = ? WORK: v = p ÷ m v = (675 kg·m/s)÷(300 kg) v = 2.25 m/s

44. Newton’s Laws • 1st Law: (inertia: objects tend to do what they are doing) • cannon ball will rest until a force is put on it • ball will roll straight until ramp puts a force on it • 2nd Law: (f = m x a) • greater force put on ball accelerates it more • greater mass of ball but greater force on water • 3rd Law: (every action has an equal but opposite reaction) • ball moves right, cannon recoils left • ball move down, water splashes up