Understanding Newton’s Laws of Motion

1. Chapter 12Forces

2. Newton’s First and Second Laws • First Law: an object at rest remains at rest and an object in motion maintains its velocity unless it experiences a net force • Objects change their state of motion when a net force is applied • Matter resists any change in motion • Because this property of matter is called inertia, Newton’s first law is sometimes called the Law of Inertia • Space travel

3. Newton’s First and Second Laws

4. Newton’s First and Second Laws • Newton's first law of motion applies to both objects in motion and objects at rest. Objects in motion have inertia because they want to remain in motion. For example a roller coaster has inertia. When it starts a drop it wants to continue moving in the same direction at a constant speed. It doesn't however because the tracks act as an outside force and change the roller coaster car's direction.

5. Newton’s First and Second Laws

6. Newton’s First and Second Laws • Newton’s first law describes what happens when no net force is acting on an object: the object remains at rest or keeps moving at a constant velocity. What happens when the net force is not zero? • Newton’s Second Law applies • Describes the effect of an unbalanced force on the motion of an object • The unbalanced force acting on an object equals the object’s mass times its acceleration

7. Newton’s First and Second Laws • Second Law: • The unbalanced force on an object determines how much an object speeds up or slows down • Net force = mass x acceleration • F = m x a • Newton = kilogram x meters/second2 • N = kg x m/s2

8. Newton’s First and Second Laws • Mike's car, which weighs 1,000 kg, is out of gas. Mike is trying to push the car to a gas station, and he makes the car go 0.05 m/s/s. Using Newton's Second Law, you can compute how much force Mike is applying to the car. • Answer = 50 newtons

9. Newton’s First and Second Laws

10. Newton’s First and Second Laws

11. Newton’s First and Second Laws • Newton’s second law is also found in football. The law states that the acceleration of an object is inversely proportional to the mass of the object and proportional to the net force. Essentially, that means that when an object's net force is increased, the acceleration will increase(kicking a football harder will usually make the ball go farther) and when an object's mass is increased, the acceleration is decreased(you can kick a foot ball a lot father that a rock!).When the force and acceleration are high, the distance will increase. In football, the net force is the kicker’s foot. If the kicker's foot exerts a harder force, the ball will go farther. If all goes well, the football should go as far as the force exerted expected

12. Newton’s First and Second Laws

13. Newton’s First and Second Laws • This is an image of a gun shootin out a bullet, an example of Newton's Second Law of Motion : f=MxA. The gun has to have force on the trigger for the bullet to shoot out.

14. Newton’s First and Second Laws • Keep an empty rectangular box and some heavy books on a table. Then push the empty box across the table. We can see that it is very easy to move the box. Keep the heavy books in the empty box, compared to the previous case we have to apply more force to this box for its motion. This is a simple example to illustrate the second law of motion.

15. Newton’s First and Second Laws

16. Newton’s First and Second Laws • If you want to calculate the acceleration, first you need to modify the force equation to get a = F/m. When you plug in the numbers for force (100 N) and mass (50 kg), you find that the acceleration is 2 m/s2. • Now let's say that the mass of the sled stays at 50 kg and that another dog is added to the team. If we assume the second dog pulls with the same force as the first (100 N), the total force would be 200 N and the acceleration would be 4 m/s2.

17. Newton’s First and Second Laws • If two dogs are on each side, then the total force pulling to the left (200 N) balances the total force pulling to the right (200 N). That means the net force on the sled is zero, so the sled doesn’t move.

18. Newton’s First and Second Laws • This is important because Newton's second law is concerned with net forces. We could rewrite the law to say: When a net force acts on an object, the object accelerates in the direction of the net force. Now imagine that one of the dogs on the left breaks free and runs away. Suddenly, the force pulling to the right is larger than the f­orce pulling to the left, so the sled accelerates to the right. • What's not so obvious in our examples is that the sled is also applying a force on the dogs. In other words, all forces act in pairs. This is Newton's third law.

19. GRAVITY • Mass: is a measure of the amount of matter in an object • Weight: is the gravitational force that an object experiences because of gravity • Will an Astronaut have the same mass on the Earth and the Moon? • Will an Astronaut have the same weight on the Earth and the Moon?

20. GRAVITY • The force on an object due to gravity is weight • All objects experience a free-fall acceleration due to gravity • Free-fall acceleration near the Earth’s surface is 9.8m/s2 • You can use Newton’s Second law to calculate your weight (F=ma) • Weight = mass x free-fall acceleration • W = mg

21. GRAVITY • The SI unit of Weight is a Newton because weight is a FORCE • A typical textbook has a mass of about 2,250 g and a weight of 2.25 kg x 9.8 m/s2 = 22N on Earth

22. GRAVITY • Law of Universal Gravitation: all objects in the universe attract each other through the force of gravity • The same force that causes objects to fall to Earth controls the motion of planets in the sky • F = G m1m2/d2 • Gravitational force increases as one or both masses increase • Gravitational force decreases as the distance between two masses increases • The symbol G in the equation is a constant • 6.67 x 10-11 N (m/kg)2

23. GRAVITY

24. GRAVITY • Gravitational force increases as mass increases • Gravitational force decreases as distance increases

25. GRAVITY • Free Fall: when Earth’s gravity is the only force acting on an object • Free fall acceleration is directed toward the center of Earth • In the absence of air resistance, all objects falling near earth’s surface accelerate at the same rate regardless of their mass • Newton’s second law states that acceleration depends on both force and mass. • A heavy object has a greater gravitational force than a light object does. • However, it is harder to accelerate a heavy object than a light object because the heavy object has more mass

26. GRAVITY • Free-fall acceleration is constant because of the law of universal gravitation

27. GRAVITY

28. GRAVITY • Air resistance can balance weight • Both air resistance and gravity act on objects moving through Earth’s atmosphere • A falling object stops accelerating when the force of air resistance becomes equal to the gravitational force on the object (the weight of the object) • Air resistance acts in the opposite direction to the weight • When air resistance and weight are equal, the object stops accelerating and reaches its maximum velocity, which is called terminal velocity (320 km/h) (200 mi/h) • Acceleration due to earth’s gravity is 9.8m/s/s

29. GRAVITY • a = Fnet/m • A: 833N/85Kg=9.8m/s/s • B: 483N/85Kg=5.68m/s/s • C: 133N/85Kg=1.56m/s/s • D: 0N/85Kg=0m/s/s (Terminal Velocity) • When parachute is opened the increased air resistance slows the sky diver down. Eventually, they reach a new terminal velocity which allows them to land safely.

30. GRAVITY • Astronauts in orbit are in free fall • Experience apparent weightlessness because they are in free fall. • The astronauts and the vehicle in which they are traveling are falling toward Earth with the same acceleration

31. GRAVITY • Projectile Motion: curved path followed by an object that is thrown, launched, or projected near the Earth’s surface • Projectile motion has two components: • Horizontal motion and vertical motion • When two motions are combined, they form a curved path • The two components are independent (they do not affect each other) • The downward acceleration due to gravity does not change the horizontal motion, and the horizontal motion does not affect the downward motion

32. GRAVITY

33. GRAVITY • Orbiting is projectile motion • An object is said to be orbiting when it is traveling in a circular or nearly circular path around another object • Spaceship orbits Earth • It is moving forward but it is also in free fall toward Earth • These two motions combine to cause orbiting • Because of free fall, the moon stays in orbit around Earth, and the planets stay in orbit around the sun

34. Newton’s Third Law • For every action force, there is an equal and opposite reaction force • When one object exerts a force on a second object, the second object exerts a force equal in size and opposite in direction on the first object • Forces always occur in pairs • Forces are equal but opposite • Sitting in a chair

35. Newton’s Third Law • Forces do not act on the same object • Although the forces are equal and opposite, they do not cancel each other because they act on different objects • Swimmer: hands and feet exert the action force on water and water exerts the reaction force on hands and feet • Note that action and reaction forces occur at the same time • But the action and reaction forces never act on the same object

36. Newton’s Third Law • Newton's third law of motion states, 'To every action there is an equal and opposite reaction'. This means that if an object A exerts a force on object B then object B exerts an equal and opposite force on object A. More crudely, when you push something, it resists being pushed and the force of resistance equals the force with which you push. When you stop pushing, the resisting force vanishes. • It is important to recognise the two forces act on different bodies. You push on the object and the object pushes on you. The two forces do not cancel each other out precisely because they act on different bodies. Suppose for example that you are a skater A, one of a pair of ice skaters.

37. Newton’s Third Law • You push on skater B with a force and the other skater pushes back with a force Both skaters move away from each other. They experience the same force, acting in opposite directions so accelerate in opposite directions. If one skater has a smaller mass than the other, then since that lighter skater will experience a larger acceleration. • Newton's third law is an aid to swimming, running and every sort of movement. When you are swimming, you push against the water with your arms and legs and the water pushes back, moving you forwards. When you go walking, you push backwards on the Earth with your feet, and the Earth pushes you forward. When a plane starts its engine, making air move towards the back of the plane, the air pushes back on the plane, making it move forward.

38. Newton’s Third Law

39. Newton’s Third Law

40. Newton’s Third Law

41. Newton’s Third Law • Momentum: • Is a property of all moving objects • For movement along a straight line, momentum is calculated by multiplying an object’s mass and velocity • Momentum = mass x velocity • p = m x v • Kg/m/s = Kg x m/s • Like velocity momentum has direction • Momentum increases as mass and velocity increase

42. Momentum • When you force an object to change its motion, you force it to change its momentum • You are changing the momentum of the ball over a period of time • As the period of time of the momentum’s change becomes longer, the force needed to cause this change in momentum becomes smaller • If you pull your glove back while you are catching a ball, you increase the time for changing the ball’s momentum • Increasing the time causes the ball to put less force on your hand • Sting to the hand is less

43. Momentum

44. Momentum • In each of the above situations, the impulse on the carts is the same - a value of 20 kg•cm/s (or cN•s). Since the same spring is used, the same impulse is delivered. Thus, each cart encounters the same momentum change in every situation - a value of 20 kg•cm/s. For the same momentum change, an object with twice the mass will encounter one-half the velocity change. And an object with four times the mass will encounter one-fourth the velocity change.

45. Momentum • In a game of pool, momentum is conserved; that is, if one ball stops dead after the collision, the other ball will continue away with all the momentum. If the moving ball continues or is deflected then both balls will carry a portion of the momentum from the collision

46. Momentum

47. Momentum • car of mass m 1   moving with a velocity of v 1   bumps into another car of mass m 2   and velocity v 2   that it is following. As a result, the first car slows down to a velocity of v′ 1   and the second speeds up to a velocity of v′ 2   . The momentum of each car is changed, but the total momentum p tot   of the two cars is the same before and after the collision (if you assume friction is negligible).

48. Momentum • The total momentum of two or more objects after a collision is the same as it was before the collision