Newton s Laws of Motion

Transcription

1 10 Newton s Laws of Motion There are many different kinds of motion. We experience some kind of motion every minute of every day. As complicated as motion is, there are only three laws that describe all motion! These laws were discovered by a man name Sir Isaac Newton. They are called Newton s 1 st Law, Newton s Second Law, and Newton s 3 rd Law. Newton s 1 st Law (Also called the Law of Inertia) Before we learn about Newton s first law, we need to understand inertia, matter and mass. Mass is the amount of matter an object has. Examples: Underline the thing with more mass, and circle the thing with more matter. 1) Elephant Mouse 2) Bicycle Car 3) Beach ball Bowling ball

2 11 4) 100kg Lead ball 70kg Aluminum ball 5) Empty balloon Filled balloon 6) Full bucket Empty bucket Explanation of number 5: Two identical empty balloons have the same amount of matter, so they have the same mass. When one of the balloons is filled with air, the filled balloon has more matter. (Air is a kind of matter.) So the filled balloon has a greater mass. Students may argue that air doesn t have mass or even that a balloon filled with helium (a type of matter) floats and an empty balloon doesn t float. The balloon filled with helium floats in earth s atmosphere because of the buoyant force (upward buoyant force = weight of air displaced by the object). Helium gas is less dense than air, so it floats. If the masses of an empty balloon and a balloon filled with helium gas are measure in a vacuum (where there is no buoyant force), the filled balloon will register a greater mass.

3 Remember that no motion is also a type of motion. 12 The more mass something has, the harder it is to change the way it is moving. Examples: 1) It is easy to change the motion of a balloon moving at 10km/h, but it is difficult to change the motion of a car (for example) traveling at 10km/h. 2) It is easy to change the motion of a rolling beach ball, but it is difficult to change the motion of a rolling. bowling ball (for example) 3) It is easy to change the motion of a pencil sitting on a desk, but it is harder to change the motion of a book (for example) sitting on a desk. Objects with more mass resist change in their less motion more than objects with mass. Inertia = Resistance an object has to a change in its motion. Answer the following questions. Use the word inertia in your answer: 1) Why it is easy to change the motion of a balloon moving at 10km/h, but it is difficult to change the motion of a car traveling at 10km/h? The car has more inertia, so it is more difficult to change its motion.

4 13 2) Why it is easy to change the motion of a rolling beach ball, but it is difficult to change the motion of a rolling bowling ball? The bowling ball has more inertia, so it is more difficult to change its motion. 3) Why it is easy to change the motion of a pencil sitting on a desk, but it is harder to change the motion of a book sitting on a desk? The book has more inertia, so it is more difficult to change its motion. 4) Why it is easy to change the motion of a but difficult to change the motion of a? 5) Explain why the items in the following picture do not move when the table is pulled away very quickly. (Remember to use the word inertia.) The items on the table have inertia. So when the table is pulled away quickly, the items resist a change in their motion, so they do not move to the left with the table. _

5 14 Newton s 1 st Law = Every object stays at rest or moves in a straight line at a constant speed unless a net force changes its motion. Use Newton s 1 st Law to answer the following question: 1) 2) 3) 1) The coin is at rest and remains at rest when the card is hit out from underneath it. There is not enough force to make with the card. 2) The hammerhead is moving downward at a constant speed. When the hammer stops suddenly, the hammerhead continues its motion downward until it is forced to stop. 3) When the force is applied slowly, the force on the upper string is greater than the force on the lower string (F upper = F pull + F ball s gravity ), so the string breaks above the ball. When the force is applied quickly, the ball continues to stay at rest because it is initially at rest. There is no additional force on the upper string, so the lower string breaks.

6 15 4) You roll a golf ball flat on the ground. On the ground is a curved wall. The ball follows the path in the figure. When it gets to the end of the wall, which way will it go: path 1, path 2, or path 3? Use Newton s 1 st Law to explain why. The golf ball will follow path 2, because it must move in a straight line at constant speed since there are no other forces acting on it. This is N s 1 st law. 5) A car is driving along a flat, straight road at 50km/h. What net force is necessary to keep this motion the same? None! Any net force will cause the motion of the car to change. There must be no net force if the car is to continue with the same motion. 6) A car is driving along a flat, straight road at 50km/h. The tires are pushing the car forward (force A), and the wind and road are pushing back on the car (force B). If the motion of the car does not change, which of the following is true? a) Force A is bigger than force B b) Force A is equal to force B. c) Force A is smaller than force B. b) A = B, because there must be no net force for motion to remain unchanged.

7 16 7) Imagine that you are floating in space. You have two identical boxes. One is empty, and one is filled with sand. How can you tell which one has the sand if you can not open either of the boxes? Shake the boxes. The box with the greater mass offers greater resistance to a change in its motion. 8) Why is an axe with more mass better at chopping wood that an axe with less mass? When the more massive axe hits the wood, it is more resistive to changing its motion than the less massive axe would be. It will hence go deeper into the wood and chop the wood more effectively. 9) When you use one hand to pull a piece of toilet paper from a roll, why is it better to pull quickly than to pull slowly? The inertia of the toilet paper roll resists a rapid change in motion more than it resists a slow change in motion. Pulling slowly will unwind the roll. Pulling quickly will rip off a piece of toilet paper. 10) Can the motion of an object change if there is no net force acting on it? No! Newton s 1 st Law states that a force is necessary to change the motion of an object.

8 17 Newton s 2 nd Law (Also called the Law of Acceleration) Newton s 1 st Law tells us how an object behaves when there is no net force acting on it. Newton s 2 nd Law tells us how an object behaves when there is a net force acting on it. Before we can learn about Newton s 2 nd Law, we must understand acceleration. Acceleration = Change is motion over time. In each of the following situations, is there acceleration? Circle YES or NO : 1) A car changes speed from 100km/hr to 35km/h. YES or NO 2) A car speeds up by 20km/h. YES or NO 3) A car traveling at 60km/h turns to the left. YES or NO 4) A skydiver jumps out of a plane and falls towards the ground faster and faster. YES or NO 5) A skydiver reaches terminal velocity and falls towards the ground at a constant speed. YES or NO

9 18 6) A car driving on a straight road at constant speed. YES or NO 7) A person sitting on the grass. YES or NO Newton s 2 nd Law = A net force on an abject causes the object to accelerate in the same direction as the net force. Newton s 2 nd Law Examples: = F = ma 1) A car drives at 50km/h east along a flat highway. The car feels a net force to the east. How does the motion of the car change? The car starts to speed up but continues to travel east. 2) A car drives at 50km/h east along a flat highway. The car feels a net force to the west. How does the motion of the car change? The car starts to slow down but continues to travel east. 3) A car drives at 50km/h east along a flat highway. The car feels a net force to the north. How does the motion of the car change? The car starts to turn towards the north.

10 19 4) A car drives at 50km/h east along a flat highway. The car feels a net force to the south. How does the motion of the car change? The car starts to turn towards the south. 5) A skydiver falls straight towards the earth at a terminal velocity of 120km/h. She feels a net force downward. A) How does her motion change? B) What situation could make this happen? A) She starts speeding up, but continues to fall straight downwards. B) She could be falling through an area of less wind resistance or she could have tucked herself into a ball. 6) A skydiver falls straight towards the earth at a terminal velocity of 120km/h. She feels a net force upward. A) How does her motion change? B) What situation could make this happen? A) She starts to slow down, but continues to fall straight downwards. B) She could be falling through an area of more wind resistance or have just deployed her parashute. 7) A skydiver falls straight towards the earth at a terminal velocity of 120km/h. She feels a net force to the left. A) How does her motion change? B) What situation could make this happen? A) She starts to fall diagonally mostly downward, but partially to the left. B) She could be falling through an area of a left wind.

11 20 8) A skydiver falls straight towards the earth at a terminal velocity of 120km/h. She feels a net force to the right. A) How does her motion change? B) What situation could make this happen? A) She starts to fall diagonally mostly downward, but partially to the right. B) She could be falling through an area of a right wind. Newton s 2 nd Law tells use that F = ma. The units of mass are (kg) kilograms The units of acceleration are meters per second squared (m/s 2 ) The units of force are newtons (N) So 1N = (1kg)x(1m/s 2 ) Answer the following questions: 1) A 1000kg car accelerates at 2.0m/s 2. What force is being made on the car? F = ma, so F = (1000kg)(2.0m/s 2 ) = 2000N 2) A 2000kg car accelerates at 1.0m/s 2. What force is being made on the car? F = (2000kg)(1.0m/s 2 ) = 2000N 3) A 500kg car accelerates at 4.0m/s 2. What force is being made on the car? F = (500kg)(4.0m/s 2 ) = 2000N

12 21 4) What do you notice about the answers to questions 1, 2, and 3? They are the same. We see then that there are two things that control how big a force is: the acceleration and the mass. So a big acceleration on a small mass and a small acceleration on a big mass could both be caused by the same force. That is, F = ma and F = ma Answer the following questions: 1) A 5000kg car accelerates at 2.4m/s 2. If an equal force is made on a 10000kg truck, what will the truck s acceleration be? (5000kg)(2.4m/s 2 ) = (10000kg)(?) So, the truck s acceleration is 1.2m/s 2. If the mass is twice as big, then the acceleration must be half as big for the same force. 2) A 1000kg car accelerates at 4.0m/s 2. If an equal force is made on a 4000kg car, what will the acceleration be? 1.0m/s 2

13 22 3) A 1000kg car accelerates at 4.0m/s 2. If an equal force is made on a 500kg car, what will the acceleration be? 8.0m/s 2 4) A 900kg car accelerates at 2.5m/s 2. If an equal force causes a second car to accelerate at 7.5m/s 2, what is the mass of the second car? (900kg)(2.5m/s 2 ) = (?)(7.5m/s 2 ) So, the mass of the second car is 300kg. 5) A 1000kg car accelerates at 2.0m/s 2. If an equal force causes a second car to accelerate at 8.0m/s 2, what is the mass of the second car? 250kg 6) A 1000kg car accelerates at 2.0m/s 2. If an equal force causes a second car to accelerate at 0.5m/s 2, what is the mass of the second car? 4000kg

14 23 Since the force equation has three quantities, (force, mass, and acceleration), we can really make three equations: 1) F = ma 2) 3) F m= a F a= m =

15 24 We can use these three equations to answer different types of questions about Newton s 2 nd Law. Answer the following questions: 1) A 550kg car accelerates at 2.0m/s 2. What is the force the engine makes on the car? 1100N 2) A 5000kg truck accelerates at 1.0m/s 2. What is the force the engine makes on the truck? 5000N 3) A kg plane accelerates at 8m/s 2. What is the force the engines make on the plane? N 4) A force of 10000N accelerates a 2000kg car. What is the acceleration of the car? 0.5m/s 2 5) A force of N accelerates a 50000kg plane. What is the acceleration of the plane? 20m/s 2 6) A force of 10000N accelerates a kg boat. What is the acceleration of the boat? 0.1m/s 2 7) A force of 1000N accelerates a car at 10m/s 2. What is the mass of the car? 100kg

16 25 8) A force of 10000N accelerates a car at 5m/s 2. What is the mass of the car? 2000kg 9) A force of 50N accelerates a bicycle at 1.0m/s 2. What is the mass of the bicycle? 50kg 10) A 980kg car accelerates at 2.45m/s 2. What is the force the engine makes on the car? 2401N 11) A force of 850N accelerates a 42.5kg box. What is the acceleration of the box? _ 20m/s 2 12) A force of 7654N accelerates a car at m/s 2. What is the mass of the car? 2432kg 13) A rocket becomes easier and easier to accelerate as it travels through space. Why is this? (Hint: About 90% of the mass of a rocket is fuel) As mass decreases (because the fuel is burned), the force necessary to make the same acceleration gets smaller and smaller, since F = ma. 14) If an object has no acceleration, can we conclude that no forces are acting on the object? Explain. No! We can only conclude that there is not net force acting on it. There may be several forces acting on it but they all must cancel each other out.

17 26 Newton s 3 rd Law (Also called the Law of Interaction) Newton s 1 st Law tells us how an object behaves when there is no net force acting on it. Newton s 2 nd Law tells us how an object behaves when there is a net force acting on it. Newton s 3 rd Law tells us how a force on an object affects other objects. Newton s 3 rd Law Examples: = When one object exerts a force on another object, the second object exerts a force of equal size on the first object in the opposite direction. 1) A book pushes down on a table (see diagram) with a force of 12N. The table pushes upward on the book with a force. of 12N 2) A hand pushes on a spring with a downward 40N force. The spring pushes on the book with an upward 40N. force

18 27 3) A girl s weight pulls downward with a of force 600N. The rings pull upward with a force of. 600N 4) See the figure. The action force is the car tires pushing on the ground. The reaction force is the ground pushing on the car tires.. 5) See the figure. The action force is the rocket pushing on the gas. The reaction force is the gas pushing on the rocket.. 6) See the figure. The action force is the earth pulling down on the ball. The reaction force is the ball pulling up on the earth..

19 28 7) As you stand on a floor, the floor exerts an upward force (normal force) on your feet. Why don t you accelerate upward from this force? See the figure. Your weight and the normal force of the floor pushing up on you are equal but in opposite direction. They cancel out to zero, so you don t accelerate. (Careful: these are NOT action-reaction forces. The reaction force of the earth pulling you down [weight] is you pulling up on the earth.) 8) A girl hangs from the ends of the rope as shown in the figure. If gravity pulls her downward with a force of 500N, what is the reading on the force scale near her left hand? 250N. The sum of the upward forces (250N + 250N) must equal the sum of the downward forces (500N). 9) For each of the following forces, what is the opposite force from Newton s 3 rd Law? a) The downward force of a hammer on a nail. b) The force of gravity pulling down on a book. c) The force of helicopter blades pushing air down. d) The force of air resistance on a thrown baseball. a) The upward force of the nail on the hammer. b) The force of gravity pulling up on the earth. c) The force of air pushing helicopter blades up. d) The force of the baseball pushing forwards on the air.

20 29 10) In each of the situations shown in the figures below, does the force scale read 0N, 100N, 200N, or something else? Why? a) 100N. The total force to the right of the spring scale is 100N b) 100N. These two situations are identical as far as the spring scale is concerned. a) b) Now that we have studied Newton s three laws, it is time to put them all together and answer questions that use more than one of Newton s laws. First, complete Newton s Three Laws: (Try to fill in the blanks without reviewing) Newton s 1 st Law = Every object stays at rest or moves in a straight line at a constant speed net force unless a changes its motion. Newton s 2 nd Law = A net force on an abject causes the object to accelerate in the same direction as the net. force F = ma Newton s 3 rd Law = When one object exerts a force on another object, the second object exerts a force of equal size on the first object in the opposite direction.

21 30 1) For this question, the two rocks in space (shown in the figure to the right) are made of the same material, so a larger rock means a larger mass. The only force is gravity. i) How does the gravitational force of rock B on rock A compare to the gravitational force of rock A on rock B in each situation? Which Law explains this? ii) It is equal in size and opposite in direction. Newton s 3 rd law. Which is bigger: the acceleration of rock A or the acceleration of rock B in each situation. Why a) Rock B, because it has less mass. b) Rock B, because it has less mass. c) The have the same acceleration, because they have the same mass. d) Rock A, because it has less mass. e) Rock A, because it has less mass. iii) Which law did you use to answer part ii)? Newton s 2 nd Law.

22 31 iv) The earth and the moon are like two rocks in space. Why does the moon orbit the earth and not the earth orbit the moon? The force on each body is the same - but in opposite directions. (Newton s 3 rd Law) The moon is accelerated much more than the earth, because it has so much less mass than the earth. (Newton s 2 nd Law) v) Which two laws did you use to answer part iv)? See above. vi) If the earth suddenly disappeared, how would the motion of the moon be different? The moon would travel in a straight line at constant speed because there would be no more forces acting on it. vii) Which law did you use to answer part vi)? Newton s 1 st Law. 2) Your empty hand is not hurt when it bangs lightly against a wall. But when you bang it against a wall while carrying a heavy load, it hurts. Why? Which of Newton s law s explains this? Your empty hand is not hurt because there is little mass, so there is little inertia - little resistance to a change in motion (i.e. stopping). With a heavy load, there is much mass and much inertia, so your hand has more of a tendency to remain moving. Your hand gets squashed a bit and it hurts. Newton s 1 st Law.

23 32 3) Before Galileo and Newton, people thought that if you dropped a stone from the mast of a ship that is moving at a constant speed in a straight line, the stone would fall to the ground behind the mast as in figure 3a. But we know that it will fall as in figure 3b. Can you explain this using Newton s laws? There is no net force in the horizontal direction, so the horizontal motion of the rock will not change it will continue moving forward at the same speed as the ship. It will then move as far forward horizontally as the ship does and falls as is shown in figure 3b. 4) Bob the painter swings from his bosun s chair to paint buildings. His weight is 500N, and the rope can hold a maximum of 300N. Why does the rope not break? Bob s weight (500N) is supported by two ropes (which together can support a maximum of 600N), so the rope doesn t break. 5) Bob the painter decides to change things a little. He ties his bosun s chair as in the figure to the right. Why does the rope break in this case? Bob s weight (500N) is supported by one rope (which can support a maximum of 300N), so the rope breaks. See ya Bob! 3a. 3b.

24 33 6) You hold an apple over your head. a) Write down all the forces on the apple and their reaction forces. b) Then you drop the apple. Identify all the forces on the falling apple and their reaction forces. a) Action: earth pulling down on apple Reaction: apple pulling up on earth. Action: hand pushing up on apple Reaction: apple pushing down on hand b) Action: earth pulling down on apple Reaction: apple pulling up on earth. Action: air pushed up on apple Reaction: apple pushing down on air 7) If we see an object that is not moving (or moving at constant speed in a straight line) but we know there is force acting on it, what conclusion can we make? No motion, or motion in a straight line at constant speed, means there is no net force acting on the object. So there must be at least one other force acting on the object to counteract the force we know is there. 8) When your car moves along the highway at a constant speed in a straight line, there is (obviously) no net force acting on the car. Then why do you have to keep pushing in the gas pedal? You must push on the gas pedal to provide a forward force for the car to equal the forces of friction (air and ground) but in the opposite direction so that the net force is zero.

25 34 9) If you push with a force of 200N to slide a box across a floor at a constant speed in a straight line, how much friction is exerted by the floor on the box? 200N in the opposite direction to motion. There must be zero net force in order that the box moves in a straight line at constant speed. 10) If a big truck and a tiny car have a head-on collision, a) which vehicle experiences the greater force? b) Which vehicle experiences the greater acceleration? Explain both of your answers. a) They each experience the same size force (in opposite directions of course). Newton s 3 rd Law. b) The tiny car will experience a larger acceleration, because its mass is less. Newton s 2 nd Law.

26 11) Sua and Mark are astronauts floating in space? They are some distance apart and connected by a long rope. If Mark starts pulling on the rope, will he pull Sua towards him, will he pull himself toward Sua, or will they both move towards each other? Explain. 35 They will both move towards each other. Mark s pull on the rope is transmitted to Sua causing her to accelerate towards Mark. By Newton s 3 rd Law, the rope pulls back on Mark with equal force causing him to accelerate towards Sua. 12) Look at the figure to the right where someone drives a nail into a piece of wood that is set on top of a stack of books on top of a girl s head. Why doesn t this hurt her? The stack of books consists of many pages that are at rest. They have inertia (because they have mass) so they resist accelerating (they resist a change in state of rest). Each page is like a different body, so when the nail is hit, there is a chain of collisions taking place on the pages all the way down to her head. There is little change in motion of the last page on top of her head, so it doesn t hurt.