* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Laws of Motion and Vectors
Angular momentum operator wikipedia , lookup
Photon polarization wikipedia , lookup
Specific impulse wikipedia , lookup
Laplace–Runge–Lenz vector wikipedia , lookup
Coriolis force wikipedia , lookup
Jerk (physics) wikipedia , lookup
Center of mass wikipedia , lookup
Fictitious force wikipedia , lookup
Centrifugal force wikipedia , lookup
Classical mechanics wikipedia , lookup
Newton's theorem of revolving orbits wikipedia , lookup
Modified Newtonian dynamics wikipedia , lookup
Relativistic angular momentum wikipedia , lookup
Seismometer wikipedia , lookup
Relativistic mechanics wikipedia , lookup
Rigid body dynamics wikipedia , lookup
Equations of motion wikipedia , lookup
Classical central-force problem wikipedia , lookup
Karry Queen, famous American novelist, was found slumped at a desk next to an empty bottle of sleeping pills. His last conversation was with the bellhop about how excited he was to be visiting England for the first time. The detective read the note and declared it a murder! Note: I have lost my will to live. My writing was the centre of my life, but now I realize they were just trashy novels. As the colour fades from my eyes, I can only hope for a better life in the next world. Why was the detective so sure the author was murdered? Finish Test? Notes 12.1 “Newton’s 1st and 2nd Laws” in “Laws of Motion” unit online. Work on Conceptual Problems Assignments: 1. Newton’s Laws Conceptual Problems - TBA To access notes and projects online: fths.ftusd.org Menu-> Staff Directory -> Olson Useful Links -> Int Sci Laws of Motion Unit Ch 12 “Forces” I don’t want to move and you can’t make me… unless there’s enough force. Mt. Graham Explain how to make objects speed up, slow down, or change direction using forces. Describe what factors determine how much objects change speed. From your own experience, what will happen? 1. A marble is placed at the top of a smooth ramp. What will happen to the marble? What force causes this? 2. A marble is rolling around in the back of a small toy wagon. The wagon stops suddenly by when it hits a rock, and the marble rolls toward the front of the wagon. Why does the marble keep going? Newton’s First Law 〉Things in motion stay in motion, things at rest stay at rest UNLESS acted on by an outside force. 〉 speed up 〉 slow down 〉 change directions Inertia Objects resist change unless there is an outside force Related to mass Bigger mass = more inertia Smaller mass = less EX- Seat belts and cup holders. Seat belts and friction between you and the seat provide and unbalanced backward force that stops you as the car stops. Cup holders stop your drink from sliding around as the car accelerates or turns corners 〉 Newton’s 2nd Law 〉 Results of applying force depends on mass and acceleration. 〉 net force = mass × acceleration, or F = ma 〉 Force is measured in newtons (N): 1 N = 1 kg m/s2 For equal forces, a larger mass accelerates less. For equal masses, a greater force produces a greater acceleration. Zookeepers lift a stretcher with a sedated lion. The total mass of the lion and stretcher is 175 kg, and the upward acceleration is 0.657 m/s2. What force is needed to produce this acceleration? 1. Use F=ma. Given: mass, m = 175 kg acceleration, a = 0.657 m/s2 Unknown: force, F = ? N 2. Insert the values into the equation, and solve. F = 175 kg 0.657 m/s2 F = 115 kg m/s2 F = 115 N Newton’s second law can also be stated as follows: The acceleration is proportional to the net force and inversely proportional to the mass. force acceleration = mass F a= m a F a m 1. What is the equation for Newton’s 2nd Law? 2. What force is needed to accelerate a 1,600 kg car forward at 2.0 m/s2? 3. A baseball accelerates downward at 9.8 m/s2. If the gravitational force is 1.4 N, what is the ball’s mass? 4. A sailboat and crew have a mass of 655 kg. If there is a 895 N force pushing the boat forward, what is the boat’s acceleration? Materials: 2 balls, ramp, stop watch How do you think mass will affect the speed of the balls? Does the heavier ball roll faster, slower, or the same speed as the lighter one? What factors probably affected the motion of the two balls? Which will reach the floor first? A. flat paper or B. ball Why are the forces on these two pieces of paper different? Draw the force diagrams! The “Soul-Ace Hotel” was holding its first birthday party and all eight of the regular customers were invited. The owner ordered the cake and cut it into 4 slices since she only expected half of the people to attend. To her dismay, everyone invited showed up. How can she make the cake into eight equal size pieces with just one cut? Finish Test? Check Grades? Review Newton’s 1st and 2nd Laws Work on Conceptual Problems Assignments: 1. Newton’s Laws Conceptual Problems - TBA Materials: 2 balls, ramp How do you think mass will affect the speed of the balls? Does the heavier ball roll faster, slower, or the same speed as the lighter one? What factors probably affected the motion of the two balls? Which will reach the floor first? A. flat paper or B. ball Why are the forces on these two pieces of paper different? Draw the force diagrams! 1. What is the equation for Newton’s 2nd Law? 2. What force is needed to accelerate a 1,600 kg car forward at 2.0 m/s2? 3. A baseball accelerates downward at 9.8 m/s2. If the gravitational force is 1.4 N, what is the ball’s mass? 4. A sailboat and crew have a mass of 655 kg. If there is a 895 N force pushing the boat forward, what is the boat’s acceleration? Many people suffer neck injuries from rear-end car collisions. How does inertia apply here? How do headrests help? If you’re being chased by an elephant, it’s a good idea to zigzag. Why is your smaller mass an advantage? A 100 N bag of nails is suspended from a rope. How many N of tension are exerted on the strand? What if there were 4 vertical strands? Usually uses F = ma… Two forces are exerted on a 2 kg object, one is 50 N east and the other is 30 N west. What is the object’s acceleration? A cart is being moved by a certain net force. If its mass suddenly doubles, how much does the acceleration change? A rocket picks up speed and significantly increases acceleration as it continues firing. Why? Please find your new seat. Tori D. Iversin N. Jay A. Tayton T. Kevin N. Tatianna M. Crystal W. Kobe T. Please find your new seat. Brittany C. Dawndreah W. Joy B. Cassie B. Mariah S. Robyn O. Cia N. Kristen P. Bash W. Romeo M. Tehya W. Delilah L. I can run, but not walk. Wherever I go, thought follows close behind. What am I? Get textbooks and finish “Motion” test – 20 minutes Notes Ch 12.2 “Gravity” Work on Conceptual Problems Quiz on Laws 1-2 and Gravity THURSDAY Assignments: 1. Newton’s Laws Conceptual Problems - TBA Objectives 〉Explain how mass and weight are related. 〉Describe gravity as attraction between objects. 〉Analyze why a projectiles’ path is curved. Weight is a measure of the gravitational force exerted on an object. Elvis is a student whose mass is 70 kg. On Earth, he weighs about 690 N. Suppose Elvis could stand on the surface of the following bodies in the solar system. Match Elvis’s weight with planet or moon. (Hint: Earth has a mass of 6.0 x 1024 kg.) Planet Elvis’s weight a. Jupiter (m = 1.9 x 1027 kg) 780 N _______ b. Venus (m = 4.9 x 1024 kg) 113 N _______ c. Neptune (m = 1.0 x 1026 kg) 260 N _______ d. Mercury (m = 3.3 x 1023 kg) 1800 N _______ e. Earth’s moon (m = 7.4 x 1022 kg) 620 N _______ Suppose Elvis is in orbit around Venus at a distance twice as far from the planet’s center as the surface of Venus is. Would you expect his weight to be greater than, less than, or equal to his weight on the surface of the planet? Weight is equal to mass times free-fall acceleration. weight = mass x free-fall acceleration w = mg How much does a 17 kg crate of books weigh? use g = 9.8 m/s2 Gravity!! Weight is measured in newtons (N). Weight is different from mass. mass = a measure of the amount of matter in an object weight = the gravitational force an object experiences because of its mass All objects in the universe attract each other through the force of gravity. Newton’s Law of Universal Gravitation gives the size of the gravitational force between two objects. Equation for universal gravitation… m1m2 F =G 2 d – m1 and m2 are the masses of the objects – d is the distance between the objects – G is a gravitational constant Equation for universal gravitation… m1m2 F =G 2 d – Depends on mass and distance of objects – Distance changes usually have more impact than mass. 1st Law An object weighs 98 N on earth. How much would it weigh on Planet X where gravitational acceleration is 6 m/s2? Use F=ma 2nd Law What force is acting on 10 kg object in free fall towards Earth? What is the net force if it encounters 15 N of air resistance? All matter is affected by gravity. Two objects always have a gravitational force between them. When something is very large, like Earth, the force is easy to detect. Gravitational force increases as mass increases. Gravitational force decreases as distance increases. free fall: acceleration due only to gravity Ignore air resistance for now. Works ideally close to Earth’s surface Accelerate at same rate REGARDLESS of mass. What is the product of the following series? (X-A) x (X-B) x (X-C) …. (X-X) x (X-Y) x (X-Z) Get textbooks? Quiz Newton’s Law 1-2 and Gravity Work on Conceptual Problems Assignments: 1. Newton’s Laws Conceptual Problems - TBA Two mothers and two daughters go shopping. They have 21 $1 bills which they split so each got $7. How is this possible? 10-15 min to work on Conceptual Problems or finish quiz Notes on Free Fall (Ch 12.2) Start Calculating Free Fall Lab Assignments: 1. Newton’s Laws Conceptual Problems - TBA Air resistance can balance weight. –terminal velocity: the velocity of a falling object when the force of air resistance is equal in magnitude and opposite in direction to the force of gravity Astronauts in orbit are in free fall. What force keeps the ball on my hand? How is the motion different if I shove it off my hand? 2 Components – horizontal and vertical Result is a curved path. Thrown, launched, fired, etc objects Near Earth’s surface Horizontal component… ignore air resistance After thrown, no horizontal forces are acting on the ball. So, the horizontal component of velocity of the ball is constant. Vertical component…ignore air resistance When you throw a ball, gravity pulls it downward, giving the ball vertical motion with an acceleration of 9.8 m/s2 on Earth. Orbiting is projectile motion. If you saw your mirror image holding a letter “d” in your left hand, what would you actually be doing? Notes on Circular Motion Finish “Calculating Free Fall Lab” Work Time Circular Motion Wksht due THURSDAY Conceptual Problems Assignments: 1. Newton’s Laws Conceptual Problems - TBA Object is traveling at a constant (uniform) speed on a circular path Period (T) – Time it takes to make one trip around the circle Distance => Circumference = 2r Speed (v) – distance / time 1.2 m Find v v = 3.77 m/s T=2s Speed is constant, but velocity is always changing This acceleration is “centripetal” acceleration Object moves in circle. At time t0 it is at O with a velocity tangent to the circle. At time t, it is at P with a velocity tangent to the circle The radius has moved angle Draw the velocity vectors so that they have the same tail. The vector connecting the heads is v Draw the triangle made by the position change (b) These are similar triangles. Equations get rearranged… Know this and this! At any given moment v is pointing tangent to the circle ac is pointing towards the center of the circle If the object suddenly broke from circular motion would travel in line tangent to circle A car goes around a curve at 20. m/s. If the radius of the curve is 50. m, what is the centripetal acceleration of the car? 1. Pick correct acceleration equation. 2. Plug in numbers. 3. Solve Two identical cars are going around two corners at 30 m/s. Each car can handle up to 1 g. The radius of the first curve is 50 m and the radius of the second is 100 m. Do either of the cars make the curve? (find the ac) Yes, second car makes it. 50 m 100 m Use an electronic balance to get object mass for the first chart. Use a spring scale to get weights in N. Use data from yesterday to calculate object acceleration. Then calculate mass from F=ma. Choose the most appropriate form of the acceleration equation given your data. a = d/t2 Circular Motion Lab Work time Circular Motion Worksheet Conceptual Problems Assignments: 1. Newton’s Laws Conceptual Problems – MONDAY 2. Parachute Lab LATE Make sure you have these equations! Know this and this! Goggles!! Balance penny on the hanger. 2. Slowly start to swing the hanger until it and the penny are going in a circle. 3. Calculate the centripetal acceleration and force of the penny. 1. Find time for 10 rotations, then divide by 10 to find T. Notes Ch 12.3 “Newton’s 3rd Law” Work time Force and Momentum Problems due MONDAY Circular Motion Worksheet Conceptual Problems Assignments: 1. Parachute Lab LATE 2. Circular Motion Worksheet LATE 3. Newton’s Laws Conceptual Problems – MONDAY 4. Force and Momentum Probs - MONDAY Objectives Explain what happens when objects exert forces on other objects. 2. Calculate momentum. 3. Describe conservation of momentum. 1. An ice skater holding a basketball is standing on the surface of a frozen pond. The skater throws the ball forward. At the same time, the skater slides on the ice in the opposite direction. 1. Is the force on the ball greater than, less than, or equal to the opposite force on the skater? Explain your answer. 2. Is the acceleration of the ball greater than, less than, or equal to the acceleration of the skater? (Hint: F=ma) Explain your answer. Newton’s 3rd Law 〉 For every force, there is an equal and opposite reaction force. 〉Ex: Friction works to stop motion. 〉Air pushes down, balloon goes up 〉Ball changes direction when hit. Details Forces always occur in pairs. For every action force, there is an equal and opposite reaction force. Forces in the pair do NOT act on the SAME object. Girl pushes on wall, wall pushes on her. Details Equal forces don’t always have equal effects. Ex: The action force of Earth pulling on a falling object is much more obvious than the force of the object pulling on Earth. Action force of bullet firing creates a reaction force that causes the gun to “kick” or “snap”. Momentum = mass in motion Momentum is proportional to mass and velocity. Which has more, a car going 30 mph or 90 mph? Which has more, a pebble sliding across the floor or a person sliding at the same speed? Force is related to change in momentum. As the time of the change becomes longer, the force needed to cause the change in momentum becomes smaller. Moving your hand back as you catch a ball means less force. Calculating straight line momentum momentum = mass x velocity, or p = mv SI units = kilograms times meters per second (kg•m/s). Momentum and velocity are in the same direction. Momentum increases as mass or velocity increase. Momentum Calculate the momentum of a 6.00 kg bowling ball moving at 10.0 m/s down the alley toward the pins. 1. List the given and unknown values. Given: mass, m = 6.00 kg velocity, v = 10.0 m/s (toward the pins) Unknown: momentum, p = ? kg • m/s (and direction) 2. Write the equation for momentum. momentum = mass x velocity p = mv 3. Insert the known values into the equation, and solve. p = mv = 6.00 kg 10.0 m/s p = 60.0 kg • m/s (toward the pins) Triskaidekaphobia is the fear of what? Tri = Deka = BONUS POINT: What does friggatriskaidekaphobia mean? Notes Ch 12.3 “Newton’s 3rd Law” Work time Force and Momentum Problems due TODAY Conceptual Problems due TODAY Conservation of Momentum due WEDNESDAY Circular Motion Worksheet LATE Assignments: 1. Newton’s Laws Conceptual Problems – TODAY 2. Force and Momentum Probs – TODAY 3. Conservation of Momentum due WEDNESDAY Collisions conserve momentum 〉 TOTAL momentum is the same before and after a collision. 〉 This is the law of conservation of momentum 〉 Possible situations… 〉Objects collide and bounce off each other. 〉Objects stick together and move in direction of the greater momentum Objects collide and bounce… momentum same before and after… 2 objects before = 2 objects after m1v1 + m2v2 = m1v1’ + m2v2’ Objects collide and stick together… momentum same before and after… 2 objects before = 1 object after m1v1 + m2v2 = (m1 + m2)v’ Objects stick together and move in direction of the greater momentum Identify the action and reaction forces when a ball is lifted and let go. Conservation of momentum results … 1 ball = 2 balls = 3 balls = When two objects collide, the momentum (increases/decreases / stays the same) What happens if you drop one ball on each side at the same time? Why? Imagine you drop 3 balls, it moves 2 that hit, and move 3 again. How is this an example of conservation of momentum? Read the following phrases. Do you notice anything odd? Bird in the the hand Once in a a lifetime Paris in the the spring Discuss Test Details Catapult Momentum Lab Work time Circular Motion Worksheet LATE Force and Momentum Problems LATE Conceptual Problems LATE Conservation of Momentum due WEDNESDAY Assignments: 1. Newton’s Laws Conceptual Problems – LATE 2. Force and Momentum Probs – LATE 3. Conservation of Momentum due WEDNESDAY Includes paper and performance test on MON Nov. 2. MC and word problems Projectile motion lab test Work solo or with a partner. YOU will provide the materials to build the catapult. Read through the lab. Check suggested materials. Start planning now, build Thursday & Friday, test MONDAY Granny Smith set her luggage down on a train as it was passing the Soul Ace Hotel. She walked forward at 1.5 kph. Half an hour later she reached the front of the train. Unable to find a place to sit, she headed back for her luggage. The train was passing City Hall which is 10 km from the hotel. How fast was the train traveling? HINT: speed = distance/time Catapult Momentum Labs? Gyroscope Activity and Ch 12 Review Plan for Catapult/bring materials Work time Conservation of Momentum due TODAY Other missing assignments Assignments: 1. Newton’s Laws Conceptual Problems – LATE 2. Force and Momentum Probs – LATE 3. Conservation of Momentum due WEDNESDAY Put this in your notebook… 1. Wind the string down towards the movable ring and pull. What factor determines whether the gyroscope balances or falls? 2. 3. Use Newton’s 2nd Law to explain #1. Draw force diagrams of the spinning gyroscope on… the pedestal a finger loop of string It is estimated that the Earth weighs 6 sextillion (1021) tons. How much more would the Earth weigh if one sextillion tons of concrete and stone were used to build a big wall? Catapult Lab Test Research, design catapult Start planning for experiment AND work on report Work time All previous assignments LATE Assignments: 1. Newton’s Laws Conceptual Problems – LATE 2. Force and Momentum Probs – LATE 3. Conservation of Momentum due LATE What do the following have in common? Ichabod Crane A missing head Katrina van Tassel Catapult Lab Test Research, design catapult Plan experiment, test, work on report Work time Ch 12 Review All other previous assignments LATE Ch 12 “Laws of Motion” test MONDAY Assignments: 1. Ch 12 Review due TODAY 2. Catapult Report due MONDAY Don’t be that guy! Prep for the lab test. A watch was discounted 20% and then another 30% at the register during a sale. Would the price be lower if there was one discount of 50%? Why or why not? Hint: Assume the watch was $100. Catapult Lab Test Get target distance, 10 minutes to prep 3 shots Ch 12 “Laws of Motion” paper test Use notes and a calculator. Quiet until ALL tests are in. Assignments: 1. Ch 12 Review LATE 2. Catapult Report due TODAY Don’t be that guy! Get car times and masses online. cars.findthebest.com or www.zeroto60times.com Decide to use either 0-60 mph or quarter mi times. convert kg to lbs by x 2.2 Use numbers to calculate acceleration and force. Everything in the study of motion is either a vector or a scalar. Examples Distance Displacement Speed Velocity Mass Acceleration Time Momentum Force A scalar is fully described by its magnitude/number Examples: Distance, Speed, Mass, Time Vectors have a magnitude AND a direction Examples: Displacement, Velocity, Acceleration, Force Write scalars with normally x m t Write vectors by Putting an arrow over it: v Using bold font: v Using italic font: v Decide if the following quantities are a vector or a scalar. Write ‘S’ for scalar and ‘V’ for vector. The acceleration of a car Vector How far you walk to school Scalar The number of students in a classroom Scalar The velocity of a bird Vector The displacement of a flight Vector The time it takes to get to school Scalar The mass of a pencil Scalar The Force required to push a truck Vector How fast a person runs Scalar A person walks 20 m northwest Vector Draw vectors as an arrow Length of the arrow is its magnitude Direction of the arrow it its direction Define the direction of using 0 to 360 degrees. Vectors can be added. Tip to Tail method Put the tip of one vector to the tail of another Draw the resultant vector from that A + B = B A A+B To subtract vectors, add the opposite. Same process as addition A + -B = -B A Multiplying and Dividing vectors by a scalar only changes the magnitude Direction is unaffected Example: 5*B B B B B B B To fully describe a vector, break it into components. Each vector has an x and y component The components determine how far in the x and y direction a vector goes A Ax Ay Write vectors using their components. We use ^ x to represent the x-direction and represent the y-direction We can write vector A as… A = 4^ x+ 3 ^y A 4 3 ^ yto If we know the components of a vector, we can find its magnitude by using the Pythagorean Theorem A2 + B2 = C2 ^ x Example: A = 4 + 3 |A|2 = 42 + 32 |A|2 = 16 + 9 |A|2 = 25 |A| = 5 ^ y When we add/subtract vectors, add/subtract their corresponding components Add/Subtract x components from x components and y components from y components ^ ^ Example add A = 4 ^ + 3 to B = 2 x+ 5 ^y x y A + B = (4 + 2)^x + (3 + 5) ^ y A + B = 6^ x+ 8 ^ y Simulate dropping a boiled egg. Would the eggs survive? Show data to verify! Hints: Calculate the force the egg experiences when it lands. Boiled eggs will usually crack if they experience a force more than 25 N. Find the mass of the parachute, cup, “egg”, clips, etc and convert to kg. Average chicken eggs have a mass of 57 g (.057 kg). Create a poster to explain the following situations: force and acceleration of the penny and “egg” Diagram the motion of the penny on the hanger. Calculate the centripetal acceleration and force of the penny on the hanger.