Unit 1 Motion and Its Interactions - PDF

Motion and its interactions Unit 1 Forces introduction Questions to address What is acceleration? How do you identify forces? What’s the difference between a force and a net force? How many forces are currently acting on the book? What is a force? A force is a push or pull t...

Motion and its interactions Unit 1 Forces introduction Questions to address What is acceleration? How do you identify forces? What’s the difference between a force and a net force? How many forces are currently acting on the book? What is a force? A force is a push or pull that acts on an object (either by contact or from afar). It is measured in Newtons. Vector → Something that has a magnitude and a direction Scalar: Something that only has magnitude. MWB - Mini Whiteboard Which of the following do you think are scalars/vectors? Divide your mini whiteboard into 2 sections (Scalars and vectors) Weight Temperature Velocity Acceleration Mass Speed What is the equation of a force? The equation of a force is F=ma F=Force m=mass a=acceleration So, do you think that Force is a vector? FORCE IS A VECTOR!!! Talk with the people around you and come up with two reasons and an example that illustrate why force is a vector. What is a net force? The difference between a force and the net force acting on an object is that the net force is the sum of all the forces acting on it. If forces point opposite each other, they cancel each other out. What is the net force acting on each box below? (Net force is a vector, so you should identify its direction AND magnitude by using an arrow) Good rule: The easiest way to figure out what direction something’s net force points is to see what direction its acceleration is, and vice versa. If I push on something and it accelerates, the net force points exactly where the acceleration pointed. MWB Activity On your mini whiteboard, draw to scenarios in nature, sport or real life where a net force is clearly present. Draw vector arrows to show the magnitude and direction of the force on the image.  Types of Forces (5 for now) Name of Force Abbr. Occurs from ______. Points in Picture the direction________. Force of Fg The Earth...towards center of Gravity Earth (usually downward) Applied Force FA Any push or pull...In direction of the push or pull. Normal Force FN A surface...Perpendicular to surface Force of Ff Air, asphalt, etc…. Opposite to Friction the object’s motion. Tension Force FT A string/rope….where the string/rope came from. Complete the Forces introduction assignment Questions What is acceleration? How do you identify forces? What’s the difference between a force and a net force? What is the difference between a balanced force and an unbalanced force? Motion introduction Unit 4 Frame of reference Any measure of position, displacement, speed and acceleration must be made to a reference frame. Distance vs displacement Distance = scalar Displacement = vector What is the distance traveled? 100m What is the displacement form the origin? 40m East Displacement or change in position Δx = xf - xi Speed vs velocity S = d/t v = displacement/t or Δx/t S = Speed (SI unit m/s) v = velocity (SI unit m/s) d = distance (SI unit m) Δx = displacement (SI unit m) t = time (SI unit s) t = time (SI unit s) Speed is a scalar quantity Velocity is a vector quantity Speed vs velocity If the object belows gets to the final position in 4 seconds, what is a. the average speed and b. average velocity of the object? a. S = d/t b. v = Δx/t S = 100/4 v = 40/4 S = 25m/s v = 10m/s East Xi Xf Questions for Consideration What is a position-time graph? What is a velocity-time graph? How do features on one graph translate into features on the other? Distance/Position-Time Graphs Show an object’s position as a function of time. x-axis: time y-axis: distance/position Distance-Time Graphs Imagine a ball rolling along a table, illuminated by a strobe light every second. 0s 1s 2s 3s 4s 5s 6s 7s 8s 9 s 10 s You can plot the ball’s position as a function of time. Distance-Time Graphs *1 10 Distance(cm) 9 8 7 6 5 4 3 2 1 time (s) 1 2 3 4 5 6 7 8 9 10 Distance-Time Graphs What are the 10 9 *1 characteristics of this 8 7 graph? 6 position 5 (cm) 4 Straight line, upward 3 2 slope 1 time (s) What kind of motion 1 2 3 4 5 6 7 8 9 10 created this graph? Constant speed Distance-Time Graphs Constant speed is represented by a straight segment on the D-T graph. *2 pos. (m) pos. (m) time (s) time (s) Constant velocity in positive Constant velocity in negative direction. direction. Distance-Time Graphs Constant speed is represented by a straight segment on the D-T graph. *3 pos. time (s) (m) A horizontal segment means the object is at rest. Distance-Time Graphs The slope of a D-T graph is equal to the object’s velocity in that segment. *1 change in y 50 slope = change in x position (m) 40 (30 m – 10 m) 30 slope = (30 s – 0 s) 20 10 (20 m) slope = (30 s) 10 20 30 40 time (s) slope = 0.67 m/s Velocity-Time Graphs A velocity-time (V-T) graph shows an object’s velocity as a function of time. A horizontal line = constant velocity. A straight sloped line = constant acceleration. Acceleration = change in velocity over time. Positive slope = positive acceleration. Not necessarily speeding up! Negative slope = negative acceleration. Not necessarily slowing down! Velocity-Time Graphs A horizontal line on the V-T graph means constant velocity. N *3 Object is moving at velocity (m/s) a constant velocity time (s) North. S Velocity-Time Graphs A horizontal line on the V-T graph means constant velocity. N *4 Object is moving at velocity (m/s) a constant velocity time (s) South. S Velocity-Time Graphs If an object isn’t moving, its velocity is zero. N velocity (m/s) Object is at rest time (s) S Velocity-Time Graphs If the V-T line has a positive slope, the object is undergoing acceleration in positive direction. If v is positive also, object is speeding up. If v is negative, object is slowing down. Velocity-Time Graphs V-T graph has positive slope. N N *5 *5 velocity (m/s) velocity (m/s) time (s) time (s) S S Positive velocity and Negative velocity and positive acceleration: positive acceleration: object is speeding up! object is slowing down. Velocity-Time Graphs If the V-T line has a negative slope, the object is undergoing acceleration in the negative direction. If v is positive, the object is slowing down. If v is negative also, the object is speeding up. Velocity-Time Graphs V-T graph has negative slope. N N *6 *6 velocity (m/s) velocity (m/s) time (s) time (s) S S Positive velocity and Negative velocity and negative negative acceleration: acceleration: object is speeding up! object is slowing down, Complete the position and velocity vs time assignment (WB 2-6) Graphs continued Unit 4 Position - time 0 10 20 30 40 50 60 70 Position - time Velocity = slope of position time graph = Δy/Δx Velocity (0-1s) = Δy/Δx = (10-0)m/(1-0)s = 10m/s Velocity (1-2s) = Δy/Δx = (20-10)m/(2-1)s = 10m/s Velocity (2-3s) = Δy/Δx = (30-20)m/(3-2)s = 10m/s Velocity (3-4s) = Δy/Δx = (40-30)m/(4-3)s = 10m/s Velocity (4-5s) = Δy/Δx = (50-40)m/(5-4)s = 10m/s Velocity - time 10 0 1 2 3 4 5  Position - time to velocity - time 0-3s: Slope = -6-(-3)/3-0 = -1m/s 3-7s: Slope = 0 m/s P (m) V 7-9s: Slope = 0.5 m/s (m/s) 6 6 9-12s: Slope = 3.67 m/s 5 5 4 4 3 3 2 2 1 1 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 -6 -6  Velocity - time to acceleration - time V a (m/s) (m/s^2) 6 6 5 5 4 4 3 3 2 2 1 1 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 -6 -6  Velocity - time to Position time Area: 3x(-1) = -3 P (m) V Area: 0 (m/s) 6 6 5 5 4 Area: 2x(0.5) = 1 4 3 3 2 2 1 Area: 4x3 = 12 1 0 1 2 3 4 5 6 7 8 9 10 11 12 0 1 2 3 4 5 6 7 8 9 10 11 12 -1 -1 -2 -2 -3 -3 -4 -4 -5 -5 -6 -6 Velocity - time to acceleration - time Slope (velocity-time) = Δy/Δx = (m/s)/s = m/s^2 = acceleration Slope (0-1s) = (-2-1)/(1-0) = -3 m/s^2 Slope (1-2s) = (1-(-2))/(2-1) = 3 m/s^2 Slope (2-3s) = (2-1)/(3-2) = 1 m/s^2 Slope (3-4s) = (2-2)/(4-3) = 0 m/s^2 Summary P-T to V-T → Find the slope V-T to A-T → Find the slope V-T to P-T → Find the area under the graph (Don’t forget negatives) A-T to V-T → Find the area under the graph (Don’t forget negatives Big idea: The area under a velocity time graph is the change in position The area under a acceleration time graph is the change in velocity. Practice - Convert the position time to a velocity time graph Recall Kinematic equations DESCUS methods savg = d/t → d = sxt → t = d/s Data vavg = Δp/Δt → (pf - pi)/t Equation Substitute a = Δv/Δt → (vf - vi)/t Calculate Units vavg = (vf + vi)/2 Sense Kinematic practice MWB - A car travels a distance of 150 kilometers in 3 hours. Calculate the speed of the car in km/h and m/s. - A cyclist increases their velocity from 5 m/s to 15 m/s in 5 seconds. What is the acceleration of the cyclist? - A runner moves from a position of 150 meters to 50 meters in 20 seconds. What was their average velocity? - A runner is running with an average velocity of 6m/s and covers a distance of 1500m. How long did it take them? Activity 2: Kinematics (pg 7,8) → Let’s practice together. - Ignore Q3 until you can do System of equations. Complete Activity 3 (pg. 9-12) Complete Activity 4 (pg. 13-16) - Homework Free body diagrams Spot the difference Fnet = 0 Fnet = to the right A rightward force is applied to a book to make it slide across a table at a constant velocity. Consider friction, but neglect air resistance. A rightward force is applied to a book to make it accelerate to the right across a table. Consider friction, but neglect air resistance. A rightward force is applied to a book to make it slide across a table at a constant velocity. Consider friction, don’t neglect air resistance. Ff Fair Recall 5 main forces for Physical science Types of Forces (5 for now) Name of Force Abbr. Occurs from ______. Points in Picture the direction________. Force of Fg The Earth...towards center of Gravity Earth (usually downward) Applied Force FA Any push or pull...In direction of the push or pull. Normal Force FN A surface...Perpendicular to surface Force of Ff Air, asphalt, etc…. Opposite to Friction the object’s motion. Tension Force FT A string/rope….where the string/rope came from. Complete pages 17-19  Turn to page 20. Activity 2: Balanced forces FN Ff Fapp Fg For questions 1-5 of the following scenarios, complete these steps: 1, Draw a dot to represent the object of interest 2. Determine all the forces that act on the object X direction → Y direction ↑ 3, Draw a Force Diagram 4. Make an x/y table to record your force equations Ff and Fapp FN and Fg Fapp - Ff = 0 FN - F g = 0 Complete Activity 2: Pages 20-21 Newton’s first law of motion Unit 4 Sir Isaac Newton Mathematician, astronomer, theologian, and physicist Lived from 1642-1727 Came up with three laws of classical physics Tested over and over until they became laws One of the most influential scientists of all time Newton’s First Law An object in motion OR at rest will stay that way unless it is acted on by UNBALANCED forces. Could be at rest or moving at a constant speed. Either speeding up or slowing down. Not accelerating. Accelerating. Another way to say it Objects that have zero NET force acting on them will be either stopped (motionless, stationery, etc.) or moving with a constant velocity. Objects that have a nonzero (any number) NET force acting on them will be accelerating in some way (could be either speeding up or slowing down). Video Newton’s second law of motion Unit 4 Formally stated as... The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. In other words... The equation F= ma tells us everything we need to know! Since F and a are on opposite sides of the equal sign, as one goes up, the other must go up (if mass is constant). F and a are directly proportional. Since m and a are the same side as the equal sign, as one goes up, the other must go down (if force is constant). M and a are inversely proportional. Problem Solving / Calculations 1. Draw a force diagram, make an x/y table 2. Find the net force 3. Use F= ma to solve for the missing variable Ex: A girl is running a race and she is sprinting forward with a 53 N force. The force of friction acting on her is 28 N. The mass of the girl is 46 kg. What is the acceleration of the girl? Newton’s third law of motion Unit 4 Newton’s 3rd Law For every action, there is an equal and opposite reaction. In other words...if one object pushes another, the second object pushes back. Example: A bird’s wings push air downward, and the air pushes upward on the bird. That’s how it flies! Force Pairs The forces on the two objects are equal in magnitude and opposite in direction. A force pair describes two forces that are on two different objects. Forces that act on the same object and cancel each other out are NOT a force pair. Why does one object not move? It is easy to forget that there is always a force acting in the opposite direction. This is the evidence we have: In a static situation, there must be an equal and opposite force, or something would be accelerating In the situation where one object accelerates, the other object slows down. For example, the foot slows down after kicking a ball, meaning a force was exerted on it. Momentum and Inertia What is momentum? Momentum is basically “mass in motion.” This is related to inertia. The inertia of an object is its resistance to a change in motion. The difference is an object at rest has inertia, but it doesn’t have momentum. p = m * v Momentum (kg*m/s) Velocity (m/s) Mass (kg) Breaking Down the Formula Because p and m are on opposite sides of the equal sign, they are directly proportional. If mass increases, the momentum increases. Because p and v are on opposite sides, they are directly proportional. If velocity increases, the momentum increases. Because m and v are on the same side, they are inversely proportional. As mass goes up, velocity must go down if momentum is constant. Complete page 40 - 42 Complete page 45 - 46 * We will get back to the pages we skipped Law of Conservation of Momentum The law of conservation of momentum states that the total momentum in a system does not change during a collision (or ever, really…) In other words...total momentum before = total momentum after OR pbefore = pafter In other words (m1v1)before = (m2v2)after Momentum is always conserved! Ex: A person with a mass of 64 kg is standing still. Their 59 kg friend is running at them with a speed of 5 m/s. What is the momentum of the system? a. The running person hugs the standing person. At what speed do the two of them continue to move? Assuming they stay in contact with each other. b. The running person bumps into the standing person and the running person continues to move forward at 3m/s. What is the speed of the other person? c. The running person bumps into the standing person and the running person now flies backwards at 3m/s. What is the speed of the other person? Complete page 43 (44 is a bonus) Complete page 47-48  Newton’s law of gravitational forces Unit 4 Newton’s Apple As the story goes, Newton was sitting under a tree and got hit in the head with a falling apple. He then began wondering more about gravitational force and how objects are attracted to Earth. The Universal Law of Gravitation Every particle attracts every other particle in the universe with a certain force The force is directly proportional to the mass of the objects ○ As mass increases, force increases The force is inversely proportional to the distance between the objects ○ As distance increases, force decreases The Mathematical Representation G = the universal gravitational constant = 6.67 x 10-11 N*(m/kg)2 ○ Since this number is SO small, the forces between small masses are small enough to be ignored Since the distance term is squared, that means that it is more significant in the equation (distance affects the force more than the mass) So why do objects fall towards Earth? According to Newton’s 3rd Law, the forces exerted on each object is the same But objects accelerate towards the Earth at a MUCH greater rate because they have a MUCH smaller mass than the Earth If you think about F = ma, the forces are the same, but the masses are different Electrical and magnetic forces Unit 4 Electrical Forces Electrical forces are due to charges (positive or negative) and the forces of attraction or repulsion they exert on each other Similar to why an atom wants equal number of protons and electrons, charges are always in a state of wanting to be neutral Things can become charged by either gaining or losing electrons ○ For example, when you rub a balloon on your hair, the balloon is taking electrons off of your head. Your hair then repels itself because all of the strands are positively charged Coulomb’s Law The force exerted by two charges is directly proportional to the strength of the charges and inversely proportional to the distance between the two charges. Where k = 9 x 109 N*m2/C2 (C stands for Coulomb’s, a unit of charge) Does it look familiar? IT SHOULD!!! Because it’s the same as the Universal Law of Gravitation! Except it’s k instead of G. What’s different between G and k? Example Problem Two coins lie 1.5 meters apart on a table. They carry identical electric charges of -0.003 C. How much electrostatic force is produced between them? Remember k = 9x109 N*m2/C2 Magnetic Forces Magnetic forces occur due to the domains in an object becoming magnetized, or all facing the same way A common misconception is that magnets have a positive and a negative charge, but actually it works by magnetizing particles inside, like this Even if a magnet is cut in half, it becomes two smaller magnets Forces are applied to other magnets or certain metals that can be affected by a magnetic field What is similar about electric and magnetic forces? Electrical and magnetic forces both exert “force at a distance” which means they can apply a force on another object without direct contact Both electrical and magnetic forces are described as fields → a description of how the forces act on something that is nearby