Circular and Projectile Motion Notes PDF

Circular and Projectile Motion 1. A ball is dropped from rest. What is its displacement after 3 seconds? 2. What is the velocity of an object under constant acceleration after 5 seconds if its initial velocity is 10 m/s and its acceleration is 3 m/s^2? Objectives Develop models to repr...

Circular and Projectile Motion 1. A ball is dropped from rest. What is its displacement after 3 seconds? 2. What is the velocity of an object under constant acceleration after 5 seconds if its initial velocity is 10 m/s and its acceleration is 3 m/s^2? Objectives Develop models to represent and analyze projectile motion and circular motion. Use multiple equations and algebraic reasoning to solve projectile motion and circular motion problems. Projectile Motion 1. You are standing at the edge of a cliff with a friend. You throw a rock straight out, horizontal to the ground, and your friend drops an identical rock from the same height. Which rock hits the ground first? They both hit the ground at the same time, since their velocity vectors i the vertical direction are the result of free-fall motion and the acceleration due to gravity. The stone you throw outward will land farther away from the cliff, however. Representing Velocity Velocity can be represented as a set of vector components which tell how fast an object is moving in the horizontal, x, and vertical, y, directions. The Pythagorean theorem is used to determine the magnitude of the velocity vector. Adding Velocities in Two Dimensions The horizontal and vertical components of velocity are independent of each other and can be added and subtracted analytically. EXPERIENCE IT! Crumple up two pieces of paper. Standing side-by-side with a friend, have your friend throw one ball horizontally at the same time you drop your ball from the same height. Which ball hits the ground first? Projectile Motion https://phet.colorado.edu/sims/html/projectile-motion/latest/pr ojectile-motion_all.html What are some common examples of projectile motion? Projectile Motion Projectile motion is the combination of uniform motion parallel to Earth’s surface and free-fall motion with constant acceleration due to gravity. An object is launched at a velocity of 40 m/s in a direction making an angle of 50° upward with the horizontal. Q1. What is the maximum height reached by the object? Q2. What is the object’s total flight time (between launch and touching the ground)? Q3. What is the object’s horizontal range (maximum x above ground)? https://quizizz.com/admin/quiz/5c61995d003092001a003e17 /projectile-motion Have a student read the text. Click to show the horizontal and vertical equations of motion. Ask: What is the horizontal displacement of a projectile dependent on? (Answer: vx, because the horizontal velocity is constant) Ask students if the vertical equations of motion look familiar. (Sample answer: Yes, they are similar to the equations for velocity and displacement for constant accelerated motion. For example, the acceleration, a, of a car on a road is now replaced by the acceleration, g, of gravity for objects in projectile motion.) Click to show the velocity graphs. Prompt students to recall that when they modeled uniform motion, they found the displacement by finding the area under the function of a velocity vs. time graph. Likewise, for projectile motion, the horizontal displacement component equals the area under the function. Ask: Is vx affected by gravity? (Answer: No, the x and y components of velocity are independent.) Why is the slope of the graph on the right negative? (Answer: Because the acceleration due to gravity is in a downward, or negative direction, and the slope is the acceleration) HW https://wordwall.net/play/4880/862/578 HW Grade 11 https://wordwall.net/resource/79008004 Modeling Projectile Motion The equations of projectile motion describe the horizontal and vertical components of an object’s velocity and displacement at all times. Horizontal motion Vertical motion Modeling Projectile Motion What is the horizontal displacement of a projectile dependent on? vx, because the horizontal velocity is constant Is vx affected by gravity? No, the x and y components of velocity are independent. Why is the slope of the graph on the right negative? : Because the acceleration due to gravity is in a downward, or negative direction, and the slope is the acceleration Q1: A professional football punter kicks a football with an initial velocity v=(15.0 m/s)x̂+(30.0 m/s)ŷ. How long the football stays in the air is known as the hang time. Determine the hang time, as well as the horizontal and maximum vertical displacements. Q2: A friend kicks a soccer ball into the air with an initial velocity v=(9.0 m/s)x^+(18 m/s)ŷ. Determine the hang time for the ball and how far away it will land from its initial position. Value Grade 10 https://wordwall.net/resource/79003604 https://classroomscreen.com/app/screen/w/2d74d6f2-9c88-4 679-8146-6dbdab537def/g/44c9769e-c69a-4635-8389-26c7 6a813e1d/s/3843e287-d67b-4f06-87fa-7dca3693db81 https://flippity.net/sm.php?x=kco9NzPo%20%20OZhcZ5,&t= Snowman%20Game&g=Flower%20Power Where is circular motion in our world? 1. Astronomy Planetary Orbits: Planets move in elliptical orbits around the sun, but the concept of circular motion helps us understand the gravitational forces at play. Galaxies: The motion of stars within galaxies can often be approximated by circular motion around a galactic center. 2. Engineering Roller Coasters: The design of roller coasters involves circular motion to create thrilling loops and turns, requiring careful calculations of speed, radius, and forces acting on riders. Machinery: Many machines utilize circular motion, such as gears, wheels, and turbines, where efficient energy transfer is crucial. Conclusion Circular motion is more than just a physics concept; it's integral to understanding many aspects of the world around us. From the paths of planets to the design of everyday object Circular Motion In uniform circular motion, an object travels in a circular path at a constant speed. The magnitude of the velocity stays the same, but the direction of the velocity constantly changes. Circular Motion Circular Motion :When an object travels in a circular path at a constant speed, the motion is called uniform circular motion. The acceleration of an object in uniform circular motion is called centripetal acceleration. Have a student read the text. Explain that you can show the velocity is center-seeking by looking at the velocity at two instances in time. Click to show the overhead view image and head-to-tail method image. Prompt students to note the head-to-tail method diagram used to determine the direction of the change in velocity. Ask: In what direction is the change in velocity? (Answer: Toward the center) Explain that the acceleration of an object in uniform circular motion is called centripetal acceleration. The magnitude is determined by using the concept of similar triangles. Ask: In what direction do you think the acceleration vector points? (Answer: Toward the center, the same as the direction of the change in velocity.)  flashcards https://quizizz.com/admin/quiz/66f7d9350d56cba8aa2bfc04?at=66f7 daa8d29bb8b24aa5bf47&flashcard_feedback=true Circular Motion