Introduction to Kinematics


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Introduction to Kinematics

  1. 1. Creative Curriculum for Children: PHYSICS Kinematics Projectiles here, there, there & everywhere.Product of Victor Hakim, C.C.C. Vice President and Director of Physical Sciences
  2. 2. One of the most common types of problems in physicsis a branch called kinematics. This deals withtrajectories and the details of how an object acts whenin motion.In Greek, kinema- means “movement” and that’sexactly what we’re studying:<<What’s the maximum height after throwing an object inthe air? What’s the maximum velocity? What will be thevelocity after n seconds?>> We’ll learn how to answer these today! ©2011 Creative Curriculum for Children [CCC]
  3. 3. First, we need a few pieces of key information: We must measure everything in what are called S. I. Units (International System of Units in French). Time is measured in seconds and displacement in meters. These yield velocity units of m/s and acceleration units in m/s/s or m/s2. We must set up our coordinate axes so that the y-axis is going up and down, and the x-axis is going left and right. Up and right are positive (+), and down and left are negative (-). y (+)x (-) x (+) y (-) ©2011 Creative Curriculum for Children [CCC]
  4. 4. Because of Earth’s gravity, there will always be an accelerationof objects downward, and we use this in our calculations as anegative number. Objects will decelerate, or lose an amount ofvelocity after every second, and it is always the same loss ofvelocity after each second.The value of Earth’s gravitational pull is always constant (closeto the surface of the Earth) and we use equations for kinematicsonly on the assumption that the acceleration downwards neverchanges. We happen to call this constant downwardsacceleration g, a value equal to about 9.81 m/s2. But we alwaysuse g = 10 m/s2. With this substitution, calculations becomeunbelievably easier. Because the acceleration points downward, the value of acceleration for projectiles is -g. Acceleration = -10 m/s2 ©2011 Creative Curriculum for Children [CCC]
  5. 5. Now for the equations.First, it’s very important that you understand themeaning of each variable:• t is the variable that stands for the time. It is measured in seconds.• v stands for velocity. Measured in m/s, this can be either positive or negative.• g stands for the acceleration on Earth. This is measured in m/s2. For problems on the Earth’s surface, the value will always be g = 10 m/s2. ©2011 Creative Curriculum for Children [CCC]
  6. 6. Don’t worry about memorizing these formulas justyet, but know how to use them and become familiar withtheir applications.1. v = v0 – gt v0 22. Maximum Height = 2g + H0These equations consider the velocity in the y-axisdirection. In other words, they only work for velocitiesthat are straight up or straight down.Equation (1) tells us the velocity, v, at any time t inseconds. v0 is a constant. It stands for the initial velocitywith which a projectile is thrown, namely, at time t=0. Wesay, “V initial.” ©2011 Creative Curriculum for Children [CCC]
  7. 7. Equation (2) tells us the maximum height a projectile will go given an initial vertical velocity (+ only). Also, H0 refers to the initial height, if I’m not shooting the projectile initially (at time t=0) from the ground. I can shoot from atop Mount Everest, 8,848 meters high, but I can still find my maximum height by setting H0 = 8,848.Equation (2): I’ll throw the ball up atinitial velocity v0, and I want to findthe maximum height that that ball willgo. ©2011 Creative Curriculum for Children [CCC]
  8. 8. Let’s try some examples.I’ll throw a projectile up at 20 m/s. What is its velocity after 4seconds?Use Equation (1). My v0 = 20. g, as always, will be equal to 10.Now, if I’m asking for the velocity after 4 seconds, simply set t=4and solve for v:v = 20 – 10x4 = -20 m/s2.Does this make sense? I’ll throw the ball upwards, because v0was positive, and the Earth will slow it down until it stops.Then, the ball will come down, and so it should be at a negativevelocity.We got a negative velocity! =] ©2011 Creative Curriculum for Children [CCC]
  9. 9. Stopping point  Starting point  Point after 4 seconds ©2011 Creative Curriculum for Children [CCC]
  10. 10. Maximum Height.I am 100 meters tall. I shoot the ball up, from my head, at 5 m/s.Find the maximum height.I think you get the idea. H0 = 100 and v0 = 5. Plug them in intoEquation (2):Max height = 52/(20) +100 You can use a calculator! = 101.25 m.Notice that the max height is only 1.25 m above the startingheight. That makes sense because I only threw it at 5 m/s, avelocity that’s not too fast. ©2011 Creative Curriculum for Children [CCC]
  11. 11. A few more tips…• It’s important to understand the problem. Picture the situation, create it, and this will help you to both set up the problem and verify that you’re final answer makes logical sense.• Become familiar with the equations so that when you get a problem, you can tell right away which equation that’s good for. Physics is all about knowing which formulas to use. Pick the right one with the variables that are given to you.• Next time, we’ll experiment with projectiles shot not perfectly vertically, but also angled a little to the side: ©2011 Creative Curriculum for Children [CCC]
  12. 12. Practice—good luck!1. If I shoot a ball up from the ground at 82 m/s, after how many seconds will it temporarily stop moving?2. From problem 1, what is the max height?3. I shot a projectile, and it reached its max height of 20 meters. With what velocity did I initially throw it up?4. If it takes 10 seconds for a ball to drop to the ground from atop a building, tell me the velocity with which the ball hit the ground (this will be the maximum magnitude of velocity in the entire experiment). ©2011 Creative Curriculum for Children [CCC]
  13. 13. Answers #1-4 1. 8.2 seconds 2. 336.2 meters 3. 20 m/s 4. -100 m/sProduct of Victor Hakim, C.C.C. Vice President and Director of Physical Sciences