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Mastering Projectile Motion and Periodic Motion Dynamics

Learn the fundamentals of projectile motion, equations, and independence of motion in 2 dimensions. Understand periodic motion, including circular motion, centripetal forces, and simple harmonic motion. Practice problems included.

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Mastering Projectile Motion and Periodic Motion Dynamics

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  1. CHAPTER 7 NOTES KONICHEK

  2. I. Projectile motion- • A Projectile- this is the object being launched • B. trajectory-The path the projectile follows.

  3. II. Independence of motion in 2 dimensions • A. The horizontal motion of a object is independent of the vertical motion. • 1. A bullet shot and one dropped will strike the ground at the same time if they are from the same height. • a. The only force acting on the bullet once outside the barrel of the gun is gravity.

  4. B. Equations to represent the motion- neglect air resistance • 1. X=VxT- this is horizontal displacement • 2. T2= 2Y/g -time for the shot to hit the ground

  5. EXAMPLE PROBLEM(P136) • A stone thrown horizontally at 15m/s at from a cliff 44m high. • SINCE THE GROUND ID ZERO THE OBJECT IS REPRESENTED BY A -44M • A)How long does it take to reach the bottom? • B) how far from the base of the cliff does the stone strike? • C) sketch the trajectory

  6. SOLUTION • A • . T2= 2(height of cliff)/g • T2=3(-44m)/9.8m/s2 = 3s • B. • X=Vt- 15m/(3s)=45m

  7. DON’T WORRY THERES AN EASIER WAY • C. Objects launched at an angle • 1. The horizontal component is small since no other forces are acting on it(Vcosθ) • 2. Vertical components are larger at the beginning • a. Object slows as it’s going up, at the top it stops(Vsinθ) • b. the vertical component then increases again but in the opposite sign when falling. • c. When the object reaches launch height it is traveling at the same velocity as the launch velocity

  8. THESE WILL MAKE YOUR LIFE EASIER  • Magical projectile motion equations • Rx= V2sin2θ/g • H= -(vsinθ)2/2g • T= -2Vsinθ/g

  9. 3. Sample problem - a ball in flight has an initial velocity of 4.47m/s at an angle of 66° above the horizontal. Find • A) How long it took the ball to land. • B) How high the ball flew. • C) Find the range

  10. III. Periodic motion-The motion of the object repeats itself. A pendulum, a Yo Yo • A. circular motion-The product of 2 forces acting on an object. • 1. F1- the outward force of inertia- tangent to the motion of the object. • 2. F2- the inward force called centripetal force.

  11. F1 IS THAT IMAGINARY FORCE • CALLED CENTRIFUGAL FORCE F1 F2

  12. B. Centripetal acceleration- This is the acceleration towards the center of the circle • 1. Ac= V2/r • 2. V= 2πr/T velocity for one time period • 3. Substituting into the equation a= (2πr/t)2/ r a=4π2r/T2

  13. C. Centripetal forces - the inward force causing uniform circular motion • 1 F= m( 4π2r/T2)

  14. IV. Simple Harmonic Motion. _ when an object is moved from an equilibrium position, and is released, moves through an equilibrium position. • A. Period- this is the time necessary for one complete cycle. • B Pendulum- an object suspended on a string which undergoes simple harmonic motion. • 1. Period of pendulum T= 2π√lg, so g= 4πl/T2

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