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HOMEWORK QUESTION

HOMEWORK QUESTION. Please do this question and hand it by Tuesday after the reading week, in class:

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HOMEWORK QUESTION

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  1. HOMEWORK QUESTION Please do this question and hand it by Tuesday after the reading week, in class: A 50kg child slides down a 45o frictionless hill for 60m, starting with an initial velocity of 2m/s. The child then slides for 10m over a flat surface that has a coefficient of kinetic friction of 0.15, and finally back up another frictionless hill with a slope of 30o. Draw a pictures of the problem and determine how far on the 2nd hill the child ends up (not the height). Physics 1B03summer - Lecture 7

  2. Oscillatory Motion (Chapter 14) • Kinematics of Simple Harmonic Motion • Mass on a spring • Energy Knight sections 14.1-14.6 Physics 1B03summer - Lecture 7

  3. M Oscillatory Motion We have examined the kinematics of linear motion with uniform acceleration. There are other simple types of motion. Many phenomena are repetitive or oscillatory. Example: Block and spring, pendulum, vibrations (musical instruments, molecules) Physics 1B03summer - Lecture 7

  4. M The spring force is always directed back towards equilibrium. This leads to an oscillation of the block about the equilibrium position. M For an ideal spring, the force is proportional to displacement. For this particular force behaviour, the oscillation is simple harmonic motion. F = -kx M x Spring and mass Equilibrium: no net force Physics 1B03summer - Lecture 7

  5. SHM: x(t) T A A = amplitude f= phase constant w = angular frequency t -A A is the maximum value of x (x ranges from +A to -A). f gives the initial position at t=0: x(0) = A cosf . w is related to the period T and the frequency f = 1/T T (period) is the time for one complete cycle (seconds). Frequency f (cycles per second or hertz, Hz) is the number of complete cycles per unit time. Physics 1B03summer - Lecture 7

  6. x(t) t Φ In general: Three constants specify the motion: Amplitude, A Angular Frequency, w Initial phase (or phase constant), f These graphs are a mathematical representation of motion as a functionof time, now how the object actually moves – notice the axes. x(t) is simply the displacement from some position. Physics 1B03summer - Lecture 7

  7. The quantity (w t + f) is called the phase, and is measured in radians. The cosine function traces out one complete cycle when the phase changes by 2p radians. The phase is not a physical angle! The period T of the motion is the time needed to repeat the cycle: units: radians/second or s-1 Physics 1B03summer - Lecture 7

  8. Example The block is at its equilibrium position and is set in motion by hitting it (and giving it an initial velocity) at time t = 0. Its motion is SHM with amplitude 5 cm and period 2 seconds. Write the function x(t). M v0 x Physics 1B03summer - Lecture 7

  9. QUIZ The block is at x0 = +5 cm, with positive velocity v0, at time t = 0. Its motion is SHM with amplitude 10 cm and period 2 seconds. If x(t) = A cos (wt +f), the phase constant f should be: M v0 x0 • 0o • 30o • 60o • -30o • -60o Physics 1B03summer - Lecture 7

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