* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lecture 19 - McMaster Physics and Astronomy
Survey
Document related concepts
N-body problem wikipedia , lookup
Jerk (physics) wikipedia , lookup
Analytical mechanics wikipedia , lookup
Wave packet wikipedia , lookup
Newton's theorem of revolving orbits wikipedia , lookup
Classical mechanics wikipedia , lookup
Renormalization group wikipedia , lookup
Work (physics) wikipedia , lookup
Brownian motion wikipedia , lookup
Centripetal force wikipedia , lookup
Newton's laws of motion wikipedia , lookup
Classical central-force problem wikipedia , lookup
Hunting oscillation wikipedia , lookup
Transcript
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 Oscillatory Motion (Chapter 14) • Kinematics of Simple Harmonic Motion • Mass on a spring • Energy Knight sections 14.1-14.6 Physics 1B03summer - Lecture 7 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) M Physics 1B03summer - Lecture 7 Spring and mass M Equilibrium: no net force The spring force is always directed back towards equilibrium. This leads to an oscillation of the block about the equilibrium position. M F = -kx M For an ideal spring, the force is proportional to displacement. For this particular force behaviour, the oscillation is simple harmonic motion. x Physics 1B03summer - Lecture 7 SHM: x A cos(t ) x(t) A T A = amplitude t = phase constant = angular frequency -A A is the maximum value of x (x ranges from +A to -A). gives the initial position at t=0: x(0) = A cos . 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 In general: x(t ) A cos(t ) x(t) Φ t Three constants specify the motion: Amplitude, A Angular Frequency, Initial phase (or phase constant), These graphs are a mathematical representation of motion as a function of time, now how the object actually moves – notice the axes. x(t) is simply the displacement from some position. Physics 1B03summer - Lecture 7 The quantity ( t + ) is called the phase, and is measured in radians. The cosine function traces out one complete cycle when the phase changes by 2 radians. The phase is not a physical angle! The period T of the motion is the time needed to repeat the cycle: x(0) A cos A cos( 2 ) so x(T ) x(0) if T 2 radians (or 360) 2 2f T units: radians/second or s-1 Physics 1B03summer - Lecture 7 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). v0 M x Physics 1B03summer - Lecture 7 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 (t ), the phase constant should be: A) B) C) D) E) M v0 x0 0o 30o 60o -30o -60o Physics 1B03summer - Lecture 7