First Approach (Section II.F)Please ALL Answer from (1-14)
- D ups reed Of - ma an ky 0.038 8 90' 4 ind = s=re strial 0.05 5m JC = 0 . 00 293 4 m 6 : 0.055m (60.03 28 ) 11) Now that we have a component F-B-D, we have a great deal of information about the F. Methods: Data Co 0.802134 forces acting on a pendulum at any given instant during its swing. FIRST APPROACH: Forces & Acceleration We also still know and believe Newton's 2" Law. We therefore know and/or can figure out the pendulum's acceleration at any instant. Find that acceleration. 1) Set up a simple pendulum by hooking a mass to a string and dangling the string from a 0 0 029 3 4 m = 0 0857 2 ring stand or similar upright apparatus. 12) We also still know and believe in relationships such as 0 . 085 0 .085 0.174. 2) Practice letting the pendulum undergo small, regular, smooth swings. 9 x = 1/2at' + Kat + x0 t's . 3) Once you have gotten used to the pendulum, hold the pendulum at a small angle from the And we have acceleration. And, oh hey, we have initial velocity too. What are we trying fully vertical (relaxed) orientation. Carefully measure this angle. This angle should be to find again? Oh, right. Time. So, what are we missing? smaller than 20 degrees. What displacement are we interested in? Well, we're trying to find the time required for 4) Record the angle here: one full period of the pendulum, in other words the time to complete one full swing back and forth. Theta (1) = 10 degrees. - mass. loog Consider the bob's path as it swings. It swings from one side to the other. Assume that 5) Carefully consider what you observe while the pendulum swings. Consider the instant the angle it reaches on the far side is approximately equal to the angle it starts from. This immediately AFTER the mass is released. path is not a straight line. But it is a fraction of a very familiar shape. And the angles can tell you exactly what fraction. 6) Draw a SYSTEM SCHEMA for the pendulum mass at this instant in time. The mass at the end of the string (often known as the bob) is your "object of focus" Come up with an expression for the distance traveled in one complete period. 7) In English, write out every Newton's 3" Law PAIR of ("action-reaction") forces implied 13) So it would appear that we now have all the information necessary to calculate or predict by your SYSTEM SCHEMA. Each "pair" should consist of two sentences. Each the following: sentence will necessarily refer to two real, identifiable, objects. Each sentence will necessarily use either the word "pull" or the word "push". Each sentence will necessarily If released at rest from a small angle away from the vertical, how much time will it take refer to some kind of direction , even if exotic or freshly motivated by the new situation for the pendulum to make a full swing to the same angle on the other side of the presented by a pendulum. Examples such as "up", "down" "up/left", "along a radius in vertical? toward a center", "along a radius out toward a circumference", etc. 14) Consider the very fair, seemingly simple and commonly asked question in (13), above. It 8) Draw a PURE FREE-BODY DIAGRAM of the pendulum mass at this instant in time would appear that we have access to all the information needed to predict time for a (immediately after the mass is released). The mass at the end of the string (often known given displacement (a fundamental physics question). Indeed, for any given instant in as the bob) is your "object of focus". time, we do. Using Newton's Laws in order to predict time for a given pendulum displacement (or the other way around) is, however, far more difficult than it sounds 9) Now carefully consider and choose a coordinate system that you believe to be convenient There is something about the pendulum - despite its simplicity and elegance of motion - or appropriate for this type of motion. How is your "x-axis" aligned? How is your "y- that makes predicting times very challenging. Why so challenging? What is the obstacle axis" aligned? to making straightforward use of Newton's Laws and kinematic equations? HINT 1: In which direction do you believe the pendulum is accelerating at this moment? 0 : 10 ' As clearly and precisely as possible, explain how/why Newton's Laws and the kinematic HINT 2: The direction of acceleration for an object traveling in a curve can be equations can be true yet not particularly helpful in making space/time predictions for a challenging to identify. Feel free to use the web and other resources to help you consider pendulum. What is true about a pendulum that has not been true of any situation we have this question. studied to this point? 10) Once you have chosen a suitable coordinate system, break up any diagonal forces from Once you confidently see how Newton's Laws can be true for all mechanical situations, your PURE F-B-D and thereby create a COMPONENT F-B-D for your pendulum bob. yet inconvenient for some, proceed to investigate time/space in a different way
