pendulum blades have a maximum displacement angle of 15 degrees and an blade arm
ID: 2171995 • Letter: P
Question
pendulum blades have a maximum displacement angle of 15 degrees and an blade arm length of 4m.a) What is the frequency of the blades?
b) what is the period of the blades oscillation?
c) what is the magnitude of the blades velocity as a function of time t?
d) if the mass of the blade is 50kg how much energy is stored in the system?
Explanation / Answer
a. puree b. L = I?, ..=> angular momentum Note: since the angular momentum is directly proportional to frequency; twice the frequency results in twice the angular momentum. Therefore, puree gives twice the angular momentum. c. Ek = ½ I?², ...=> kinetic energy is proportional to the square of the frequency. Therefore, the mix setting will give thrice the Ek of stir setting. d. Period: T = 1/f, ..=> f = 3500/60 = 58.33 rev/s T = 1/58.33 = 17 ms e. T = Ia, ...where: moment of inertia: I = 4.5x10^5 kg m² and angular acceleration: a = ?? / ?t ? = 2pf = 2p*3500/60 = 366.52 rad/s, ...=> angular frequency of stir setting. ?' = 2p*(3)3500/60 = 1099.55, ...=> angular frequency of liquefy setting. a = ?? / ?t = (1099.55 - 366.52)/0.75 = 977.38 rad/s² torque: T = I a = 4.5x10^5(977.38) = 4398x10^5 N m f. ? = ?t + ½ a t² = 366.52*0.75 + 0.5*977.55*0.75² =
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