X A doughnut has a mass of 50 grams when it is 10 cm around. A machine has 12 do
ID: 1788598 • Letter: X
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X A doughnut has a mass of 50 grams when it is 10 cm around. A machine has 12 doughnuts attached to a rotating arm that starts from rest and after 5 revolutions has obtained full speed and spins at 20 rpm. That arm is used to coat a chocolate stripe on the outside edge of the doughnut (a) what is the angular acceleration; (b) How much time did it take to get to full speed?; (c) what is the speed at which the chocolate is coating the doughnut? (e) What is the moment of inertia for the doughnut? (f) What torque is required to make the doughnut rotate? (g) How much energy is imparted to the spinning doughnut? (h) What is the angular momentum of the wheel? Two loud speakers at 10 m and 20 m away are driven by the same amplifier and emit pure sinusoidaliwave in phase. If the speed of sound is 345 m/s, (a) for what frequencies does constructive interference occur at a point 5 meters out from the amplifier? For what frequencies does destructive interference occur at that same point? Archimedes was told to take the King's "gold" crown and prove it was gold without damaging the 3.5 kg crown. So wise Archimedes devised a way to put the crown in the water and figure out the density (Pgold 19300 kg/m2) of the crown by holding it underwater and then pulling it out. Find the tension on his string both in and out of water when it is not moving A solid ball, a solid cylinder and a ring each with the mass of 1 kg and a radius of 10 cm are set at the starting line of an inclined plane that is 2 m long and raised to a height of 75 cm. What order will reach the bottom of the inclined plane and what will be each of the object's speeds at the bottom. (Assume that the masses are uniformly distributed) On a day when the speed of sound was 345 m/s, the fundamental frequency of a organ pipe 220 Hz. (a) How long is the stopped pipe? (b) The second overtone of this pipe has the same wavelength as the third harmonic of an open pipe, how long is the open pipe? A spring of mass of 5 kg is resting on a frictionless horizontal surface and is pressed against a spring with a spring constant of 500 N/m, compressing the spring 25 cm and then released. (a) 3) 4) 5) 9 6) 8) 8 2 fh) how fast will the ering he going at x =0 m?:Explanation / Answer
3) given m = 50 grams
d = 10 cm
12 doughnuts
wi = 0 ( starts from rest)
wf = 20 rpm = 20*2*pi rad/60 s = 2.094395 rad/s
theta = 5 revolutions = 10pi radians
hence
a. let angular acceleration be alpha
then
2*alpha*theta = wf^2 - wi^2
alpha = 0.06981317 rad/s/s
b. time taken to reach wf = t
wf = wi + alpha*t
t = 29.99 s
c. speed at which chocolate is coating the doughnut = wf*d = 0.2094395 m/s
e. moment of inertia of doughnut = md^2 = 0.05*0.1^2 = 0.0005 kg m^2
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