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Big ben in london, has an hour hand 2.7m long with a mass of 60kg and a minute hand 4.5m long with a mass of 100kg. calculate the total rotational kinetic energy of the two hands about the axis of rotation. (you may model the hands as long, thin rods rotated about one end. assume the hour and minute hands are rotating at a constant rate of one revolution per 12 hours and 60 minutes, respectively.)

Respuesta :

Yna9141
First, calculate for the circumference which is equivalent to the distance covered by the tip of the two hands of the clock.


Hour hand:  (2)(3.14)(2.7 m) = 16.956 m
Minute Hand: (2)(3.14)(4.5 m) = 28.26 m

Then, calculate for the rotational speed of both,
  
12 hours and 60 minutes = 13 hours = 46800 s

Hour hand: v = (16.956 m)/(46800 s) = 3.623 x 10^-4 m/s
Minute hand: v = (28.26 m) / (46800 s) = 6.038 x 10^-4 m/s

Lastly, calculate for the kinetic energy through the equation,
     KE = 0.5 mv²

Substituting the known values,
 Hour hand = (0.5)(60 kg)(3.623 x 10^-4 m/s)² = 3.937 x 10^-6 J
 Minute hand = (0.5)(100 kg)(6.038 x 10^-4 m/s)² = 1.823 x 10^-5 J


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