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A bus contains a 1500 kg flywheel (a disk that has a 0.600 m radius) and has a total mass of 10,000 kg. (a) Calculate the angular velo
Question
A bus contains a 1500 kg flywheel (a disk that has a 0.600 m radius) and has a total mass of 10,000 kg.
(a) Calculate the angular velocity the flywheel must have to contain enough energy to take the bus from rest to a speed of 20.0 m/s, assuming 90.0% of the rotational kinetic energy can be transformed into translational energy.
(b) How high a hill can the bus climb with this stored energy and still have a speed of 3.00 m/s at the top of the hill? Explicitly show how you follow the steps in the Problem-Solving Strategy for Rotational Energy.
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Physics
3 years
2021-08-16T21:43:53+00:00
2021-08-16T21:43:53+00:00 1 Answers
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Answer:
Explanation:
moment of inertia of flywheel = 1/2 m R²
= .5 x 1500 x .6²
= 270 kg m²
If required angular velocity be ω
rotational kinetic energy = 1/2 I ω²
= .5 x 270 x ω² = 135 ω²
kinetic energy of bus when its velocity is 20 m/s
= 1/2 x 10000 x 20²
= 2000000 J
Given 90 % of rotational kinetic energy is converted into bus’s kinetic energy
135 ω² x 0.9 = 2000000 J
ω²=16461
ω = 128.3 radian /s
b )
Let the height required be h .
Total energy of bus at the top of hill = mgh + 1/2 m v²
m ( gh + .5 v²)
= 10000 ( 9.8h + .5 x 3²)
From conservation of mechanical energy theorem
10000 ( 9.8h + .5 x 3²) = 2000000
9.8h + .5 x 3² = 200
9.8h = 195.5
h = 19.95 m .