Answer:
18695271.3209 J
989.167794757 s
Explanation:
r = Radius = [tex]\dfrac{1.7}{2}=0.85\ m[/tex]
N = 2970 rpm
m = Mass of flywheel = 1070 kg
P = Power = [tex]1.89\times 10^4\ W[/tex]
Moment of inertia
[tex]I=\dfrac{1}{2}mr^2\\\Rightarrow I=\dfrac{1}{2}1070\times 0.85^2\\\Rightarrow I=386.5375\ kgm^2[/tex]
Angular speed
[tex]\omega=2970\times \dfrac{2\pi}{60}\\\Rightarrow \omega=311.017672705\ rad/s[/tex]
Kinetic energy
[tex]K=\dfrac{1}{2}I\omega^2\\\Rightarrow K=\dfrac{1}{2}386.5375\times 311.017672705^2\\\Rightarrow K=18695271.3209\ J[/tex]
The kinetic energy is 18695271.3209 J
Time is given by
[tex]t=\dfrac{E}{P}\\\Rightarrow t=\dfrac{18695271.3209}{1.89\times 10^4}\\\Rightarrow t=989.167794757\ s[/tex]
The time taken is 989.167794757 s
The kinetic energy and time would be denoted as follows:
1). [tex]18695271.32 J[/tex]
2). [tex]989.16s[/tex]
1). Given that,
Mass that the cylinder has = 1070 Kg
Diameter = 1.70 m
Radius
[tex]= 1.70/2 \\= 0.85m[/tex]
Also,
Angular speed = 2970 rev/min
v = 2970 × 2π/60
[tex]= 311.01 rad/s[/tex]
Now, we need to find kinetic energy,
K.E. [tex]= 1/2 m v^2[/tex]
by putting the values,
= 1/2 × 386.53 ×311.01
= 18695271.32 J
b). Given,
Average power to run the bus = 1.89m
[tex]Time = E/p[/tex]
[tex]= 18695271.32/(1.89[/tex] × [tex]10^4[/tex])
[tex]= 989.16s[/tex]
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