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Answer:
8.91 J
Explanation:
mass, m = 8.20 kg
radius, r = 0.22 m
Moment of inertia of the shell, I = 2/3 mr^2
= 2/3 x 8.2 x 0.22 x 0.22 = 0.265 kgm^2
n = 6 revolutions
Angular displacement, θ = 6 x 2 x π = 37.68 rad
angular acceleration, α = 0.890 rad/s^2
initial angular velocity, ωo = 0 rad/s
Let the final angular velocity is ω.
Use third equation of motion
ω² = ωo² + 2αθ
ω² = 0 + 2 x 0.890 x 37.68
ω = 8.2 rad/s
Kinetic energy,
K = 0.5 x 0.265 x 8.2 x 8.2
K = 8.91 J
To solve this problem it is necessary to apply the concepts related to the Moment. The moment in terms of the Force and the time can be expressed as
F = Force
At the same time the moment can be expressed in terms of mass and velocity, mathematically it can be given as
Where
m = Mass
Change in velocity
Our values are given as
By equating the two equations we can find the Force,
Therefore, the net average force will be:
The negative symbol indicates that the direction of the force is upwards.