During a football game, the running back changes direction from running 4.5 m/s [N] to 4.5 m/s [S] over 8 s. What is the acceler
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Answer:
K_{total} = 19.4 J
Explanation:
The total kinetic energy that is formed by the linear part and the rotational part is requested
let's look for each energy
linear
= ½ m v²
rotation
= ½ I w²
the moment of inertia of a solid sphere is
I = 2/5 m r²
we substitute
= ½ mv² + ½ I w²
angular and linear velocity are related
v = w r
we substitute
K_{total} = ½ m w² r² + ½ (2/5 m r²) w²
K_{total} = m w² r² (½ + 1/5)
K_{total} = m w² r²
let's calculate
K_{total} = 6.40 16.0² 0.130²
K_{total} = 19.4 J
To solve this problem it is necessary to apply the concepts related to the law of Malus which describe the intensity of light passing through a polarizer. Mathematically this law can be described as:
Where,
Indicates the intensity of the light before passing through the polarizer
I = Resulting intensity
= Indicates the angle between the axis of the analyzer and the polarization axis of the incident light
From the law of Malus when the light passes at a vertical angle through the first polarizer its intensity is reduced by half therefore
In the case of the second polarizer the angle is directly 60 degrees therefore
In the case of the third polarizer, the angle is reflected on the perpendicular, therefore, its angle of index would be
Then,
Then the intensity at the end of the polarized lenses will be equivalent to 0.09375 of the initial intensity.