Respuesta :
Answer:
h =[tex] 7v^2/10g [/tex]
Explanation:
The total energy is kinetic energy and rotational energy.
This will be equal to the potential energy at the moment of rest
Therefore [tex] mgh = mv^2/2 + Iw^2/2 [/tex]
where I = moment of inertia = [tex] 2/5MR^2 and w = v^2/R^2[/tex]
substituting into the first equation, then
[tex] mgh = mv^2/2 + mv^2/5 [/tex]
Hence [tex] gh = v^2(1/2 + 1/5) [/tex]
[tex] h =7v^2/10g [/tex]
The vertical height of the bowling ball has been found as [tex]\dfrac{7v^2}{10g}[/tex].
The  moment of inertia has been defined as the rotational movement of the body with respect to the axis. The moment of inertia has been the sum of the mass of each particle with the product of the square of distance.
Computation for vertical height
The moment of inertia has been equal to the potential energy of the body at rest.
The potential energy has been given as:
[tex]mgh=\dfrac{mv^2}{2} +\dfrac{I\omega^2}{2}[/tex]
Where, the mass of the body has been m
The gravitational constant has been, g
The vertical height of the body has been h
The moment of inertia of the body, I
The angular velocity of the body, [tex]\omega[/tex]
The velocity of the body, v
The given moment of inertia of the ball has been, [tex]I=\dfrac{2}{5}mr^2[/tex]
Substituting the value for the vertical height of bowling ball:
[tex]mgh=\dfrac{mv^2}{2} +\dfrac{2}{5}mr^2\;\times \dfrac{\omega^2}{2}\\gh=v^2(\dfrac{1}{2}\;+\;\dfrac{1}{5} )\\h=\dfrac{7v^2}{10g}[/tex]
The vertical height of the bowling ball has been found as [tex]\dfrac{7v^2}{10g}[/tex].
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