00:01
In this problem, we have been given that there is a bowling ball and this balling ball is encountering a vertical rise of 0 .76 meters.
00:12
Also, it's given that at this lowest position, its translational speed is 3 .7 meter per second.
00:21
And we have to determine the translation speed of this bowling ball at this topmost point.
00:28
So here we consider the moment of inertia of this balling ball, which is a solid sphere, that's 2 by 5 mr square.
00:36
And now we observe that at the lowest point, the total energy is just the kinetic energy, which is the kinetic energy of translation, plus the kinetic energy of rotation, which is half i omega square.
00:51
And omega is angular speed, which can be written as v square by r square, provided that r is the radius of this balling ball.
01:00
And also we observed that the final kinetic energy that can be computed just the way we computed the initial kinetic energy.
01:08
So final kinetic energy will be half m v square plus half i into v square by r square.
01:17
And here let's substitute the initial velocity as you so it will be half m u square plus half i u square by r square.
01:25
And now we apply the work energy theorem and according to that the network done is the change in kinetic energy so first we simplify the kinetic energy putting the value of i as 2 by 5 m r square in both these expressions we observed that the final kinetic energy that turns out to be 7 by 10 mv square and the initial kinetic energy that turns out to be 7 by 10 m u square so putting the values here and indicating the network done by the gravity, which will be the gravitational force acting in the downward direction, and the displacement is in the upward direction...