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In a game at a carnival, a contestant rolls a ball up the slope with an initial speed vi. The object of the game is to roll the ball in such a way that it will get “stuck” in the depression at B and not return back down the slope. This will happen if the ball’s speed when it gets to point A is essentially zero. (The speed of the ball at point A really has to be greater than zero in order for the ball to make it past point A, but
the speed at point A must be greater than zero only by an arbitrarily small amount, so that we can say that the condition for the ball not to return is essentially that the speed at A must be zero.) Assuming that the ball rolls without slipping and that energy losses due to friction are negligible, find the initial speed vi required to make the
speed of the ball at point A zero. Let the mass of the ball be called M and let the radius of the ball be called R. Treat the ball as a solid sphere.

Sagot :

Initial speed of ball will be 2.7m/s.

When a body is rotating about an axis, then it has kinetic energy.

And this energy is called rotational kinetic energy.

It is given as -  R.K.E. = 1/2 Iω²

And if a ball is rolling without slipping.

Then the moment of inertia of the solid ball is written as -

I = 25MR²

Vi = Rω

Here it is given in the problem that-

height(h) = 0.53m

Now by the conservation of energy we can write the equation as -

1/2MVi² + 1/2Iω² = Mgh

so that -

(1/2)MVi² + (1/2)×(2/5MR²) ×(Vi/R)² = Mgh(1/2)Vi² + (1/5)Vi²

= gh(7/10)Vi² = 9.8 × 0.53

Vi = 2.7 m/s

So that the initial velocity of ball came out to be 2.7m/s after applying all concepts or rotational motion.

Learn more about rotational motion here:

https://brainly.com/question/2136775

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