ONLY question 14 please. minimum initial height at which her car can be released

Question

ONLY question 14 please.

minimum initial height at which her car can be released that still allows the car to stay in contact with the track at the top of the loop. A marble is placed at the top of an inverted hemispherical bowl of radius R = 0.23 m. It starts from rest and slides down the bowl without friction. Draw a free body diagram when the marble reaches an angular position theta = 33.3 degree,. From your FBD, sketch the approximate direction of the acceleration. Calculate the radial component of the acceleration (assuming that the radius of the marble is negligible). (Hint: First find the velocity at theta = 33.3 degree.) What is the tangential component of the acceleration when theta = 33.3 degree? (Hint: Use Newton's second law.) What is the magnitude of the normal force when the marble loses contact with the bowl? Draw a free body diagram for the angular position where the marble loses contact with the bowl. Draw the direction of the acceleration next to you FBD. What is the angle theta when the marble loses contact with the bowl?

Explanation / Answer

14. Normal force just before the time of loosing contact= mgcos-(mv^2)/r

you can now cross check also when it had loosed the contact normal force=0 and at that condition

mgcos=mv^2/r

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