Physics Help Forum Question ?
 Jun 5th 2017, 08:42 AM #2 Physics Team     Join Date: Jun 2010 Location: Morristown, NJ USA Posts: 2,272 Start by determining the velocity of the pumpkin as a function of theta. From energy principles, $\displaystyle v^2 = \sqrt {2g \Delta h}$, where $\displaystyle \Delta h$ is the vertical height that the pumpkin descends: $\displaystyle \Delta h = R(1-\cos \theta)$. Next determine the radial acceleration of the pumpkin as a function of theta, based on $\displaystyle a_r = v^2/R$ Finally, recognize that the pumpkin loses contact when the radial acceleration exceeds the component of acceleration due to gravity (g) that operates in the radial direction, which is $\displaystyle g \cos \theta$. Can you take it from here?