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# Newton's Laws of Motion

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A large globe, with a radius of about 5 m, was built in Italy between 1982 and 1987. Imagine that such a globe has a radius R and a frictionless surface. A small block of mass m slides starts from rest at the very top of the globe and slides along the surface of the globe. The block leaves the surface of the globe when it reaches a height h(crit) above the ground. The geometry of the situation is shown in the figure for an arbitrary height h. (see attachment)

Using Newton's 2nd law, find v(crit) , the speed of the block at the critical moment when the block leaves the surface of the globe. Assume that the height at which the block leaves the surface of the globe is h(crit).
Express the speed in terms of R, h(crit) and g, the magnitude of the accleration due to gravity. Do not use theta in your answer.

Use the law of conservation of energy to find v(crit). This will give you a difference expression for v(crit) than you found in the previous part. Express v(crit) in terms of R, h(crit) and g.

Find h(crit), the height from the ground at which the block leaves the surface of the globe.
Express h(crit) in terms of R.