A block of mass 0.79kg starts from rest at point A and slides down a frictionles

Question

A block of mass 0.79kg starts from rest at point A and slides down a frictionless hill of height h. At the bottom of the hill it slides across a horizontal piece of track where the coefficient of kinetic friction is 0.48. This section (from points B to C) is 5.14m in length. The block then enters a frictionless loop of radius r= 2.19m. Point D is the highest point in the loop. The loop has a total height of 2r. Note that the drawing below is not to scale.
1. What is the minimum speed of the block at point D that still allows the block to complete the loop without leaving the track?
2. What is the minimum kinetic energy for the block at point C in order to have enough speed at point D that the block will not leave the track?
3. What is the minimum kinetic energy for the block at point B in order to have enough speed at point D that the block will not leave the track?

4. What is the minimum height from which the block should start in order to have enough speed at point D that the block will not leave the track?

Explanation / Answer

1. The min speed at D is what provides the centrifugal force at the top that equals the mass' weight

mv

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