What is the minimum kinetic energy for the block at point C in order to have eno

Question

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? 22.8 J

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?

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?

I need help with the last two questions, I'm plain stuck... Please help, thank you!

A block of mass 0.40kg 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 0.26. This section (from points B to C) is 5.06m in length. The block then enters a frictionless loop of radius r= 2.33m. 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. figure showing above setup What is the minimum speed of the block at point D that still allows the block to complete the loop without leaving the track? 4.78 m/s 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? 22.8 J 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? 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

C. Minimum KE = 22.8 + 2*2.33*9.8 = 68.46 J

D. minimum height = [{68.46 + 0.26*0.4*9.8*5.06}/(0.4*9.8)] = 18.77 m

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