A mass starts at the top of a quarter circular ramp with some radius at a speed

Question

A mass starts at the top of a quarter circular ramp with some radius at a speed of 11 m/s. It then travels on a horizontal surface without friction, around a circular loop without falling off, on another horizontal surface without friction, up a ramp with a length of 28 meters, with a coefficient of kinetic friction of 0.77 which is inclined at 37 degrees. It then ends up on a horizontal frictionless surface moving at a speed of 24 m/s. What is the radius of the quarter circular ramp, in meters, the mass started?

Explanation / Answer

energy of mass = 0.5*m*121 + m*g*R

work done by friction = 0.77* mgcos(37) *28

gravity = mgsin(37)*28

so equation wor done by all forces =Change in KE

0.5*m*121 + m*g*R - 0.77* mgcos(37) *28 - mgsin(37)*28 = 0.5* m * 576

R = 57.2836879592 m

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